CONTENTS

Chapter No. Description Page No.

1 Physical Quantities and Measurements 5

2 Kinematics 28

3 Dynamics 52

4 Turning Effects of Forces 80

5 Work, Energy and Power 105

6 Mechanical Properties of Matter 127

7 Thermal Properties of Matter 148

8 Magnetism 161

9 Nature of Science 181

(i) Bibliography 194

(ii) Glossary 195

(iii) Index 198

4
 Chapter
1 Physical Quantities and
Measurements
Student Learning Outcomes

After completing this chapter, students will be able to:

• [SLO: P-09-A-01] Differentiate between
physical and non-physical quantities
• [SLO: P-09-A-02] Explain with examples
that physics is based on physical quantities
[Including that these consist of a magnitude
and a unit]
• [SLO: P-09-A-03] Differentiate between
base and derived physical quantities and
units.
• [SLO: P-09-A-04] Use the seven units of
System International (SI) along with their
symbols and physical quantities (standard
definitions of SI units are not required)
• [SLO: P-09-A-05] Analyse and express numerical data using scientific notation [in
measurements and calculations.]
• [SLO: P-09-A-06] Analyse and express numerical data using prefixes
[interconverting the prefixes and their symbols to indicate multiple and submultiple
for both base and derived units.]
• [SLO: P-09-A-07] Justify and illustrate the use of common lab instruments to
measure length [Including least count of instruments and how to measure a variety
of lengths with appropriate precision using Tapes, Rulers and Vernier Callipers and
Micrometres (including reading the scale on analogue and digital callipers and
micrometres)]
• [SLO: P-09-A-08] Justify and illustrate the use of measuring cylinders to measure
volume [Including both measurement of volumes of liquids and determining the
volume of a solid by displacement]
• [SLO: P-09-A-09] Justify and illustrate how to measure time intervals using lab
instruments [Including clocks and digital timers.
• [SLO: P-09-A-10] Identify and explain the reason for common sources of human
and systematic errors in experiments.
• [SLO: P-09-A-11] Determine an average value for an empirical reading [Including
small distance and for a short interval of time by measuring multiples (including the
period of oscillation of a pendulum)] The uncertainty in measurements and describe
the need using significant figures for recording and stating results of various
measurements.

5
 • [SLO: P-09-A-12] Differentiate between precision and accuracy.
• [SLO: P-09-A-13] Round off and justify measured estimates to make them
reasonable. [Based on empirical data to an appropriate number of significant figures]
• [SLO: P-09-A-14] Determine the least count of a data collection instrument
(analogue) from its scale.

We are living in a physical world where we observe many natural

phenomena and objects around us such as Sun, stars, moon, oceans, plants,
winds, rains, etc. People have always been curious to know the reality of such
happenings. This has led certain people to investigate the facts and laws working
in this world. This field of observation and experimentation to understand about
the world around us is known as science. Everything in our lives is closely linked
to science and the discoveries made by the scientists. In order to obtain reliable
results from experiments, the primary thing is to make accurate measurements.
Physical quantities and their measurements have always been the matter
of interest for the scientists. They have been investigating to improve the
methods and instruments for accurate measurements of the physical quantities.
In this chapter, we will discuss physical quantities, their measurements and
related contents.

1.1 Physical and Non-Physical Quantities

We describe various natural phenomenon, events and human behaviour

using some of their features and terms such as love, affection, fear, wisdom,
beauty, length, volume, density, time, temperature, etc. Some of these can be
measured directly and indirectly using some tools and Quick Quiz
Is a non-physical
instruments such as length of an object using a ruler, time
quantity has
duration of an event using a clock, the temperature (the dimensions?
degree of hotness) of somebody using a thermometer.
They are called physical quantities. The foundation of physics rests upon physical
quantities through which the laws and principles of physics are expressed.
Other quantities quoted above such as love, affection, fear, wisdom, and
beauty cannot be measured using tools and instruments. They often pertain to
the perception or interpretation of the observer. They can be described or
6
qualitatively or compared using some pre-determined criteria, indices or
through survey techniques. Non-physical quantities mostly help to understand
and to analyse human behaviour, emotions and social interactions.

Table 1.1
Quick Quiz: Complete the following

Feature Physical Quantity Non-Physical Quantity

1. Measurement Yes No

2. Instrument used

3. Numerical value and unit

4. Examples 1. 1.
2. 2.

1.2 Base and Derived Physical Quantities

Physics is a science of physical world where we interact with many
different types of material objects. These objects are exposed in terms of their
measurable features known as physical quantities such as length, breadth,
thickness, mass, volume, density, time, temperature, etc. Out of these, the
scientists have selected arbitrarily some quantities to play a key role. They are
called base quantities. All the quantities which can be described in terms of one
or more base quantities are called derived physical quantities. For example,
speed is a derived quantity which depends on distance and time which are base
quantities whereas density of a material is described in terms of mass and
volume.
Measurement of a Physical Quantity
A measurement is a process of comparison of an unknown quantity with a
widely accepted standard quantity.
Activity 1.1
The teacher should facilitate this activity and initiate discussion as per direction.
One student should measure the length of a writing board with his hand. The same should
be repeated by four or five students. Are all the measurements same? If they differ, then
why? What is the solution to avoid confusion?

7
 In the early days people used to measure length using hand or arm, foot
or steps. This measurement may result in confusion as the measurement of
different people may differ from
each other because of different
sizes of their hands, arms or steps.
To avoid such confusion, there is a
need of a standard so that
measurement by any person may
result the same. This standard of
measurement is known as a unit.

A measurement consists of two

parts, a number and a unit. A
measurement without unit is
meaningless.

Not very far in the past, every

country in the world had its own
units of measurements. However,
The International Prototype kilogram
problems were faced when people
of different countries exchanged scientific information or traded with other
countries using different units. Eventually, people got the idea of standardizing
the units of measurements which could be used by all countries for efficient
working and growth of mutual trade, business and share scientific information.

1.3 International System of Units

The international committee on Table
Table 1.2
1.2
w e i g h t s a n d m e a s u r e s i n 1 9 6 1 Sr.
Sr Physical
Physical
Unit
Unit Symbol
Symbol
recommended the use of a system consisted No. . quantity
quantity
of seven base units known as international 1. 1 Length
Length metre
metre m
m
system of units, abbreviated as SI. This 2. 2 Mass
Mass kilogram
kilogramme kg
kg
system is in use all over the world.
3.
3 Time
Time second
second ss
Use of SI measurements helps all
scientists to share and compare their 4. 4 Temperature
Temperature kelvin
kelvin K
K

observations and results easily. The seven 5. 5 Electric

Electriccurrent
current ampere
ampere A
A
base units are given in Table 1.2. Their values 6.
6 Intensity
Intensity of light
of light candela
candela cd
cd
are fixed with reference to international Amount
Amount of of
7.
7 mole
mole mol
mol
standards. substance
substance
8
Derived Units
Base units cannot be derived from one Table 1.3
another and neither can they be resolved into Sr. Physical
Unit Symbol
anything more basic. While the units of derived No. quantity
1. Area square metre m²
quantities such as speed, area, volume, force,
pressure and electric charge can be derived 2. Volume cubic metre m³

using the base units. These units are called Speed metre per
3. ms–¹
second
derived units. 4. Force newton N
The units which can be expressed in
5. Pressure pascal Pa
terms of base units are called derived units.
6. Electric charge coulomb C
For example, Area = length × breadth
7. Plane angle radian rad
= metre × metre
= square metre
= metre² or m² Quick Quiz

Speed = Distance/Time = metre/second = m s–1 (a) Write the unit of charge in

terms of base unit ampere
A few derived units with specific names and and second.
symbols are given in Table 1.3. (b) Express the unit of pressure
"pascal" in some other units.
SI Prefixes
The SI is a decimal system. Prefixes are used to write units by powers of 10.
The big quantities like 50000000 m and small quantities like 0.00004 m are not
convenient to write down. The use of prefixes makes them simple. The quantity
50000000 m can be written as 5 × 10 m. Similarly, the quantity 0.00004 m can be
7

written as 4 × 10 m.
−5

Prefixes are the words or symbols added before SI unit such as milli,
centi, kilo, mega, giga (Table1.4). The prefixes given in Table 1.4 should be
known for use of SI units effectively. For example, one thousandth (1/1000) of
a metre is millimetre. The thickness of a thin wire can be expressed
conveniently in millimetres whereas a long distance is expressed in kilometres
which is 1000 metres.
Multiples and sub-multiples of mass measurement are given in Table 1.5
whereas multiples and sub-multiples of length are given in Table 1.6. The
following examples will explain the meaning of prefixes.

9
 5000
(I) 5000 mm = m =5m Table 1.4: Prefixes used with SI units
1000
Powers
50000 Prefix Symbol
of Ten
(ii) 50000 cm = m = 500 m
100 atto a 10–18
3000 femto f 10–15
(iii) 3000g = kg = 3 kg pico p
1000 10–12
nano n 10–9
(iv) 2000 μs = 2000 × 10 ⁶ s= 2 × 10 ³ s
– –
micro μ 10–6
= 2 ms milli m 10–3
centi c
1.4 Scientific Notation 10–2
deci d 10–1
It is short way of representing very kilo k 103
large or very small numbers. Writing mega M 106
otherwise, the values of these quantities, take giga G 109
up much space They are difficult to read, their
tera T 10¹²
relative sizes are difficult to visualize and they
peta P 10¹⁵
are awkward to use in calculations. Their
decimal places are more conveniently exa E 10¹⁸
expressed as powers of 10. The numerical part Table 1.5
of the quantity is written as a number from 1 to
100 kg
9 multiplied by whole number powers of 10. To 1 quintal
write numbers using scientific notation, move 10 quintal or
1 tonne
the decimal point until only one non-zero 1000 kg
digit remains on the left. Then count the Table 1.6
number of places through which the decimal
point is moved and use this number as the 1m 100 cm
power or exponents of 10. The average 1 cm 10 mm
distance from the Sun to the Earth is 1 km 1000 m
138,000,000 km. In scientific notation, this 1 mm 10–³ m
distance would be written as 1.38 × 10⁸ km. 1 cm 10–² m
The number of places, decimal moved to the 1 km 10³ m
left is expressed as a positive exponent of 10. Quick Quiz
Diameter of hydrogen atom is about 100 m is equal to:
0.000,000,000,052 m. To write this number in (a) 1000 μm (b) 1000 cm
scientific notation, the decimal point is moved (c) 100,000 mm (d) 1 km
11 places to the right. As a result, the diameter
is written as 5.2 × 10–¹¹ m. The number of Do You Know?
places moved by the decimal to the right is The kilogram is the only base
expressed as a negative exponent of 10. unit that has a prefix.

10
 Example 1.1 For Your Information!

Solve the following: The negative exponents have

values less than one. For
(a) 5.123 × 10⁴ m + 3.28 × 10⁵ m example, 1 ×10–² = 0.01
(b) 2.57 × 10-² mm – 3.43 × 10-3 mm Quick Quiz
Solution Express the f o llow ing into
scientific notation.
(a) 5.123 × 10⁴ m + 3.28 × 10⁵ m
a) 0.00534 m b) 2574.32 kg
= 5.123 × 10⁴ m + 32.8 × 10 m
4
c) 0.45 m d) 0.004 kg
= (5.123 + 32.8) 104 m e) 186000 s
= 37.923 × 104 m For Your Information!
= 3.7923 × 105 m Addition and subtraction of
numbers is only possible if they
(b) 2.57 × 10-2 mm – 3.43 × 10-3 mm have the same exponents. If they do
not have the same exponents, make
= 2.57 × 10-2 mm – 0.343 ×10-2 mm them equal by the displacement of
= (2.57 - 0.343) 10-2 mm the position of the decimal point.
= 2.227 × 10-2 mm For Your Information!
= 2.227 ×10-2 × 10-3 m Use of SI units require special
= 2.227 × 10-5 m care, particularly in writing prefixes.
 Each unit is represented by a
Example 1.2 symbol not by an abbreviation.
For example, for SI not S.I., for
Find the value of each of the following second s not sec, for ampere A
not amp, for gram g not gm.
quantities:  Symbols do not take plural form.
(a) (4 × 10³ kg) (6 × 10⁶ m) For example, 10 mN, 100 N, 5 kg,
60 s.
(b) 6 × 10⁶ m³  Full name of unit does not begin
with capital letter. For example,
2 × 10-² m² metre, second, newton except
Celsius.
Solution  Symbols appear in lower case, m
formetre,s for second,
(a) (4×10³ kg) (6×10⁶ m)=(4×6)×10³ + ⁶ kg m exception is only L for litre.
= 24 × 10⁹ kg m  Symbols named after scientist's
name have initial letters capital.
= 2.4 × 10¹⁰ kg m For example, N for newton, K for
kelvin and Pa for pascal.
(b) 6 × 10⁶ m³ = 6 × 106–(–2) m3–2  Prefix is written before and close
2 × 10-² m² 2 to SI unit. Examples: ms, mm,
mN, not m s, m m, m N.
= 3 × 10 m8

 Units are written one space

1.5 Length Measuring Instruments apart. For example, N m, N s.
 Compound prefixes are not
Metre Rule: Length is generally allowed. For example,
measured using a metre rule in the laboratory. (i) 7 μμs should be written as 7 ps.
(ii) 5 × 104 cm should be written as
The smallest division on a metre scale is 1 mm. 5 × 10² m.
11
The smallest measurement that can be taken with a
metre rule is 1 mm. One millimetre is known as least
count of the metre rule.
Least count is the smallest measurement that Measuring Tape: It can
can be taken accurately with an instrument. measure 1 mm to several
metres. Its least count is
To measure the length of an object, the metre 1 mm. It is used to measure
ruler is placed in such a way that its zero coincides longer distances.

one edge of the object and then the reading in front 1.5 cm 1.8 cm 2.0 cm
incorrect correct incorrect
of the other edge is the length of the object. One A B C

common source of error comes from the angle at 0 1 2 3

which an instrument is read. Metre ruler should
Fig. 1.1
either be tipped on its edge or read when the
person's eye is directly above the ruler as shown in Fig. 1.1 at point B. If the metre
ruler is read from an angle, such as from point A or C, the object will appear to be
of different length. This is known as parallax error.

Vernier Callipers For Your Information!

Parallax error is due to
It is an instrument used to measure small incorrect position of eye
w h e n t a k i n g
lengths down to 1/10th of a millimetre. It can be used measurements. It can be
to measure the thickness, diameter, width or depth avoided by keeping eye
perpendicular to the scale
of an object. The two scales on it are: reading.
(a) A main scale which has marking of 1mm each. Do You Know?
(b) A Vernier (sliding) scale of length 9 mm and it Some specific lengths in (m)
Football ground 9.1 × 10¹
is divided into 10 equal parts.
Man 1.8 × 10⁰
Least count of a Vernier Callipers is the Thickness of
book page 1.0 × 10 ⁴
−

difference between one main scale division (M.S) and

Diameter of
7.0 × 10−³
one Vernier scale (V.S) division. pencil
Hence, Least count = 1 M.S div – 1V.S div
Do You Know?
= 1mm – 0.9 mm = 0.1 mm Vernier callipers was
invented by a French
Usually, the least count is found by dividing
Scientist Pierre Vernier in
the length of one small division on main scale by the 1631.

12
total number of divisions on the Vernier scale which is again 1 mm/10 = 0.1 mm.
The parts of the Vernier Callipers are shown in Fig. 1.2 .
Inside jaws
C D

Tail

Main scale

Vernier scale

A B
Outside jaws Fig. 1.2
There are two Jaws A and B to measure external dimension of an object
whereas jaws C and D are used to measure internal dimension of an object. A
narrow strip that projects from behind the main scale known as tail or depth
gauge is used to measure the depths of a hollow object.
Measurement Using Vernier Callipers
Suppose, an object is placed between the two
jaws, the position of the Vernier scale on the main
scale is shown in Fig. 1.3. 4 5

1. Read the main scale marking just infront of Main scale

0 5 10

Vernier scale
zero of the Vernier scale. It shows 4.3 cm. Fig. 1.3
2. Find the Vernier scale marking or division
which is in line with any of the main scale marking.
This shows:
Length of object = Main scale reading + (Least 0 1 2
count × Vernier scale reading).
= 4.3 + 0.01 × 4 = 4.34 cm 0 5 10 Main scale
(a) Vernier scale
3. Checking for zero error. Following are some
important points to keep in mind before checking
0 1 2
zero error:
(a) If on joining the jaws A and B, the zeros of the 0 1 10 Main scale
(b) Vernier scale
main scale and Vernier scale do not exactly coincide
Fig. 1.4
with each other then there is an error in the
instrument called zero error.
13
(b) If the zero of the Vernier scale is on the right side of the zero of the main
scale (Fig. 1.4-a) then this instrument will show slightly more than the actual
length. Hence, these zero errors are subtracted from the observed measurement.
To find the zero error, note the Laboratory Safety Rules
number of the division of the Vernier  Handle all apparatus and chemicals
carefully and correctly. Always check the
scale which is exactly in front of any label on the container before using the
division of the main scale. Multiply this substance it contains.
number with the least count. The  Do not taste any chemical unless
otherwise instructed by the teacher.
resultant number is the zero error of this
 Do not eat, drink or play in the
instrument. The observed reading is laboratory.
corrected by subtracting the zero error  Do not tamper with the electrical mains
from it. and other fittings in the laboratory.
Never work with electricity near water.
(c) If the zero of the Vernier scale is on  Don't place flammable substance near
the left side of the zero of the main scale naked flames.
(Fig. 1.4b), then instrument will show  Wash your hands after all laboratory
slightly less than the actual length. work.

Hence, the zero error is added in the Activity 1.2

observed measurement. For example, if 3 The teacher should facilitate to perform this
is the number of divisions coinciding with activity by making groups. Each group
should place ten coins one above the other.
any main scale division then 3 is
Record their total height using a metre rule.
subtracted from 10 and the result is then Divide by 10.
mult iplie d with the least count. What is the thickness of one coin?
Now find the thickness of one coin using
Therefore, the zero error in this case will
Vernier Callipers.
be 0.7 mm. For correction, it is added in What is the result?
the observed reading. Each group should comment on the
measurement using the two instruments.
Micrometer Screw Gauge
It is used to measure very small lengths such as diameter of a wire or
thickness of a metal sheet. It has two scales:
(a) The main scale on the sleeve which has markings of 0.5 mm each.
(b) The circular scale on the thimble which has 50 divisions. Some
instruments may have main scale marking of 1 mm and 100 divisions on
the thimble.
When the thimble makes one complete turn, the spindle moves 0.5 mm
(1 scale division) on the main scale which is called pitch of the screw gauge. Thus,
its least count is:
Least count = Pitch of the screw gauge 0.5 mm
= = 0.01 mm
No. of divisions on the circular scale 50
The parts of the screw gauge are shown in Fig. 1.5.
14
 The object that is to be measured is placed Limitations of measuring
between the anvil and the spindle. Instruments
Least
anvil spindle sleeve The thimble is turned Instrument Range
count
to move the spindle.
Measuring 1 cm
Tape
to 1 mm
ratchet several metres
1 mm
Metre rule to 1 mm
1m
Vernier 0.1 mm
Callipers
to 0.1 mm
15 cm
The ratchet prevents over tightening by 0.01 mm
Micrometer
making a click sound when the micrometer is to 0.01 mm
Screw gauge 2.5 cm
ready to be read.
Fig. 1.5

Checking for Zero Error 15

If the zero of the circular scale coincides with horizontal 0

10
5
0
line, there is no zero error (Fig. 1.6-a). 95
90
If it is not exactly in front of the horizontal line of the (a) 85

main scale on joining the anvil and spindle then there is a zero 20
15

error in the screw gauge (Fig. 1.6-b). If zero of the circular scale 0 105
is below the horizontal line then it will measure slightly more
0
95

than the actual thickness and hence, zero error will be (b) 10
90

subtracted from the observed measurement. 5

0
0
If the zero of the circular scale is above the horizontal 95
90

line (Fig. 1.6-c), then it will show slightly less than the actual 85
80

thickness and hence, the zero error will be added to the (c)
Fig. 1.6
observed measurement.
Measurement Using Screw Gauge
Suppose when a steel sheet is placed
in between the anvil and spindle, the
0 5 30
position of circular scale is shown in Fig.1.7. 25
(a) Read the marking on the sleeve just 20
before the thimble. It shows 6.5 mm.
(b) Read the circular scale marking Fig. 1.7

which is in line with the main scale. This shows 25. Hence,
Thickness = main scale reading + (circular scale reading × L.C.)
= 6.5 mm + 25 × 0.01 mm
= 6.5 mm + 0.25 mm = 6.75 mm
15
Activity 1.3 For Your Information!
The teacher should facilitate the activity by making groups and The most precise balance is
ask them to find the thickness of 100 sheets of a textbook using the digital electronic
a micrometre screw gauge. Dividing this thickness by 100, balance. It can measure
estimate the thickness of one sheet. mass of the order of 0.1mg
Activity 1.4
The teacher should help each group to make a paper scale having least count 0.2 cm and 0.5 cm.

1.6 Mass Measuring Instruments

Physical Balance
There are many kinds of balances used
for measuring mass of an object. In our daily
life, we use the term weight instead of mass. In
Physics, they have different meanings. Mass is
the measure of quantity of matter in a body
whereas the weight is the force by which the
body is attracted towards the Earth. Weight
Fig. 1.8
can be measured using spring balance
(Fig. 1.8). The mass of an object is found by
comparing it with known standard masses.
This process is called weighing. In laboratories,
we use physical balance shown in Fig. 1.9
which is based on the principle of levers. The
process of measurement is given below:
1. Level base of the balance using levelling
screws until the plumb line is exactly above
Fig. 1.9
the pointed mark.
2. Turn the knob so that the pans of the balance are raised up. Is the beam
horizontal and pointer at the centre of the scale? If not, turn the balancing
screws on the beam so that it becomes horizontal.
3. Place the object to be weighed on the left pan.
4. Place the known weight from the weight box in the right pan using forceps.
5. Adjust the weight so that pointer remains on zero or oscillates equally on
both sides of the zero of the scale.
6. The total of standard masses (weights) is a measure of the mass of the object
in the left pan.

16
1.7 Time Measuring Instruments
Stopwatch
The duration of time of an event is measured
by a stopwatch as shown in Fig. 1.10. It contains two Fig. 1.10 Mechanical Stopwatch
needles, one for seconds and other for minutes. The
dial is divided usually into 30 big divisions each being
further divided into 10 small divisions. Each small
division represents one tenth (1/10) of a second. Thus,
one tenth of a second is the least count of this Fig. 1.11 Digital Stopwatch

stopwatch. While using, a knob present on the top of the device is pressed. This
results in the starting of the watch. The same knob is again pushed to stop it. After
noting the reading, the same knob is again pressed to bring back the needles to
the zero position. Now-a-days, electronic/digital watches (Fig. 1.11) are also
available which can measure one hundredth part of a second.
Activity 1.5 Model of a sandclock
The teacher should arrange the required articles and help students to make a
model of a sandclock as shown in the figure. Using two glass funnels, adhesive
tape, two lids, and dry sand. Observe how much time it takes for the sand to flow
down once completely. Make a paper scale from this and paste on the glass
funnels along straight side.
Sandclock
1.8 Volume Measuring Instruments
Measuring Cylinder
It is a cylinder made of glass or transparent plastic
with a scale divided in cubic centimetres (cm3 or cc) or wrong
millilitres (mL) marked on it. It is used to find the volume
of liquids and non-dissolvable solids. correct
The level of liquids in the cylinder is marked to find wrong
the volume. In order to read the volume correctly, the
cylinder must be placed on a horizontal surface and the
eye shall be kept in level with meniscus of water surface
as shown in Fig. 1.12. The meniscus is the top level of the
liquid surface. Water in the cylinder curves downward Fig. 1.12
and its surface is called concave surface. The reading is Measuring cylinder

taken corresponding to the bottom edge of the surface. The mercury in the
cylinder curves upward. Its surface is convex and the reading is taken
corresponding to the top edge. The cylinder can be used to find the volume of
solids.
17
 Activity 1.6 Caution: While taking a
The teacher should facilitate the groups to perform this activity reading, keep your eye in
following the given instructions. front and in line with the
1. Take a liquid in which the given solid lower meniscus of the
does not dissolve. water.
2. Note the initial position of liquid B
surface. A Do You Know?
3. Put the solid in the cylinder Ancient Chinese used to
containing liquid. estimate the volume of
4. Note again the position of liquid
grains by sounding their
surface in the cylinder which rises due to solid. containing vessels.
5. The difference of the two readings is the volume of the solid.
Displacement Can Method
If the body does not fit into the measuring cylinder, then an overflow can
or displacement can of wide opening is used as shown in Fig. 1.13. Place the
displacement can on the horizontal table. Pour water in it until it starts
overflowing through its opening. Now tie a piece of thread to the solid body and
Side
opening

(a) Beaker (b) Body

Fig. 1.13 Displacement can or Overflow can
Do You Know?
lower it gently into the displacement can. The
Despite the use of SI in most
body displaces water which overflows through the countries, the old measure is
side opening. The water or liquid is collected in a still in use, such as printers type
beaker and its volume is measured by the is measured in point. One point
measuring cylinder. This is equal to the volume of is 1/72 of an inch equivalent to
solid body. 0.35 mm.
Activity 1.7
The teacher should facilitate the groups to take a
metallic ball or a pendulum bob. Measure its diameter
and then volume by placing it in between two wooden
blocks alongside a ruler. Then use measuring cylinder
and comment on the result of this two onset activities.

1.9 Errors in Measurements For Your Information!

The symbol of the
Measurements using tools and instruments are
base units are
never perfect. They inherit some errors and differ from universal independent
their true values. The best we shall do is to ensure that the of the language used
errors are as small as reasonably possible. A scientific in the written text.
18
measurement should indicate the estimated error in the measured values.
Usually, there are three types of experimental errors affecting the
measurements.
(i) Human Errors (ii) Systematic Errors (iii) Random Errors

(i) Human Errors

They occur due to personal performance. The limitation of the human
perception such as the inability to perfectly estimate the position of the pointer
on a scale. Personal errors can also arise due to faulty procedure to read the scale.
The correct measurement needs to line up your eye right in front of the level. In
timing experiments, the reaction time of an individual to start or stop clock also
affects the measured value. Human error can be reduced by ensuring proper
training, techniques and procedure to handle the instruments and avoiding
environmental distraction or disturbance for proper focusing. The best way is to
use automated or digital instruments to reduce the impact of human errors.
(ii) Systematic Errors
They refer to an effect that influences all measurements of particular
measurements equally. It produces a consistence difference in reading. It occurs
due to some definite rule. It may occur due to zero error of instrument, poor
calibration of instrument or incorrect marking. The effect of this kind of error can
be reduced by comparing the instrument with another which is known to be
more accurate. Thus, a correction factor can be applied.

(iii) Random Errors

Itissaidto occur when repeated Quick Quiz
measurements of a quantity give different values
Identify Personal, Systematic
under the same conditions. It is due to some and Random errors:
unknown causes which are unpredictable. 1. Your eye level may move
The experimenter have a little or no control a bit while reading the
over it. Random error arise due to sudden meniscus.
fluctuation or variation in the environmental 2. Air current may cause
conditions. For example, changes in temperature, the balance to fluctuate.
pressure, humidity, voltage, etc. The effect of 3. The balance may not be
random errors can be reduced using several or properly calibrated.
multiple readings and then taking their average or 4. Some of the liquid may
mean value. Similarly, for the measuring time period have evaporated while it
of oscillating pendulum, the time of several is being measured.
oscillations, say 30 oscillations is noted and then
mean or average value of one oscillation is
determined.
19
1.10 Uncertainity in a Measurement
There is no such thing as a perfect measurement. Whenever a physical
quantity is measured except counting, there is inevitably some uncertainty about
its determined value due to some instrument. Uncertainty in Digital
This uncertainty may be due to use of a number Instruments
of reasons. One reason is the type of instrument Some modern measuring
being used. We know that every measuring instruments have a digital scale.
instrument is calibrated to a certain smallest We usually estimate one digit
division and this fact puts a limit to the degree beyond what is certain. With
of accuracy which can be achieved while digital scale, this is reflected in
measuring with it. Suppose that we want to fluctuation of the last digit.
measure the length of a straight line with the
help of a metre rule calibrated in millimetres. Let the end point of the line lies
between 10.3 cm and 10.4 cm marks. By convention, if the end of the line does
not touch or cross the midpoint of the smallest division, the reading is confined
to the previous division. In case the end of the line seems to be touching or have
crossed the midpoint, the reading is extended to the next division. Thus, in this
example, the maximum uncertainty is ± 0.05 cm. It is, infact, equivalent to an
uncertainty of 0.1 cm equal to the least count of the instrument divided into two
parts, half above and half below the recorded reading.
The uncertainty in small length such as diameter of a wire and short
interval of time can be reduced further by taking multiple readings and then
finding average value. For example, the average time of one oscillation of a
simple pendulum is usually found by measuring the time for thirty oscillations.
The uncertainty or accuracy in the value of a measured quantity can be
indicated conveniently by using significant figures.
1.11 Significant Figures
We can count the number of candies in a jar and know it exactly by
counting but we cannot measure the height of the jar exactly. All measurements
include uncertainties depending upon the refinement of the instrument which is
used for measurement.
It is important to reflect the degree of uncertainty in a measurement by
recording the observation in significant figures.
The significant figures or digits are the digits of a
measurement which are reliably known.
Figure 1.14 shows a rod whose length is
measured with a ruler. The measurement shows the
length in between 4.6 cm and 4.7 cm. Since the length Fig. 1.14

of the rod is slightly more than 4.6 cm but less than 4.7 cm, so the first student
estimates it to be 4.6 cm whereas the second student takes it as 4.7 cm. The first
student thinks that the edge is nearer to 6 mm mark whereas the
20
second student considers the edge of the rod nearer to 7 mm mark. It is difficult
to decide what is the true length. Quick Quiz
Both students agree on digit 4 Name some repetitive processes
but the next digit is doubtful which has occuring in nature which could serve as
reasonable time standard.
been determined by estimation only
and has a probability of error. Therefore, it is known as a doubtful digit. In any
measurement, the accurately known digits and the first doubtful digit are
known-as significant figures.
The following points are to be kept in mind while determining the number
of significant figures in any data. All digits from 1 to 9 are significant. However,
zeros may or may not be significant. In case of zeros, the following rules apply:
(a) A zero between two digits is considered significant. For example in 5.06m, the
number of significant figures is 3.
(b) Zeros on the left side of the measured value are not significant. For example,
in 0.0034 m, the number of significant figures is 2.
(c) Zeros on the right side of a decimal are considered significant. For example, in
2.40 mm the significant digits are 3.
(d) If numbers are recorded in scientific notation, then all the digits before the
exponent are significant. For example, in 3.50 × 104m, the significant figures
are 3.
Quick Quiz
How many significant figures are there in each of the following?
(a) 1.25 × 102 m (b) 12.5 cm (c) 0.125 m (d) 0.000125 km

1.12 Precision and Accuracy

A physical measurements should be precise as well as accurate. These are
two separate concepts and need clear distinction. Generally, precision of a
measurement refers to how close together a group of measurements actually are
to each other. Accuracy of a measurement refers how close the measured value is
to some accepted or true value.
(a) (b) (c)

Precise not accurate Accurate not precise Accurate and precise

Fig. 1.15
A classic illustration is helpful to distinguish the two concepts. Consider a
target or bullseye hit by arrows in Fig. 1.15. To be precise, arrows must hit near
each other (Fig.1.15-a) and to be accurate, arrows must hit near the bullseye
21
(Fig. 1.15-b). Consistently hitting near the centre of bullseye indicates both
precision and accuracy (Fig. 1.15-c). When these concepts are applied to
measurements, the precision is determined by the instrument being used for
measurement. The smaller the least count, the more precise is the measurement.
A measurement is accurate if it correctly reflects the size of the object being
measured. Accuracy depends on fractional uncertainty in the measurement.
Infact, it is relative measurement which is important. The smaller the size of
physical quantity, the more precise instrument is needed to be used. The
accuracy of measurement is reflected by the number of significant figures, the
larger is the number of significant figures, the higher is the accuracy.
Table 1.7 Some Timing Devices
Type of clock/watch Use and accuracy
Atomic clock Measures very short time intervals of about 10-10 seconds.
Digital stopwatch Measures short time intervals (in minutes and seconds)
to an accuracy to ±0.01 s.
Analogue stopwatch Measures short time intervals (in minutes and seconds)
to an accuracy to ±0.1 s.
Ticker-tape timer Measures short time intervals of 0.02 s.
Watch/Clock Measures longer time intervals in hours, minutes and
seconds.
Pendulum clock Measures longer time intervals in hours, minutes and
seconds.
Radioactive decay clock Measures (in years) the age of remains from thousands
of years ago.
1.13 Rounding off the digits
When rounding off numbers to a certain number of significant figures, do
so to the nearest value. If the last digit is more than 5, the retained digit is
increased by one and if it is less than 5, it is retained as such.
For example:
(i) Round to 2 significant figures: 2.512 × 10³ m.
Answer: 2.5 × 10³ m
(ii) Round to 3 significant figures: 3.4567 × 10⁴ kg.
Answer: 3.46 × 10⁴ kg
For the integer 5, there is an arbitrary rule:
If the number before the 5 is odd, one is added to the last digit retained.
If the number before the 5 is even, it remains the same:

22
For example: Do You Know?
(i) Round to 2 significant figures: 4.45 × 102 m.
(ii) Round to 2 significant figures: 4.55 × 102 m.
Answer: 4.4 × 102 m
Answer: 4.6 × 10 m
2

Sometimes, logic is applied to decide the fate

of a digit. If we round to 2 significant figures
An Electronic timer
4.452 × 102 m, the answer should be 4.5 × 102 m since can measure time
4.452 × 102 m is more closer to 4.5 × 102 m than intervals as short as
one-ten thousands
4.4 × 102 m. (1/10,000) of a second.

KEY POINTS
 A physical quantity can be measured directly or indirectly using some instruments.
 Non-physical quantity is not measurable using an instrument. It qualitatively depends
on the perception of the observer and estimated only.
 Base quantities are length, mass, time, temperature, electric current, etc.
 Derived quantities are all those quantities which can be defined with reference to
base quantities. For example, speed, area, volume, etc.
 Standard unit does not vary from person to person and understood by all the
scientists.
 Base units of system international are: metre, kilogram, second, ampere, candela,
kelvin and mole.
 The units which can be expressed in terms of base units are called derived units.
 Scientific notation is an internationally accepted way of writing numbers in which
numbers are recorded using the powers of ten or prefixes and there is only one
non-zero digit before the decimal.
 Least count is the least measurement recorded by an instrument.
 Vernier Callipers is an instrument which can measure length correct up to 0.1 mm.
 Screw guage is an instrument which can measure length correct up to 0.01 mm.
 Measurements using instruments are not perfect. There are inevitable errors in the
measured values, may be due to human errors, systematic errors and random errors.
 Measurements using instruments errors are uncertain to some extent depending
upon the limitations or refinement of the instrument.
 Significant figures are the accurately known digits and first doubtful digit in any
measurement.
 The precision is detemined by the instrument being used for measurement whereas
the accuracy depends on relative measurement reflected by the number of significant
figures.

23
 EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
1.1. The instrument that is most suitable for measuring the thickness of a few
sheets of cardboard is a:
(a) metre rule (b) measuring tape
(c) Vernier Callipers (d) micrometer screw gauge
1.2. One femtometre is equal to:
(a) 10–⁹ m (b) 10–¹⁵ m
(c) 10 m (d) 10¹⁵ m
9

1.3. A light year is a unit of:

(a) light (b) time
(c) distance (d) speed
1.4. Which one is a non-physical quantity?
(a) distance (b) density
(c) colour (d) temperature
1.5. When using a measuring cylinder, one precaution to take is to:
(a) check for the zero error
(b) look at the meniscus from below the level of the water surface
(c) take several readings by looking from more than one direction
(d) position the eye in line with the bottom of the meniscus
1.6. Volume of water consumed by you per day is estimated in:
(a) millilitre (b) litre
(c) kilogram (d) cubic metre
1.7. A displacement can is used to measure:
(a) mass of a liquid (b) mass of a solid
(c) volume of a liquid (d) volume of a solid
1.8. Two rods with lengths 12.321 cm and 10.3 cm are placed side by side, the
difference in their lengths is:
(a) 2.02 cm (b) 2.0 cm (c) 2 cm (d) 2.021 cm
1.9. Four students measure the diameter of a cylinder with Vernier Callipers.
Which of the following readings is correct?
(a) 3.4 cm (b) 3.475 cm (c) 3.47 cm (d) 3.5 cm
1.10. Which of the following measures are likely to represent the thickness of a
sheet of this book?
(a) 6 × 10–²⁵ m (b) 1 × 10–⁴ m
(c) 1.2 × 10 ¹⁵ m
–
(d) 4 × 10–² m
1.11. In a Vernier Callipers ten smallest divisions of the Vernier scale are equal to
nine smallest divisions of the main scale. If the smallest division of the
main scale is half millimetre, the Vernier constant is equal to:
(a) 0.5 mm (b) 0.1 mm
(c) 0.05 mm (d) 0.001 mm
24
 B Short Answer Questions
1.1. Can a non-physical quantity be measured? If yes, then how?
1.2. What is measurement? Name its two parts.
1.3. Why do we need a standard unit for measurements?
1.4. Write the name of 3 base quantities and 3 derived quantities.
1.5. Which SI unit will you use to express the height of your desk?
1.6. Write the name and symbols of all SI base units.
1.7. Why prefix is used? Name three sub-multiples and three multiple
prefixes with their symbols.
1.8. What is meant by:
(a) 5 pm
(b) 15 ns
(c) 6 μm
(d) 5 fs
Main scale
1.9. (a) For what purpose, a Vernier Callipers is 0 1 2 3 4

used?
(b) Name its two main parts. 0 5 10
(c) How is least count found? Vernier scale

(d) What is meant by zero error?

5.9 cm 6.0 cm 6.1 cm
1.10. State least count and Vernier scale B C
A
reading as shown in the figure and hence,
find the length.
0 1 2 3 4 5 6
1.11. Which reading out of A, B and C shows the
correct length and why?
C Constructed Response Questions
1.1. In what unit will you express each of the following?
(a) Thickness of a five-rupee coin:
(b) Length of a book:
(c) Length of football field:
(d) The distance between two cities:
(e) Mass of five-rupee coin:
(f) Mass of your school bag:
(g) Duration of your class period:
(h) Volume of petrol filled in the tank of a car:
(i) Time to boil one litre milk:

25
1.2. Why might a standard system of measurement be helpful to a tailor?

1.3. The minimum main scale reading of a micrometer 80

screw gauge is 1 mm and there are 100 divisions on the

0
70

circular scale. When thimble is rotated once, 1 mm is its 60

measurement on the main scale. What is the least

count of the instrument? The reading for thickness of a steel rod as shown
in the figure. What is the thickness of the rod?
1.4. You are provided a metre scale and a bundle of pencils; how can the
diameter of a pencil be measured using the metre scale with the same
precision as that of Vernier Callipers? Describe briefly.
1.5. The end of a metre scale is worn out. Where will you place a pencil to find
the length?
1.6. Why is it better to place the object close to the metre scale?
1.7. Why a standard unit is needed to measure a quantity correctly?
1.8. Suggest some natural phenomena that could serve as a reasonably
accurate time standard.
1.9. It is difficult to locate the meniscus in a wider vessel. Why?
1.10. Which instrument can be used to measure:
(i) Internal diameter of a test tube. (ii) Depth of a beaker.

D Comprehensive Questions

1.1. What is meant by base and derived quantities? Give the names and
symbols of SI base units.
1.2. Give three examples of derived unit in SI. How are they derived from base
units? Describe briefly.
1.3. State the similarities and differences between Vernier Callipers and
micrometer screw gauge.
1.4. Identity and explain the reasons for human errors, random errors and
systematic errors in experiments.
1.5. Differentiate between precision and accuracy of a measurement with
examples.

26
 E Numerical Problems
1.1 Calculate the number of second in a (a) day (b) week (c) month and state
your answers using SI prefixes. (86.4 ks, 604.8 ks, 2.592 Ms)
1.2 State the answers of problem 1.1 in scientific notation.
[8.64 × 10⁴ s, 6.048 × 10⁵ s, 2.592 × 10⁶ s]
1.3 Solve the following addition or subtraction. State your answers in
scientific notation.
(a) 4 × 10 ⁴ kg + 3 × 10 ⁵ kg (b) 5.4 × 10–⁶ m – 3.2 × 10–⁵ m
– –

[(a) 4.3 × 10–⁴ kg (b) – 2.66 × 10–⁵ m]

1.4 Solve the following multiplication or division. State your answers in
scientific notation.
6 × 10⁸ kg
(a) (5 × 10⁴ m) × (3 × 10 ² m) (b)
–

3 × 10⁴ m³

(a) 1.5 × 10³ m² (b) 2.0 × 10⁴ kg m–³

1.5 Calculate the following and state your answer in scientific notation.
(3 × 10² kg) × (4.0 km)
5 × 10² s²
(2.4 × 10³ kg m s–²)
1.6 State the number of significant digits in each measurement.
(a) 0.0045 m (b) 2.047 m (c) 3.40 m (d) 3.420 × 104 m
[(a) 2 (b) 4 (c) 3 (d) 4]
1.7 Write in scientific notation:
(a) 0.0035 m (b) 206.4 × 10² m
[(a) 3.5 × 10–³ m, (b) 2.064 × 10⁴ m)]
1.8 Write using correct prefixes:
(a) 5.0 × 10⁴ cm (b) 580 × 10² g (c) 45 × 10–⁴ s [(0.5 km, 58 kg, 4.5 ms)]
1.9 Light year is a unit of distance used in Astronomy. It is the distance
covered by light in one year. Taking the speed of light as 3.0 × 10⁸ m s-¹,
calculate the distance.
(9.46 × 10¹⁵ m)
1.10 Express the density of mercury given as 13.6 g cm in kg m .
-3 -3

(1.36 × 104 kg m-³)

27
 Chapter
2 Kinematics
Student Learning Outcomes

After completing this chapter, students will be able to:

[SLO: P -09 - B -01] Differentiate between scalar and vector quantities:
[A scalar has magnitude (size) only and that a vector quantity has magnitude and direction.
Students should be able to represent vectors graphically]
[SLO: P -09 - B - 0 2] Justify that distance, speed, time, mass, energy, and temperature are scalar
quantities.
[SLO: P -09 - A - 0 3] Justify that displacement, force, weight, velocity, acceleration are vector
quantities.
[SLO: P -09 - A - 0 4] Determine graphically, the resultant of two or more vectors.
[SLO: P -09 - B - 0 5] Differentiate between different types of motion [i.e; translatory, {linear,
random, and circular); rotatory and vibratory motions and distinguish among them.]
[SLO: P -09 - B - 0 6] Differentiate between distance and displacement, speed and velocity.
[SLO: P -09 - B - 0 7] Define and calculate average speed [average speed = (total distance
travelled)/ (total time taken)]
[SLO: P -09 - B - 0 8] Differentiate between average and instantaneous speed (speed shown by
speedometer of a vehicle is the speed at any instant.)
[SLO: P -09 - B -09] Differentiate between uniform velocity and non -uniform velocity
[SLO: P -09 - B -10] Define and calculate acceleration [Includes deriving the units of acceleration
as ms-2 from the formula a = Δv /Δt and using the formula to solve problems. This also includes
knowing that that deceleration is negative acceleration and using fact in calculations.]
[SLO: P -09 - B -11] Differentiate between uniform acceleration and non -uniform acceleration
[SLO: P -09 - B -12] Sketch, plot and interpret distance, time and speed-time graphs
[This includes determining from the shape of a distance -time graph when an object is:
[(a) at rest, (b) moving with constant speed, (c) accelerating, (d) decelerating. Students are also
required to know how to calculate speed from the gradient of a distance - time graph. It also
includes determining from the shape of a speed -time graph when an object is:
(a) at rest, (b) moving with constant speed, (c) moving with constant acceleration.]
[SLO: P -09 - B - 13] Use the approximate value of
g as 10m/s² for free fall acceleration near Earth to
solve problems
[SLO: P -09 - B -14] Analyse the distance
travelled in speed vs time graphs [By determining
the area under the graph for cases of motion with
constant speed or constant acceleration]
[SLO: P -09 - B -15] Calculate acceleration from
the gradient of a speed-time graph
[SLO: P -09 - B -16] State that there is a universal
speed limit for any object in the universe that is
approximately 3 × 108 m s–1
[Students should just be aware that this phenomenon is true; they do not need to study relativity
in any depth. The purpose is that students appreciate that there is a universal speed limit].

28
 Mechanics is the branch of physics that deals with the motion of objects
and the forces that change it.
Generally, mechanics is divided into two branches:
1. Kinematics 2. Dynamics
Kinematics is the study of motion of objects without referring to forces.
On the other hand, dynamics deals with forces and their effect on the motion of
objects.
In our everyday life, we observe many objects in motion. For example,
cars, buses, bicycles, motorcycles moving on the roads, aeroplanes flying
through air, water flowing in canals or some object falling from the table to the
ground.
The motion of these objects can be studied with or without considering the force
which causes motion in them or changes it.

2.1 Scalars and Vectors

Before we study kinematics in detail, we should know about the nature of
various physical quantities. Some quantities are called scalars and the others
vectors.

A scalar is that physical quantity which can be

described completely by its magnitude only.

Magnitude includes a number and an appropriate unit. When we ask a

shopkeeper to give us 5 kilograms of sugar, he can fully understand how much
quantity we want. It is the magnitude of mass of sugar. Mass is a scalar quantity.
Some other examples of scalar quantities are distance, length, time, speed,
energy and temperature. Scalar quantities can be added up like numbers.
For example, 5 metres + 3 metres = 8 metres.
On the other hand,

A vector is that physical quantity which needs

magnitude as well as direction to describe it completely.

The examples of vector quantities are displacement, velocity,

acceleration, weight, force, etc. The velocity of a car moving at 90 kilometre per
hour (25 m s−1) towards north can be represented by a vector. Velocity is a vector
quantity because it has magnitude 25 m s−1 and direction (towards north).
Vectors cannot be added like scalars. There are specific methods to add up
vectors. These methods take their directions also into consideration.
29
Representation of vectors
In the text book, symbol used for a vector is a bold face letter such as A, v,
F and etc. Since we cannot write in bold face script on paper, so a vector is
→ → →→
written as the letter with a small arrow over it, i.e. A, v, F, d. The magnitude of a
vector is given by italic letter without arrow head. A vector can be represented
graphically by drawing a straight line with an arrow head at one end. The length
of line represents the magnitude of the vector quantity according to a suitable
scale while the direction of arrow indicates the direction of the vector.
v
To represent the direction, two mutually N
perpendicular lines are required. We can draw one
line to represent east-west direction and the other
θ
line to represent north-south direction as shown in W E
Fig.2.1(a). The direction of a vector can be given O

with respect to these lines. Mostly, we use any two

lines which are perpendicular to each other. S
Horizontal line (x x ) is called x-axis and vertical line A vector v making an angle θ
( y y ) is called y-axis (Fig. 2.1-b). The point where towards north from east
these axes meet is known as origin. The origin is Fig 2.1 (a)
y
usually denoted by O. These axes are also called F

A vector is drawn starting from the origin of

30
the reference axes towards the given direction. The x x
O

O
direction is usually given by an angle θ (theta) with
x-axis. The angle with x-axis is always measured from
y
the right side of x-axis in the anti-clockwise direction.
A Vector F making angle 30O
Example 2.1 with x-axis
Fig. 2.1 (b)
Draw the velocity vector v; a velocity of 300 m s-1
at an angle of 60° to the east of north. For Your Information!
For geographical direction, the
Solution reference line is north – south
i. Draw two mutually perpendicular lines whereas for Cartesian coordinate
indicating N, S, E & W. system +ve x-axis is the reference.
ii. Select a suitable scale. If 100 m s-1 = 1 cm, N P
v
then 300 m s-1 are represented by 3 cm line.
iii. Draw 3 cm line OP at an Angle of 60o 60
O

W E
starting from N towards E. O

iv. Make an arrow head at the end of line OP.

The OP is the vector v.
30 S Fig. 2.2
Example 2.2
Draw a force vector F having magnitude of 350 N and acting at an angle of 60°
with x-axis.
Solution Q
(i.) Draw horizontal and vertical lines to represent F
x-axis and y-axis as shown in Fig. 2.3. y
(ii.) Scale: If 100 N = 1 cm, then
60°
350 N = 3.5 cm x x
O
(iii.) Draw 3.5 cm line OQ at an angle of 60° with x-axis.
(iv.) Make an arrow head at the end of the line OQ. The y
OQ is the vector F.
Fig. 2.3
Resultant Vector
We can add two or more vectors to get a single vector. This is called as
resultant vector. It has the same effect as the combined effect of all the vectors to
be added. We have to determine both magnitude and direction of the resultant
vector, therefore, it is quite different from that of scalar addition. One method of
addition of vectors is the graphical method.

Addition of Vectors by Graphical Method

y
Let us add two vectors v1 and v2 having
magnitudes of 300 N and 400 N acting at angles
of 30o and 60o with x-axis. By selecting a suitable
60O
scale 100 N = 1cm, we can draw the vectors as
30
O

shown in Fig. 2.4 (a). x x

O
To add these vectors, we apply a rule
called head-to-tail rule, which states that:

y Fig. 2.4 (a)

To add a number of vectors, redraw their representative lines

such that the head of one line coincides with the tail of the other.
The resultant vector is given by a single vector which is directed
from the tail of the first vector to the head of the last vector.

31
 y
Measured length of resultant vector is 6.8 cm v v₂
(Fig.2.4-b). According to selected scale,
magnitude of the resultant vector v is 680 N and
direction is angle 49O with x-axis. 60O
We can find the resultant vector of more than
49O v₁
two vectors by adding them with the same way
applying head-to-tail rule. x 30 O

O x

2.2 Rest and Motion y

Fig. 2.4 (b)

When we look around us, we see many things like buildings, trees, electric
poles, etc. which do not change their positions. We say that they are in a state of
rest.

Fig. 2.5 (a)

If a body does not change its position with
respect to its surroundings, it is said to be at rest.
Suppose a motorcyclist is standing on the road (Fig. 2.5-a). An observer
sees that he is not changing his position with respect to his surroundings i.e., a
nearby building, tree or a pole. He will say that the motorcyclist is at rest.
Now let us see what does motion mean? When the motorcyclist is driving
(Fig. 2.5-b), the observer will notice that he is continuously changing his position
with respect to the surroundings. Then the observer will say that the motorcyclist
is in motion.
If a body continuously changes its position with
respect to its surroundings, it is said to be in
motion.
The state of rest or motion of a body is always
relative. For example, a person standing in the
Fig. 2.5 (b)
compartment of a moving train is at rest with
respect to the other passengers in the compartment but he is in motion with
respect to an observer standing on the platform of a railway station.
32
2.3 Types of Motion
We observe different types of motion in our daily life. A train moves almost
along a straight line, the blades of a fan rotate about an axis, a swing vibrates
about its mean position. Generally, there are three types of motion of bodies.
1. Translatory motion 2. Rotatory motion 3. Vibratory motion
1. Translatory Motion
If the motion of a body is such that every
particle of the body moves uniformly in
the same direction, it is called tanslatory
motion. For example, the motion of a
train or a car is tanslatory motion (Fig.2.6).
Translatory motion can be of three types: Fig. 2.6 The motion of a train is translatory motion
(i.) Linear Motion
If the body moves along a straight line, it is
called linear motion. A freely falling body is
the example of linear motion.
(ii.) Random Motion (a) Irregular path (b) The motion of bee
If the body moves along an irregular path Fig. 2.7 is random motion
(Fig. 2.7), the motion is called random motion.
(iii.)Circular Motion
The motion of a body along a circle is called circular
motion. If a ball tied to one end of a string is whirled, it
moves along a circle. A Ferris wheel is also an example of
Circular Motion
circular motion (Fig.2.8). Fig. 2.8
2. Rotatory Motion
If each point of a body moves around a fixed point (axis),
the motion of this body is called rotatory motion. For
example, the motion of an electric fan and the drum of a
Rotatory motion of a fan
washing machine dryer is rotatory motion (Fig.2.9). The Fig. 2.9
motion of a top is also rotatory motion.

3. Vibratory Motion
When a body repeats its to and fro motion about a fixed
position, the motion is called vibratory motion. The motion
of a swing in a children park is vibratory motion (Fig. 2.10).
Fig. 2.10 Vibratory motion
33
2.4 Distance and Displacement
We know that motion is the action of an object going from one place to
another or change of position. The length between the original and final
positions may be measured in two ways as either distance or displacement.
The distance is the length of actual path of the motion.

Let a person be travelling from Lahore to Multan in a car. On reaching

Multan, he reads the speedometer and notices that he has travelled a distance of
320 km. It is the distance travelled by that person. Obviously, it is not the shortest
distance from Lahore to Multan, as the car took many turns in the way. He did not
travel along a straight line.

The displacement of an object is a vector quantity whose magnitude is

the shortest distance between the initial and final positions of the motion
and its direction is from the initial position to the final position.
We can also call this as the change in position. B

Note that displacement is a vector quantity d

whereas distance is a scalar quantity. Following
example will explain the difference between
distance and displacement. A
Fig. 2.11
Suppose a car travels from a position A to B. The curved line is the actual path
followed by the car (Fig. 2.11). The total distance covered by the car will be equal
to the length of the curved line AB. The displacement d is the straight line AB
directed from A to B as indicated by the arrow head. The SI unit for the
displacement is the same as that of distance.
2.5 Speed and Velocity Do You Know?

Brain Teaser! We are often interested to

know how fast a body is moving. For
this purpose, we have to find the
distance covered in unit time which
is known as speed. If a body covers a
distance S in time t, its speed v will be
The car while moving written as:
Thefastest land
on a circular road mammal (cheetah)
Distance v = S
may have constant and the fastest fish
speed, but its velocity Speed = (sailfish) have the
Time t same highest
is changing at every
or S = vt .......................... (2.1) recorded speed of
instant. Why? 110 km h–¹.
34
The speed is a scalar quantity. The SI unit of speed is m s-¹ or km h-¹.
It is obvious that speed of a vehicle does not remain constant throughout the
journey. If the reading of the speedometer of the vehicle is observed, it is always
changing. The speed of a vehicle that is shown by its speedometer at any instant
is called instantaneous speed. Practically we make use of the average speed. It
is defined as:
Total distance covered S
Average speed = or vav =
Total time taken t
Example 2.3
An eagle dives to the ground along a 300 m path with an average speed of
60 m s ¹. How long does it take to cover this distance?
–

For Your Information!

Solution
Total distance covered = S = 300 m
Average speed = va = 60 m s–1
Total time taken = t = ?
S
Using the equ ation vav = Mount st. Helens erupted
S t in 1980, causing rocks to
or t=
vav travel at velocities up to
400 km h-1
putting the values t = 300 m / 60 m s–1 = 5 s

Velocity
The speed of an object does not tell anything about the direction of
motion. To take into account the direction, the vector concept is needed. For this,
we have to find the displacement d between the initial and final positions.

The net displacement of a body in unit time is called velocity.

If a body moves from point A to B along a curved path as shown in Fig.2.11, the
displacement d is the straight line AB, then
Average velocity = Displacement or vav =
d ............ (2.2)
Time t
Velocity is a vector quantity. The Equation (2.2) shows that the direction of
velocity v is the same as that of displacement d. The SI unit of velocity is also m s–1
or km h–1. Consider the example of a car moving towards north at the rate of
70 km h–1.To differentiate between speed and velocity, we shall say that the speed

35
of car is 70 km h–1 which is a scalar quantity. The For Your Interest!
velocity of the car is a vector quantity whose
magnitude is 70 km h–1 and is directed towards north.
Uniform and Non-uniform Velocity
The velocity is said to be uniform if the speed and Time-lapse photo of
direction of a moving body does not change. If the motorway traffic, the
speed or direction or both of them change, it is velocity of cars showing
known as variable velocity or non-uniform velocity. straight lines. White lines
are the headlights and the
Practically, a vehicle does not move in a straight line red lines are taillights of
throughout its journey. It changes its speed or its vehicles moving in
direction frequently. The example of a body moving opposite directions.
with uniform velocity is the downward motion of a
paratrooper. When a paratrooper jumps from an aeroplane, he falls freely for a
few moments. Then the parachute opens. At this stage the force of gravity acting
downwards on the paratrooper is balanced by the resistance of air on the
parachute that acts upward. Consequently, the paratrooper moves down with
uniform velocity.
2.6 Acceleration
Whenever the velocity of an object is increasing, we
say that the object is accelerating. For example, when
a car overtakes another one, it accelerates to a greater
velocity (Fig.2.12). In contrary to that the velocity
decreases when brakes are applied to slow down a
While overtaking, a car
bicycle or a car. In both the cases, a change in velocity accelerates to a greater velocity.
occurs. Fig. 2.12

Acceleration is defined as the time rate of change of velocity.

The change in velocity can occur in magnitude or direction or both of them. The
acceleration is positive if the velocity is increasing and it is negative if the velocity
is decreasing. Negative acceleration is also called deceleration or retardation.
Acceleration is a vector quantity like velocity, but the direction of acceleration is
that of change of velocity. If a body is moving with an initial velocity vi and after
some time t its velocity changes to vf , the change in velocity is ∆v = vf - vi that
occurs in time t. In this case, rate of change of velocity i.e., acceleration will be
average acceleration.

36
 Change in velocity
Average acceleration= Fascinating Snap:
Time taken This is a photograph
vf - vi ............................ of a falling apple
aav = (2.3) dropped from som
t
∆v height. The images of
Equation (2.3) can be written as aav t apple are captured
The SI unit of acceleration is = m s−². by the camera at 60
If acceleration a is constant, then Eq 2.3 can be flashes per second.
The widening spaces
written as vf = vi + at between the images
Uniform and Non-uniform Acceleration indicate the
acceleration of the
If time rate of change of velocity is constant, apple.
the acceleration is said to be uniform.
If anyone of the magnitude or direction or both of them changes it is called
variable or non-uniform acceleration. In this class, we will solve problems only for
the motion of the bodies having uniform acceleration and not the variable
acceleration.
Example 2.4
A plane starts running from rest on a run-way as shown in the figure
below. It accelerates down the run-way and after 20 seconds attains a velocity of
252 km h ¹. Determine the average acceleration of the plane.
−

vi = 0 t = 0 vf t = 20 s

Solution:
Initial velocity = vi=0
Final velocity = vf = 252 km h−1
252 × 10³ m
= = 70 m s−1
60 × 60 s
Time taken = t = 20 s
Average acceleration = aav = ?
v –v
Using aav = f i
t
Putting the values
aav = 70 m s − 0
−1

20 s
aav = 3.5 m s−2 37
2.7 Graphical Analysis of Motion
A graph is a pictorial diagram in the
form of a straight line or a curve which shows y

the relationship between two physical

quantities. Usually, we draw a graph on a
paper on which equally spaced horizontal and x
x o
vertical lines are drawn. Generally, every 10
th

line is a thick line on the graph paper. In order

to draw a graph, two mutually perpendicular
y
thick lines xoxʹ and yoý are selected as x and y
Fig. 2.13
axes as shown in Fig 2.13. The point where the
two axes intersect each other is known as origin o. Positive values along x-axis are
taken to the right side of the origin and negative values are taken to the left side.
Similarly, positive values along y-axis are taken above the origin whereas
negative values are taken below the origin. Normally, the independent quantity
is taken along x-axis and dependent variable quantity along y-axis. For example,
in distance-time graph, t is independent and S is dependent variable. Therefore,
t should be along x-axis and S along y-axis.
To represent a physical quantity along any axis, a suitable scale is chosen
by considering the minimum and maximum values of the quantity.

Distance-Time Graph
Distance-time graph shows the relation between distance S and time t taken by a
moving body.
Let a car be moving in a straight line on a motorway. Suppose that we measure its
distance from starting point after every one minute, and record it in the table
given below:
Time
t (min) 0 1 2 3 4 5

Distance
0 1.2 2.4 3.6 4.8 6.0
S (km)

38
Follow the steps given below to draw a graph on a centimetre graph paper:
i. Take time t along x-axis and distance S along y-axis.
ii. Select suitable scales (1 minute = 1 cm) along x-axis and (1.2 km =1 cm)
along y-axis. The graph paper shown here is not to the scale.
y
iii. Mark the values of each big division along x
and y axes according to the scale. 6.0
iv. Plot all pairs of values of time and distance by
4.8
marking points on the graph paper.

S (km)
v. Join all the plotted points to obtain a best 3.6
straight line as shown in Fig. 2.14. From the 2.4
table, we can observe that car has covered 1.2
equal distance in equal intervals of time. This
3 4 5 X
shows that the car moves with uniform O 1 2
t (min)
speed. Therefore, a straight line graph Fig. 2.14
between time and distance represents motion with uniform speed.
Now consider another journey of the car as recorded in the table given below:
Time
0 1 2 3 4 5
t (min)
Distance
0 0.240 0.960 2.160 3.840 6.000
S (km)
Table shows that speed goes on increasing in equal intervals of time. This is very
obvious from the graph as shown in Fig. 2.15. The graph line is curved upward.
This is the case when the body (car) is moving with certain acceleration.
y
6.000

5.000

4.000
S (km)
3.000

2.000

1.000
0
O0 1 2 3 4 5 X
t (min)
Fig. 2.15

39
In another case, consider the following table:
Time
0 1 2 3 4 5
t (min)
Distance
0 2.0 3.1 4.0 4.6 5.0
S (km)
The graph line is curved downwards. This shows that distance travelled in the
same interval of time goes on decreasing, so speed is decreasing. This is the case
of motion with deceleration or negative acceleration as shown in Fig.2.16.

5.0

4.0
S (km)

3.0

2.0

1.0

0
1 2 3 4 5
t (min)
Fig. 2.16
Now consider another case.
Time
0 1 2 3 4 5
t (min)
Distance
1.2 1.2 1.2 1.2 1.2 1.2
S (km)

Graph line is horizontal in this case (Fig 2.17). It shows that the distance covered
by the car does not change with change in time. It means that the car is not
moving; it is at rest.
y

2.0

1.6
S (km)

1.2

0.8

0.4

O 1 2 3 4 5 x
t (min)
Fig. 2.17
40
2.8 Gradient of a Distance-Time Graph
The gradient is the measure of slope y
of a line.
Consider the distance-time graph of Q
uniform speed again. Select any two S₂
values of time t1 and t2. Draw two

S(m)
vertical dotted lines at t1 and t2 on

(S2 - S₁ )
x-axis. These lines meet the graph at
points P and Q. From these points
P θ
draw horizontal lines to meet y-axis S1 R
(t - t )
at S1 and S2 respectively as shown in 2 1

Fig.2.18.
O t1 t (s) t2 x
Distance covered in this time
interval is S₂ – S₁ = S Fig. 2.18
Time taken t₂ – t₁ = t

The slope or gradient of the graph is the measure of tangent θ of the triangle RPQ:
RQ
Slope =
PR
S₂ – S₁ S
Slope = =
t₂ – t₁ t
From Eq. (2.1), S = v a , the average speed during the time interval t.
t
Figure 2.17 shows that S = tan θ = slope of graph line, therefore,
t
Gradient of the distance-Time graph is equal to the average
speed of the body.

2.9 Speed-Time Graph

Suppose we can note the speed of the same car after every one second
and record it in the table given below, we can draw the graph between speed v
versus time t. This is called speed-time graph.
Table
Time t (s) 0 1 2 3 4 5
Speed v
0 8 16 24 32 40
(m s−¹)
41
Take t along x-axis and v along y-axis. Scale can be selected as 1 s = 1 cm (x-axis)
and speed 10 m s −1 = 1 cm along y-axis.
Shape of the graph is shown in Fig. 2.19· It is a straight line rising upward. This
shows that speed increases by the same amount after every one second. This is a
motion with uniform acceleration. It is also evident from the table.

40

32
v (m s −1 )

24

16

O 1 2 3 4 5 X
t (s)
Fig. 2.19

Now consider another case. The observations are recorded in the table given
below:

Table
Time t (s) 0 1 2 3 4 5
Speed v
20 20 20 20 20 20
(m s−¹)

In this case, graph line is horizontal (Fig. 2.20) parallel to time x- axis. It shows that
speed does not change with change in time. This is a motion with constant
speed.
y
30
v (m s−1 )

20

10

O 1 2 3 4 5 X
t (s)
Fig. 2.20
42
2.10 Gradient of a Speed-Time Graph
Now consider the speed-time graph (Fig. 2.21). The speeds at times t₁ and t₂ are
v₁ and v₂ respectively. The change in speed in a time interval (t₂ - t₁) is (v₂ -v₁).
Therefore, Y

Change in speed
Slope =
Total time taken Q
v₂
(v₂ – v₁)
or Slope =
(t₂ – t₁)

(v₁ - v₁)
∆v
Slope = t v

∆v P
But = a, the average acceleration. v₁ R
t (t₂ - t₁)

O t₁ t (s) t₂ X
Fig. 2.21
Hence Gradient of the speed-Time graph is equal
to the average acceleration of the body.
This shows that when a car moves with constant acceleration, the velocity-time
graph is a straight line which rises through same height for equal intervals of time.
Graph of Fig. 2.19 is redrawn in Fig. 2.22 to find its slope. The speed v₁ at
time t₁ is the same as speed v₂ at time t₂, hence, the change in speed is also zero.
(v₂ – v₁) Y
v₂ – v₁ = 0. Thus, the slope = =0 3
v (m s −1 )

(t₂ – ₁)
When the speed of the object is 20

constant, the speed-time graph is a 10

horizontal straight line parallel to time v₁ v₂
axis. O 1 2 3 4 5 X
t₁ t (s) t₂
This shows that the acceleration Fig. 2.22
of this motion is zero. It is the motion without the change in speed.
2.11 Area Under Speed-Time Graph
The distance moved by an object can also be determined by using its
speed-time graph. For example, figure 2.23 shows that the object is moving
with constant speed v. For a time-interval t, the distance covered by the object
as given by Eq. 2.1 is v × t.
43
This distance can also be found by Y
calculating the area under the speed-time v
graph. The area under the graph for time
v v
interval t is the area of rectangle of sides t
t
and v. This area is shown shaded in Fig.2.23
O Fig. 2.23 t t X
and is equal to v × t. Thus, area under
speed-time graph up to the time axis is Y
numerically equal to the distance covered v A
by the object in time t.
Now consider another example shown in
Fig. 2.24. Here, the speed of the object v
increases uniformly from 0 to v in time t.
t
The average speed is given by O Fig. 2.24 t B X

vav = 0 2+ v = 2 1 v

Distance covered = average speed × time = 1/2 v × t. Mini Exercise

If we calculate the area under speed-time graph, it
is equal to the area of the right-angled triangle
shown shaded in Fig. 2.24. The base of the triangle
distance cyclist B
is equal to t and the perpendicular is equal to v.
Area of a triangle = 1/2 (perpendicular × base)
= 1/2 (v × t)

We see that this area is numerically equal to the time

distance covered by the object during the time
The distance-time graph shows
interval t. Therefore, we can say that: the motion of three cyclists.
The area under the speed-time graph up to the
(a) What does each line on the
time axis is numerically equal to the distancegraph represent?
covered by the object. (b) Which cyclist travelled the
most distance?
2.12 Solving Problems for (c) Which cyclist travelled at
Motion Under Gravity the greatest speed? the
lowest speed? at constant
Three equations of motion are used to solve speed?
problems for motion of bodies. If v i is the initial
velocity of the body, v f is the final velocity, t is the time taken, S is the distance
covered and a is the acceleration, then:
v f = v + at ---------------- (1)
1
S = vti + 2 at ---------------- (2)
2

2aS = v f² – v ² ---------------- (3) 44

While applying these equations, the following assumptions are made:
(i.) Motion is always considered along a straight line
(ii.) Only the magnitudes of vector quantities are used.
(iii.) Acceleration is assumed to be uniform.
(iv.) The direction of initial velocity is taken as positive. Other quantities which
are in the direction of initial velocity are taken as positive. The quantities in
the direction opposite to the initial velocity are taken as negative.
2.13 Free Fall Acceleration
When a body is falling freely under the action of gravity of the Earth, the
acceleration acting on it is the gravitational acceleration and is denoted by g. The
direction of gravitational acceleration is always downwards. Its value is 9.8 m s ²,
−

but for convenience we shall use the value of g as 10 m s−².

For Your Information! Since the freely falling bodies move vertically
downwards in a straight line with uniform
acceleration g, so the three equations of
motion can be applied to the motion of such
bodies. While applying equations of motion,
the acceleration a is replaced by g. Thus,
equations of motion for freely falling bodies
can be written as:
v f = v + gt - ---------------(1)
1
Light and heavier objects when fall S = vti + 2 gt - ---------------(2)
2

through vacuum, move side by side.

2gS = vf² – v² - ---------------(3)
It should be remembered that while using these For Your Information!
equations, the following points should be kept in mind:
(i.) If a body is released from some height to fall
freely, its initial velocity vi will be taken as zero.
(ii.) The gravitational acceleration g will be taken as
positive in the downward direction. All other
quantities will also be taken as positive in the
downward direction. The quantities in the
direction opposite to the acceleration will be
taken as negative.
Acceleration of free fall g is
(iii.) If a body is thrown vertically upward, the value 10 m s −² for all objects.
of g will be negative and the final velocity will be
zero at the highest point.
45
 Example 2.5
An iron bob is dropped from the top of a tower. It reaches the ground in 4
seconds. Find: (a) the height of the tower (b) the velocity of the ball as it strikes
the ground.
Solution
For freely falling body:
Initial velocity = vi = 0
Acceleration = g = 10 m s ²
−

Time = t = 4s
Height (distance) = S = h = ?
Final velocity = vf = ?
(a) According to second equation of motion,
1
S= vt + gt²
2
i
1
Putting the values, h = 0 x 4 s + × 10 m s−² × (4)² s²
2
h = 80 m
(b) From the first equation of motion, we have
v f = v + gt
Putting the values, v f = 0 + 10 m s−² × 4s = 40 m s−¹
Example 2.6
An arrow is thrown vertically upward with the help of a bow. The velocity of the
arrow when it leaves the bow is 30 m s−¹. Determine time to reach the highest
point? Also, find the maximum height attained by the arrow.
Solution
Here, acceleration will be taken as negative, for the arrow is thrown vertically
upward.
Initial velocity = v i = 30 m s−¹
Final velocity = vf = 0
Acceleration = g = -10 m s ²
−

Time =t=?
Height S = h = ?
From first equation of m otion: v + gt
vf = i
vf – vi
or t = -
0 – 30 m s−¹
Putting the values t = = 3s
–10 m s−²
46
Now from the third equation of motion:
2gS = vf² – vⁱ²
v ² – vⁱ²
or S = f
2 (-g)
0 – (30)² m² s−²
Putting the values h = 2 × 10 m s−² = 45 m

Relativity
In 1905, famous scientist Albert Einstein proposed his revolutionary
theory of special relativity which modified many of the basic concepts of physics.
According to this theory, speed of light is a universal constant. Its value is
approximately 3 ×108 m s−1. Speed of light remains the same for all motions. Any
object with mass cannot achieve speeds equal to or greater than that of light.
This is known as universal speed limit.
KEY POINTS
 A scalar is that physical quantity which can be described completely by its magnitude
only.
 A vector is that physical quantity which needs magnitude as well as direction to
describe it completely.
 To add a number of vectors, redraw their representative lines such that the head of
one line coincides with the tail of the other. The resultant vector is given by a single
vector which is directed from the tail of the first vector to the head of the last vector.
 Translatory motion, rotatory motion and vibratory motions are different types of
motion.
 Position of any object is its distance and direction from a fixed point.
 The shortest distance between the initial and final positions of a body is called its
displacement.
 Distance covered by a body in a unit time is called its speed.
 Time rate of displacement of a body is called its velocity.
 The velocity is said to be uniform if the speed and direction of a moving body does not
change, otherwise it is non-uniform velocity.
 Rate of change of velocity of a body is called its acceleration.
 If change of velocity with time is constant, the acceleration is said to be uniform,
otherwise it is non-uniform.
 A graph that shows the relation between distance and time taken by a moving body is
called a distance-time graph.
 A graph that shows the relation between the speed and time taken by a moving body
is called a speed-time graph.
 Gradient or slope of the distance-time graph is equal to the average speed of the
body. Slope of the speed-time graph is equal to the acceleration of the body.

47
  The area under speed-time graph is numerically equal to the distance covered by the
object.
 Following are three equations of motion:
vf = vi+ at
S = vti + ½ at 2
2aS = vf2- vi2
 Gravitational acceleration g acts downward on bodies falling freely. The magnitude of
g is 10 m s −2 .

EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
2.1 The numerical ratio of displacement to distance is:
(a) always less than one (b) always equal to one
(c) always greater than one (d) equal to or less than one
2.2 If a body does not change its position with respect to some fixed point,
then it will be in a state of:
(a) rest (b) motion
(c) uniform motion (d) variable motion
2.3 A ball is dropped from the top of a tower, the distance covered by it in the
first second is:
(a) 5 m (b) 10 m (c) 50 m (d) 100 m
2.4 A body accelerates from rest to a velocity of 144 km h-1 in 20 seconds.
Then the distance covered by it is:
(a) 100 m (b) 400 m (c) 1400 m (d) 1440 m
2.5 A body is moving with constant acceleration starting from rest. It covers a
distance S in 4 seconds. How much time does it take to cover one-fourth
of this distance?
(a) 1 s (b) 2s (c) 4 s (d) 16 s
2.6 The displacement time graphs of two objects A and B are shown in the
figure. Point out the true statement from the following: A

(a) The velocity of A is greater than B. S

(b) The velocity of A is less than B. B

(c) The velocity of A is equal to that of B.

(d) The graph gives no information in this regard.
2.7 t
The area under the speed-time graph is numerically equal to:
(a) velocity (b) uniform velocity
(c) acceleration (d) distance covered

48
2.8 Gradient of the speed-time graph is equal to:
(a) speed (b) velocity (c) acceleration (d) distance covered
2.9 Gradient of the distance-time graph is equal to the:
(a) speed (b) velocity (c) distance covered (d) acceleration
2.10 A car accelerates uniformly from 80.5 km h ¹ at t = 0 to 113 km h−¹
−

at t = 9 s. Which graph best describes the motion of the car?

(a) (b) (c) (d)
v v v v

t t t t
B Short Answer Questions
2.1 Define scalar and vector quantities.
2.2 Give 5 examples each for scalar and vector quantities.
2.3 State head-to-tail rule for addition of vectors.
2.4 What are distance- time graph and speed-time graph?
2.5 Falling objects near the Earth have the same constant acceleration. Does this
imply that a heavier object will fall faster than a lighter object?
2.6 The vector quantities are sometimes written in scalar notation (not bold
face). How is the direction indicated?
2.7 A body is moving with uniform speed. Will its velocity be uniform? Give
reason.
2.8 Is it possible for a body to have acceleration? When moving with:
(i) constant velocity
(ii) constant speed
C Constructed Response Questions
2.1 Distance and displacement may or may not be equal in magnitude. Explain
this statement.
2.2 When a bullet is fired, its velocity with which it leaves the barrel is called the
muzzle velocity of the gun. The muzzle velocity of one gun with a longer
barrel is lesser than that of another gun with a shorter barrel. In which gun is
the acceleration of the bullet larger? Explain your answer.
2.3 For a complete trip, average velocity was calculated. Its value came out to be
positive. Is it possible that its instantaneous velocity at any time during the
trip had the negative value? Give justification of your answer.
49
2.4 A ball is thrown vertically upward with velocity v. It returns to the ground in
time T. Which of the following graphs correctly represents the motion?
Explain your reasoning.
(a) ( b) (c) ( d)
v v v v

T
2 T T
2 T 2 T T
0 0 0 t 0 T t
t T t 2

2.5 The figure given below shows the distance - time graph for the travel of a
cyclist. Find the velocities for the segments a, b and c.
b
2.0
1.8
S (km)

1.6
1.4
1.2
a c
1.0
0.8
Distance

0.6
0.4
0.2
0
0 2 4 6 8 10 12 14 16 18 20
Time t (min)

2.6 Is it possible that the velocity of an object is zero at an instant of time, but its
acceleration is not zero? If yes, give an example of such a case.
D Comprehensive Questions
2.1 How a vector can be represented graphically? Explain.
2.2 Differentiate between:
(i) rest and motion
(ii) speed and velocity
2.3 Describe different types of motion. Also give examples.
2.4 Explain the difference between distance and displacement.
2.5 What do gradients of distance-time graph and speed-time graph represent?
Explain it by drawing diagrams.
2.6 Prove that the area under speed-time graph is equal to the distance covered
by an object.
2.7 How equations of motion can be applied to the bodies moving under the
action of gravity?

50
 E Numerical Problems
2.1 Draw the representative lines of the following vectors:
(a) A velocity of 400 m s ¹ making an angle of 60 with x-axis.
− O

(b) A force of 50 N making an angle of 120O with x-axis.

2.2 A car is moving with an average speed of 72 km h ¹. How much time will it
−

take to cover a distance of 360 km? (5 h)

2.3 A truck starts from rest. It reaches a velocity of 90 km h−¹ in 50 seconds. Find
its average acceleration. (0.5 m s−²)
2.4 A car passes a green traffic signal while moving with a velocity of 5 m s−¹. It
then accelerates to 1.5 m s−². What is the velocity of car after 5 seconds?
(12.5 m s−¹)
2.5 A motorcycle initially travelling at 18 km h−¹ accelerates at constant rate of
2 m s−². How far will the motorcycle go in 10 seconds? (150 m)
2.6 A wagon is moving on the road with a velocity of 54 km h−¹. Brakes are
applied suddenly. The wagon covers a distance of 25 m before stopping.
Determine the acceleration of the wagon. (-4.5 m s−²)
2.7 A stone is dropped from a height of 45 m. How long will it take to reach the
ground? What will be its velocity just before hitting the ground?
(3 s, 30 m s−¹)
2.8 A car travels 10 km with an average velocity of 20 m s−¹. Then it travels in the
same direction through a diversion at an average velocity of 4 m s−¹ for the
next 0.8 km. Determine the average velocity of the car for the total journey.
(15.4 m s−¹)
2.9 A ball is dropped from the top of a tower. The ball reaches the ground in
5 seconds. Find the height of the tower and the velocity of the ball with
which it strikes the ground. (125 m, 50 m s-1)
2.10 A cricket ball is hit so that it travels straight up in the air. An observer notes
that it took 3 seconds to reach the highest point. What was the initial
velocity of the ball? If the ball was hit 1 m above the ground, how high did it
rise from the ground?
(30 m s−¹, 46 m)

51
 Dynamics
Chapter
3
Student Learning Outcomes

After completing this chapter, students will be able to:

[SLO: P -09 - B -17] Illustrate that mass is a measure of the quantity of matter in an object
[SLO: P -09 - B -18] Explain that the mass of an object resists change from its state of rest or
motion (inertia)
[SLO: P -09 - B -19] Describe universal gravitation and gravity. State Newton's Law of
gravitation. (Include problems related to gravitation.)
[SLO: P -09 - B -20] Define and calculate weight [Weight is the force exerted on an object
having mass by a planet's gravity, and use w = mg]
[SLO: P -09 - B -21] Define and calculate gravitational field strength [This includes being able
to state that a gravitational field is a region in which a mass experiences a force due to
gravitational attraction. Students should be able to define gravitational field strength (g) as
force per unit mass use the equation gravitational field strength = weight/mass g = w /m (and
know that this is equivalent to the acceleration of free fall)]
[SLO: P -09 - B -22] Justify and illustrate the use of mechanical and electronic balances to
measure mass [understanding the internal workings of the electronic balance is not required;
just how to practically use the instrument in appropriate situations]
[SLO: P -09 - B -23] Justify and illustrate the use of a force meter (spring balance) to measure
weight.
[SLO: P -09 - B -24] Differentiate between contact and noncontact forces
[SLO: P -09 - B -25] Differentiate between different types of forces [including weight
(gravitational force), friction, drag, air resistance, tension (elastic force), electrostatic force,
magnetic force, thrust (driving force), and contact force]
[SLO: P -09 - B -26] State that there are four fundamental forces and describe them in terms
of their relative strengths [These are the gravitational, electromagnetic, strong and weak
nuclear forces. Students should know that Pakistani Scientist won the Nobel Prize for helping
prove that the weak force and the electromagnetic force are actually unified]
[SLO: P -09 - B -27] Represent the forces acting on a body using free body diagrams
[SLO: P -09 - B -28] State and apply Newton's first law
[SLO: P -09 - B -29] Identify the effect of force on velocity [It may change the velocity of an
object by changing its direction of motion or its speed]
[SLO: P -09 - B -30] Determine the resultant of two or more forces acting in the same plane.
[SLO: P -09 - B -31] State and apply Newton's second law in terms of acceleration
[SLO: P -09 - B -32] State and apply Newton's third law
[SLO: P -09 - B -33] Explain with examples how Newton's third law describes pairs of forces of
the same type acting on different objects
[SLO: P -09 - B -34] State the limitations of Newton's laws of motion
[SLO: P -09 - B -36] Analyse the dissipative effect of friction
[SLO: P -09 - B -37] Analyse the dynamics of an object reaching terminal velocity
[SLO: P -09 - B -38] Differentiate qualitatively between rolling and sliding friction
[SLO: P -09 - B -39] Justify methods to reduce friction.
[SLO: P -09 - B -40] Define and calculate momentum
[SLO: P -09 - B -41] Define and calculate impulse [Use the equation Impulse= F Δt = m ΔV ]
[SLO: P -09 - B -42] Apply the principle of the conservation of momentum to solve simple
problems in one dimension
[SLO: P -09 - B -43] Define resultant force in terms of momentum.

52
 In kinematics, we studied the motion of objects. If the position, velocity
and acceleration were known at any time, then the position and velocity of the
moving body at another time could be completely described. But one of the
things left out of this discussion was the cause of acceleration produced in the
body. If a stone is dropped from a height, it is accelerated downward. It is
because the Earth exerts a force of gravity on the stone that pulls it down. When
we drive a car or motorcycle, the engine exerts a force which produces
acceleration. We will observe that whenever there is acceleration, there is always
a force present to cause that acceleration. Dynamics is concerned with the forces
that produce change in the motions of bodies.
3.1 Concept of Force
A common concept of a force is a push or a
pull that starts, stops or changes the magnitude and
direction of velocity of a body. We come across many
forces in our daily life. Some of them we apply on
other bodies and some are acting on us. For
example, when we open a door, we push or pull it by
applying force. When we are sitting in a car, we push
against the seat as the car turns round a corner.
Force transfers energy to an object. Take the
example of a man who moves a wheelbarrow with its Fig. 3.1

load. The man first applies force to lift it and then applies force to push it (Fig.3.1).
He applies a different amount of force on each handle when turning the
wheelbarrow around the corner in order to keep it from tipping over. The
examples of forces acting on us are the force of gravity acting downward, the
force of friction which helps us to walk on the ground and many others.
Types of Forces
There are two major types of forces:
1. Contact Forces 2. Non-contact Forces
1. Contact Forces
A contact force is a force that is exerted by one object on the other at the
point of contact. Applied forces (push a pull and twist) are contact forces. Some
other examples of contact forces are the following:
(i) Friction
It is the force that resists motion when the surface of one object comes in
contact with the surface of another.
53
(ii) Drag
The drag force is the resistant force caused by the motion of a body
through a fluid. It acts opposite to the relative motion of any object moving with
respect to surrounding fluid.
(iii) Thrust
It is an upward force exerted by a liquid on an object immersed in it. When
we try to immerse an object in water, we feel an upward force exerted on the
object. This force increases as we push the object deeper into the water. A ship
can float in the sea due to this force which balances the weight of the ship.
(iv) Normal Force
It is the force of reaction exerted by the surface on an object lying on it.
This force acts outward and perpendicular to the surface. It is also called the
support force upon the object.
(v) Air Resistance
It is the resistance (opposition) offered by air when an object falls through it.
(vi) Tension Force
It is the force experienced by a rope when a person or load pulls it.
(vii) Elastic Force
It is a force that brings certain materials back to their original shape after
being deformed. Examples are rubber bands, springs, trampoline, etc.
2. Non-contact Forces
A non-contact force is defined as the force between two objects which are
not in physical contact. The non-contact forces can work from a distance. That is
why, these are sometimes called as action-at-a-distance. There is always a field
linked with a non-contact force. Due to this property, non-contact forces are also
called field forces. A few examples of non-contact forces are described below:
(i) Gravitational Force
An apple falling down from a tree is one of the best examples of
gravitational force (Fig. 3.2). When we throw an object upward, it is the
gravitational force of the Earth that brings it back to the
Earth. In fact, the gravitational force is an attractive force
that exists among all bodies which have mass. It is a
long-range force given by Newton's law of gravitation:
F = G m1 m 2 where m1 and m2 are two
r2
masses distant r apart and G is constant of gravitation. Its value
is 6.67 × 10–11 N m2 kg–2. The Sun's gravitational force keeps the
Earth and all other planets of our solar system in fixed orbits. Fig. 3.2
Similarly, the gravitational force of the Earth keeps the moon in its orbit. It also
keeps the atmosphere and oceans fixed to the surface of the Earth. Even an
object resting on a surface exerts a downward force called its weight due to
attractive force of the Earth also known as gravity.
54
(ii) Electrostatic Force
An electrostatic force acts between two charged
objects. The opposite charges attract each other and
similar charges repel each other as shown in Fig. 3.3. Force Force
Like gravitational force, electrostatic force is also a
long-range force.
(iii) Magnetic Force
It is a force which a magnet exerts on other
Fig. 3.3
magnets and magnetic materials like iron, nickel and
cobalt. You might have observed that iron pins
attracted in the presence of a magnet without any
physical contact (Fig. 3.4). Magnetic force between the
poles of two magnets can be either attractive or
repulsive. This can be observed very easily by bringing
different poles of two magnets close to each other. Like
poles repel and unlike poles attract each other. Fig. 3.4
(iv) Strong and Weak Nuclear Forces
These are also non-contact forces acting between the subatomic
particles. We will study these forces in the next section.
3.2 Fundamental Forces
There are four fundamental forces in nature. These are:
1. Gravitational force 2. Electromagnetic force
3. Strong nuclear force 4. Weak nuclear force
Every force comes under any of these forces.
Gravitational Force
The gravitational force has been discussed in the previous section. We
often talk about this force. It is the weakest one among all four forces. Being a
long range force, it extends to infinite distance although it becomes weaker and
weaker.
Electromagnetic Force
It is the force that causes the interaction
between electrically charged particles. Electrostatic
and magnetic forces come under this category. These
are long-range forces. The areas in which these forces
act are called electromagnetic fields. Electromagnetic Fig. 3.5
A moving magnet
forces are stronger than gravitational and weak produces electric current
55
nuclear forces. This force causes all chemical reactions. It binds together atoms,
molecules and crystals etc. At macroscopic level, it is a possible cause of friction
between different surfaces in relative motion.

Strong Nuclear Forces

It holds the atomic nuclei together by binding the

protons and neutrons in the nucleus over coming
repulsive electromagnetic force between positively
charged protons. It is also a short-range force with
the order of 10 ¹⁴m. If the distance between
−

nucleons increases beyond this range, this force

ceases to act. Fig. 3.6
The binding force of
protons and neutrons
Weak Nuclear Force in the nucleus

Weak nuclear force is responsible for the

Electron
disintegration of a nucleus. For example, the
weak nuclear force executes the β-decay (beta Proton Neutron

decay) of a neutron, in which a neutron Neutrino

transforms into a proton (Fig.3.7). In the process,
a β-particle (electron) and an uncharged particle
called antineutrino are emitted. In other words,
we can say that due to weak nuclear force
radioactive decay of atoms occurs. However, Fig. 3.7

weak nuclear force is stronger than the gravitational force but weaker than the
electromagnetic force. It is a short-range force of the order 10-17 m.

Unification of Weak Nuclear and Electromagnetic Forces

A Pakistani scientist Dr. Abdus Salam along with Sheldon Glashow and
Steven Weinberg were awarded in 1979 Nobel Prize in Physics for their
contributions to the unification of the weak nuclear force and electromagnetic
force as electroweak force. Although these two forces appear to be different in
everyday phenomena, but the theory models them as two different aspects of
the same force. Its effects are observed for the interactions taking place at very
high energy.

56
3.3 Forces in a Free- Body Diagram
External forces acting on an object may
include friction, gravity, normal force, drag, Applied force
tension in a string or a human force due to
pushing or pulling.
Suppose a book is pushed over the
surface of a table top as shown in Fig.3.8(a).
Then how can we represent the forces acting
on the body using free-body diagram?
Free-body diagrams are used to show Fig. 3.8 (a)
the relative magnitudes and directions of all
the forces acting on an object in a given
situation. In other words, a free-body diagram Normal force
is a special example of the vector diagrams.
Usually, the object is represented by a Friction Applied force
box and the force arrows are drawn outward
from the centre of the box in the directions of
forces as shown in Fig.3.8(b). The length of a
Weight
force arrow (line) reflects the magnitude of the
force and the arrow head indicates the Fig. 3.8 (b)
direction in which the force acts. Each force is
labelled to indicate the exact type of force.

3.4 Newton’s Laws of Motion

Do You Know?
Newton’s First Law of Motion
Sir Isaac Newton was born
It is our common observation that a force in Lincolnshire on January
is required to move or to stop a body. A book 4, 1643. The name of his
placed on a table remains there unless a force is famous book is “Principia
applied to move it (Fig.3.9). A ball rolling on floor Mathematica”.

should continue to move with the same velocity

in the absence of an applied force. But practically,
we see that it is not true. The ball stops after
covering some distance. In fact, an opposing
force (friction) causes the ball to stop. Newton
expressed such observations in his first law of
motion which states that:
57 Fig. 3.9
 A body continues its state of rest or of uniform motion in a
straight line unless acted upon by some external force.

When a fast-moving bus stops suddenly, the passengers tend to bend forward. It
is because they want to continue their motion. On the other hand, when the bus
starts moving quickly from rest, the passengers are pushed back against the seat.
This time, the tendency of passengers is to retain their state of rest.
According to first law of motion, a bus moving on the road should
continue its motion without any force exerted by the engine. But practically, we
see that if the engine stops working, the bus comes to rest after covering some
distance. It is because of the friction between the tyres of the bus and the road. All
the bodies moving on the Earth are stopped by the force of friction. If you were in
outer space and throw an object away where no force is acted upon it, the object
would continue to move forever with constant velocity.
The first law of motion also provides us another definition of force which is
stated as follows:

Force is an agency which changes or tends to change

the state of rest or of uniform motion of a body.

In simple words, we can say that force causes acceleration.

Inertia A Demonstration of
Property of Inertia
A net force is required to change the velocity of
objects. For instance, a net force may cause a
bicycle to pick up speed quickly. But when the same
force is applied to a truck, any change in the motion
may not be observed. We say that the truck has
more inertia than a bicycle. The mass of an object is
a measure of its inertia. The greater the mass of an
object, the greater is its inertia.

The property of a body to maintain its state of rest or

of uniform motion in a straight line is called inertia.
As a result of the role of inertia in Newton's
first law, this law is sometimes called as law of When the table cloth is pulled
inertia. abruptly, the objects remain in
their original position on the
table.
58
Newton’s Second Law of Motion
Newton's first law indicates that if no net force acts on an object, then the
velocity of the object remains unchanged. The second law deals with the
acceleration produced in a body when a net force acts upon it. Newton's second
law can be stated as:

If a net external force acts upon a body, it accelerates the body in the
direction of force. The magnitude of acceleration is directly proportional to
the magnitude of force and is inversely proportional to the mass of the body.

If a net force of magnitude F acts on a body of mass m and produces an

acceleration of magnitude a, then the second law can be written mathematically
as:
and a ∝ F
1
a ∝
m
So F
a ∝
m
F
or a = (constant)
m

According to SI units, if m = 1 kg, a = 1 m s-2, F = 1 N, then the value of the

constant will be 1. Therefore, the above equation can be written as:

a= 1× F
m
or F = m a .............................. (3.1)

First law of motion provides the definition of force, i.e., a force produces
an acceleration in a body. By the second law of motion (F = ma), we can calculate
mathematically, the amount of force required to produce a certain amount of
acceleration in a body of known mass. The SI unit of force is newton (N).

One newton is the force which produces an

acceleration of 1 m s ² in a body of mass 1 kg.
–

From Eq 3.1 1 N = 1 kg m s-2

59
 Effect of Force on Velocity
Newton’s second law also tells that a force can change the velocity of a
body by producing acceleration or deceleration in it. As velocity is a vector
quantity, so the change may be in its magnitude, direction or in both of them.

Newton’s Third Law of Motion

Whenever there is an interaction between two
bodies A and B, such that the body A exerts a force on
A
body B, the force is known as action of A on B. In
response to this action, the body B exerts a force on
the body A. This force is known as reaction of B on A.
For example, when we press a spring, the force exerted B
by our hand on the spring is action. Our hand also
experiences a force exerted by the spring. This is the
force of reaction (Fig.3.10). Newton expressed these
action and reaction forces in his third law of motion. It
is stated as: Fig. 3.10
For every action, there is always Do You Know?
an equal and opposite reaction.
R
Since, action and reaction do not act F
on the same body but they act on two
different bodies, so they can never balance
each other. Thus, Newton's third law can also
be expressed as follows:
I f one body exerts a force on a second body, In space, an astronaut throws a
the second body also exerts an equal and wrench, as a reaction he moves in
opposite force on the first body. opposite direction.

Forces Act in Pairs

We have study that forces act in pairs when two objects interact, i.e.,
action and reaction forces. We often notice a force that seems to make
something happen but usually we do not notice the other force involved. Here
are some examples of pairs of forces involved in accordance with Newton's third
law of motion.
60
(I) Consider a block lying on a table as shown in Fig. 3.11.
The force acting downward on the block is the weight. The block exerts a
downward force on the table equal to its weight w. The table also exerts a
reaction force Fn on the block. The two forces on the block balance each other
and the block remains at rest.
Fn

w
R F

w
Fig. 3.12
Fn
Fig. 3.11

(ii) When a bullet is fired from a gun, the bullet moves in the forward direction
with a force F. This is the force of action. The gun recoils in the backward direction
with a reaction force R (Fig. 3.12).

3.5 Limitations of Newton’s Laws of Motion

We have already explained that Newton's laws of motion can be applied
with very high degree of accuracy to the motion of objects and velocities which
we come across in everyday life.
The problems arise when we deal with the motion of elementary particles
having velocities close to that of light. For that purpose, relativistic mechanics
developed by Albert Einstein is applicable.
After all this discussion, we can say that Newton's laws of motion are not
exact for all types of motion, but provide a good approximation, unless an object
is small enough or moving close to the speed of light.
Mini Exercise
Look at the photographs below. Identify the pairs of forces acting in each
photograph.

Fig. 3.13 Fig. 3.14 Fig. 3.15

61
3.6 Mass and Weight
Commonly, we consider mass and weight as the same quantities but
scientifically, mass and weight are two different quantities. When we say that the
weight of this object is 5 kg, it is not true. In fact, 5 kg is the mass of the object. The
simplest definition of mass is that it is a measure of the quantity of matter in a
body. Scientifically, mass of a body can be defined as:

The characteristic of a body which determines the magnitude of acceleration

produced when a certain force acts upon it is known as mass of the body.

Mass is a scalar quantity. It remains the same everywhere. Practically, mass

is measured by an ordinary balance. The SI unit of mass is kilogram (kg).
Weight is a gravitational force acting on the object. It is a vector quantity
directed downward, towards the centre of the Earth.

The weight of an object is equal to the force with

which the Earth attracts the body towards its centre.

Gravitational Field

The gravitational field is a space around a mass in which another mass

experiences a force due to gravitational attraction. The gravitational field
strength is defined as the gravitational force acting on unit mass. Thus, mass m
on the surface of the Earth exerts a force known as its weight w given by w = m g,
where g is the gravitational field strength. Its value is 10 N kg-1.
As the value of g varies from place to place and also with altitude,
therefore, the value of weight does not remain the same everywhere.
It varies from place to place according to variation in g. Though an
object's weight may vary from one place to another, but at any particular
location, its weight is proportional to its mass. Thus, we can conveniently
compare the masses of two objects at a given location by comparing their
weights. The weight cannot be measured by an ordinary balance. A spring
balance can be used to measure the weight. The SI unit of weight is newton (N).
62
 Example 3.1
A 10 kg block moves on a frictionless horizontal surface with an
acceleration of 2 m s−². What is the force acting on the block?
Solution
Mass of a block = m = 10 kg
Acceleration = a = 2 m s−2
Force = F = ?
By Newton's second law of motion, F = ma
Putting the values, F = 10 kg × 2 m s = 20 kg m s−2 = 20 N
−2

Example 3.2
A force of 7500 N is applied to move a truck of mass 3000 kg. Find the
acceleration produced in the truck. How long will it take to accelerate the truck
from 36 km h–¹ to 72 km h–¹ speed?
Solution
Mass of truck = m = 3000 kg
Force applied = F = 7500 N
Acceleration = a =?
Initial speed = vi = 36 km h−1
36 × 1000 m
= = 10 m s−1
60 × 60 s
72 × 1000 m
Final speed = v f = 72 km h−1 = = 20 m s−1
60 × 60 s
Time = t = ?
By Newton’s second law, F = ma
F
or a =
m
7500 N
Putting the values, a = = 2.5 m s−2
3000 kg
Now, using first equation of motion,
v f = v + at
v – v
or t = f i

a
Putting the values, t = 20 m s−1 − 10 m s−1 = 4 s
2.5 m s−2
63
3.7 Mechanical and Electronic Balances
Balance scales are commonly used to compare masses of objects or to
weigh objects by balancing them with standard weights.

Mechanical Balances
A mechanical balance consists of a
rigid horizontal beam that oscillates on a
central knife edge as a fulcrum. It has two
end knife edges equidistant from the centre.
Two pans are hung from bearings on the end
knife edges (Fig.3.16). The material to be
weighed is put in one pan. Standard weights
Fig. 3.16
are put on the other pan. The deflection of
the balance may be indicated by a pointer
attaches to the beam. The weights on the
pan are adjusted to bring the beam in
equilibrium.
There is another type of mechanical
balances which are used to weigh heavy
items like flour bags, cement bags, steel
bars, etc. These are called mechanical
platform balances (Fig.3.17). Standard
weights are not required to use this balance.
Its reason is that the fulcrum of the beam of
such a balance is kept very near to its one
end. Therefore, much smaller weights have
to be put at the other end of beam to bring it
to equilibrium. These smaller weights have
already been calibrated to the standard
weights. Fig. 3.17
Electronic Balances
No standard weights are required to
use in an electronic balance (Fig.3.18). Only
it has to be connected to a power supply.
There are some models which can operate
by using dry cell batteries. An electronic
balance is more precise than mechanical
balance. When an object is placed on it, its
mass is displayed on its screen. Now-a-days,
Fig. 3.18
64
electronic balances also display the total price of the material if the rate per kg is
fed to the balance.
Force Meter
A force meter is a scientific instrument that measures
force. It is also called as a newton meter or a spring balance
(Fig.3.19). Now a days digital force meters are also available.
You have already learnt about mechanical and electronic
balances. They measure mass of the objects in kilograms or its
multiples. On the other hand, force meter measures force
directly in newtons (N).
An ordinary force meter has a spring inside it. Upper
end of the spring is attached to a handle. A hook is attached to
the lower end the spring that holds the object. A pointer is also
attached to the spring at its upper end. A scale in newtons is
provided along the spring such that the pointer coincides with
zero of the scale when nothing is hung with the hook.
The object to be weighed is hung
with the hook. The mass of the object Fig. 3.19

causes the spring to compress. The

pointer indicates the weight of the
object. However, some force meters are
also based on the stretching of the
spring when a load is hung. In this case,
Do You Know?
the pointer is attached at the lower end
of the spring.
In some spring balances, the
scale measures the mass which can be
readily converted into newtons by The weight
of 100 g
multiplying the mass in kg with the value
mass is 1 N.
of g = 10 m s-2.
A digital force meter measures
directly the weight of the object in
Fig. 3.20
newtons (Fig. 3.20).

65
3.8 Friction
When a cricket ball is hit by the bat, it moves on the ground with a
reasonably large velocity. According to Newton's first law of motion, it should
continue to move with constant velocity. But, practically, we observe that it
eventually stops after covering some distance. Does any force act on the ball in
opposite direction that stops the ball? Yes, it is the force of friction between the
ball and the ground that opposes the motion of the ball.

Dissipative Effect of Friction

Friction is a dissipative force due to which the energy is wasted in doing
work to overcome against friction. The lost energy appears in the form of heat.
A very common example of energy dissipation is
the rubbing of hands (Fig.3.21). When we rub our hands,
heat is produced due to friction and our hands become
warm. Similarly, the temperature of machines rises due
to friction between its moving parts that can cause many
problems. The tyres of vehicles also wear out after
becoming too hot due to friction between tyres and
Fig. 3.21 Rubbing hands
road.
Shooting of stars seen in the sky at night also happen due to friction of air.
These are actually asteroids that enter the Earth's atmosphere. As they are
moving, air resistance causes generation of heat. Their temperature becomes so
high that they start burning and ultimately disintegrate.
Do You Know?
On a wet road, the water does not form
wet layer between the tyre surface and the road
surface due to the spaces in the tread pattern on
the tyre. This reduces the chances of skidding of
vechicles on wet roads.

Sliding Friction
The friction between two solid surfaces is called sliding friction which can
be divided into two categories.
1. Static friction 2. Kinetic friction

66
Static Friction Fn
Let us consider the motion of a block Fs F=T
on a horizontal surface. The arrangement is
shown in Fig. 3.22. When a weight is put in
the pan, a force F = T equal to the sum of this mg
weight and weight of the pan acts on the
block. This force tends to pull the block. At Fig. 3.22
the same time an opposing force appears For Your Information!
that does not let the block move. This Some frogs can cling
opposing force is the static friction FS. to a vertical surface,
such as this leaf,
Kinetic Friction because of the static
If we go on adding more weights in f r i ction between
the pan one by one in small steps, a stage will their feet and the
come when the block starts sliding on the surface.

horizontal surface. This is the limit of static friction that is equal to the total
weights including pan. When the block is sliding, friction still exists. It is known as
kinetic friction.
Do You Know?
When a shuttle re-enters the Earth’s atmosphere, the friction caused by the
atmosphere raises the surface temperature of the shuttle to over 950°C.

Terminal Velocity
When an object falls freely, it is accelerated by an amount g = 10 m s−2. But
practically the acceleration may be different. Air resistance plays an important
role in determining how fast an object accelerates when it falls.
If we drop a cricket ball and a piece of Styrofoam of the same weight from
a certain height, they will hit the ground at the same time only if there were no air
resistance. Both would fall with the same acceleration
g = 10 m s−2. Practically, the ball in air, would drop faster.
The Styrofoam having larger surface would face greater
opposing force of the air and thus moves slowly.
Experiments have been made in this respect and
it was found that the faster an object falls the more air
resistance will be exerted on it. A speed is finally attained
at which the upward force of air resistance balances the
downward force of gravity. When this happens, the Fig. 3.23
object stops accelerating. It keeps falling at a constant A paratrooper falling with
terminal velocity
67
velocity. This constant velocity achieved by an object is called its terminal
velocity. Even a heavy object like a meteorite does not gain an infinite velocity as
it falls to the Earth.
This principle applies to paratroopers. Air resistance acting against the
large surface area of a parachute allows for descent at a safer velocity (Fig.3.23).
Do You Know?

Friction in human joints is very low because

our bodies contain a natural lubricating
system. Consequently, though our bones Bones Lubricating
rub against each other at the points as we Fluid
move, yet bones do not normally wear out,
even after many years of use. Knee joint

Rolling Friction
The static and kinetic friction which we have studied so far is the sliding
friction. There is another type of friction which is called rolling friction. When an
object rolls over a surface, the friction produced is called rolling friction. The idea
o f r o l l i n g f r i c t i o n i s For Your Information!
a s s o c i a t e d w i t h t h e Practically, the contact point is
concept of wheel. In our not perfectly circular; it becomes
everyday life, we observe flat under pressure as shown in
that a body with wheels figure. This flat portion of the
faces l ess f r i ct ion as wheel has the tendency to slide
compared to a body of the against the surface and does
same size without wheels. produce a frictional force.
Ball bearings also play the same role as is played by the wheels. Many machines
in industry are designed with ball bearings so that the moving parts roll on the
ball bearing and friction is greatly reduced. The rolling friction is about one
hundred times smaller than the sliding friction.
The reason for the For Your Information!
rolling friction to be less A hovercraft is a kind of ship
than the sliding friction is that can move over the
that there is no relative surface of water and ground
motion between the b o t h . A i r i s e j e c t e d
wheel and the surface underneath by powerful
over which it rolls. The fans forming a cushion of
w h e e l t o u c h e s t h e air. The hovercraft moves
surface only at a point. It over the cushion of air which
does not slide. offers very small resistance.

68
Methods to Reduce Friction
The following methods are used to reduce friction:
(i) The parts which slide against each other are highly polished.
(ii) Since, the friction of liquids is less than that of solid
surfaces, therefore, oil or grease is applied between
the moving parts of the machinery.
(iii) As rolling friction is much less than the sliding
friction, so sliding friction is converted into rolling Fig. 3.24
friction by the use of ball bearings (Fig. 3.24) in the machines and wheels
under the heavy objects.
(iv) Frictional force does not act only among solids, high speed vehicles,
aeroplanes and ships also face friction
while moving through air or water. If the
front of a vehicle is flat, it faces more
resistance by air or water. Therefore, the
bodies moving through air or water are
streamlined to minimize air or water
friction. In this case, the air passes Fig. 3.25 Streamline air flow over
smoothly over the slanting surface of a speedy car
vehicle. This type of flow of air is known as streamline flow. A streamline
flow over the car is shown in Fig. 3.25. The vehicles designed pointed from
the front are said to be streamlined.
3.9 Momentum and Impulse
Suppose that a bicycle rider and a heavy truck are moving with the same
speed, which one can be stopped easily, depends on the quantity of motion of
the moving body. It is our common observation that quantity of motion in a
moving body depends on its mass and velocity. Greater is the mass, the greater
will be the quantity of motion. Similarly, greater is the velocity, the greater will be
quantity of motion. This quantity of motion is called momentum and denoted by
p. It is defined as:
The momentum of a moving body is the product of its mass and velocity.
Therefore, p = m × v............................. (3.2)
Like velocity momentum is also a vector quantity. The SI unit momentum is
(kg m s–1). It can also be written as (N s).

69
 When a ball is hit by a bat, the force is exerted on the ball for a very short
interval of time. In such cases, it is very difficult to calculate the exact magnitude
of the force. However, initial velocity vi of the ball and final velocity vf after
collision can be found easily.
During a time interval ∆ t, the average acceleration a is given by
∆v v − vi
a = = f (3.3)
∆t ∆

According to Newton's second law of motion, the value of average force

acting during the interval ∆ t will be:
∆v
F = ma = m( )
∆t
or F × ∆ t = m(∆v) = m (vf − vi) (3.4)
Equation (3.4) shows that F and ∆ t cannot be exactly known but their
product which is equal to the change of momentum (mvf – mvi) can be
calculated. For such cases, the product F × ∆ t is called as Impulse of the force.

When a large force F acts on an object for a short interval of time, the impulse
of the force is defined as the total change in momentum of the object.

Dividing both sides of Eq.3.4 by ∆t, we have

m(∆v)
F = ...................................... (3.5)
∆t
where m(∆v) is the change in momentum ∆p. Equation (3.5) gives the value of
force in terms of momentum i.e., force acting on an object is equal to the change
in momentum of the object per unit time.
∆p
F = . ............ (3.6)
∆t
Equation (3.6) suggests to define Newton’s second law of motion in terms of
momentum i.e.,
The rate of change of momentum of a
body is equal to the force acting on it.

The direction of change in momentum is that of the force.

70
 Do you know? For Your Information!
A cricketer draws his The arrow penetrates into the apple,
hands back to and in response, the momentum of
reduce the impact the apple changes. Conversely, the
of the ball by apple applies an opposing
increasing the time. force to the arrow, and in
response, the momentum of the arrow changes.

Packing of Fragile Objects

Fragile objects such as glassware may break easily due to
jerks or by the direct impact with hard objects during
their transportation.
To protect them soft, packing materials are used for
these objects. These materials reduce the effect of quick
change in momentum. Consequently, the force acting on the fragile objects
is greatly reduced. Special materials like Styrofoam, corrugated cardboard
sheets, bubble wrap are used for the packing of such objects.
Crumple Zones

A crumple zone of an Crumple zone

Air bag Seatbelts

automobile is a structural
feature designed to compress
during an accident to absorb
deformation energy from the
impact. Typically, crumple
zones are located in front and
behind of the main body of
the vehicle.
Crumple zones work by managing crash energy absorbing within the outer
parts of the vehicle, rather than being directly transmitted to the occupants.
This is achieved by controlled weakling of outer parts (plastic bumpers, etc.)
of the vehicle, while strengthening of the passenger cabin.

Example 3.3
A bullet of mass 15 g is fired by a gun. If the velocity of the bullet is 150 m s–¹,
what is its momentum?
Solution
Mass of bullet = m = 15 g = 0.015 kg
71
Velocity of bullet = v = 150 m s−1
Momentum = p = ?
Using the formula, p = mv
Putting the value, p = 0.015 kg × 150 m s−¹
or p = 2.25 kg m s ¹
−

Example 3.4
A cricket ball of mass 160 g is hit by a bat. The ball leaves the bat with a
velocity of 52 m s–¹. If the ball strikes the bat with a velocity of -28 m s–¹ (opposite
direction) before hitting, find the average force exerted on the ball by the bat.
The ball remains in contact with the bat for 4 × 10–³ s.
Solution
Mass of ball m = 160 g = 0.16 kg
Initial velocity vi = −28 m s ¹
−

Final velocity vf = 52 m s−¹

Time of contact t = 4 ×10−³ s
Average force F=?
From Eq. (3.6), we have
m(vf − vi)
F =
t
Putting the values, 0.16 kg [52 m s−¹ − (−28 m s−¹)]
F=
4 × 10−³ s
or F = 3200 N

3.10 Principle of Conservation of Momentum

v₁ v₂
The collection of objects is known as a ‘system’. If no
external force acts on any object of the system, it is
known as isolated system. Consider a system of two m₁ m₂

balls of masses m₁ and m₂. Suppose that the balls F -F

are moving with velocities v1 and v2 along a straight

m₁ m₂
line in the same direction. If v1 > v2 , the balls will v₁ v₂
collide as shown in Fig. 3.26. If their velocities
become v₁ , and v ₂ respectively after collision, then
Total momentum of the system before collision = m₁v₁ + m₂v₂ Fig. 3.26

Total momentum of the system after collision = m₁v₁ + m₂v₂

The principle of conservation of momentum states that:
72
 If no external force acts on an isolated system, the final total momentum
of the system is equal to the initial total momentum of the system.
This means, that:
Total momentum of the Total momentum of the
=
system before collision system after collision
or m₁v₁ + m₂v₂ = m₁v ₁ + m₂v ₂
To explain this principle, let us consider the collision of two identical balls
in which the second ball is at rest.
v₁ v₂ = 0
When there is collision of two balls, there is
a transfer of momentum from one ball to another. F −F

The ball at rest gains momentum and starts

moving whereas the striking ball slows down. If v₁ = ₀
v₂ = v₁
the balls are identical, we will observe that there is
a total transfer of momentum. The striking ball Fig. 3.27

comes to rest and the other ball starts moving with the same speed (Fig.3. 27). It
means that second ball gains momentum equal to that lost by the first one. If the
first ball stops after collision, the second ball moves with the momentum of the
first ball. This suggests that the total momentum of the two balls after collision
remains the same as total momentum before collision.
The principle of conservation Seatbelts
of momentum is applicable When a moving car stops suddenly,
not only to macro-objects the passengers move forward
but also for micro-objects toward the windshield. Seatbelts
prevent the passengers from
like atoms and molecules. moving. Thus, chances of hitting the
passengers against the windshield
or steering wheel are reduced.
Example 3.5
A bullet of mass m 1 is fired by a gun of mass m₂. Find the velocity of the
gun in terms of velocity of bullet v₁ just after firing.

Solution
Before firing, the velocity of bullet as well as that of gun was zero.
Therefore, total momentum of bullet and gun was also zero. After firing, the
bullet moves forward with velocity v₁ whereas the gun moves with velocity v₂.
73
According to law of conservation of momentum,
Total momentum before firing = Total momentum after firing
Putting the values, 0 = m₁v₁ + m₂v₂
m₂v₂ = − m₁v₁
or
−m₁v₁
v₂ =
m₂
The negative sign in this equation, indicates that the gun moves
backward, i.e. opposite to the bullet. It is because of the backward motion of the
gun that the shooter gets a jerk on his shoulder.

Example 3.6
A ball of mass 3 kg moving with a velocity of 5 ms−1 collides with a
stationary ball of mass 2 kg and then both of them move together. If the friction is
negligible, find out the velocity with which both the balls will move after collision.

Solution
Mass of first ball = m1 = 3 kg
Velocity of first ball before collision = v 1= 5 m s−l
Mass of second ball = m2 = 2 kg
Velocity of second ball before collision = v2 = 0
Velocity of both the balls after collision = v = ?
Total mass of balls after collision = m1 + m
By law of conversion of momentum,
Total momentum before collision = Total momentum after collision
or m₁ v₁ + m2 v2 = (m₁ + m ) v
Putting the values,
3 kg × 5 m s−l + 0 = (3 kg + 2 kg) v
15 kg m s−l = 5 kg × v
v = 3 m s−l

74
 KEY POINTS
 A force is a push or a pull that starts, stops and changes the magnitude and direction
of velocity of a body.
 A contact force is a force that acts at the point of contact between two objects.
 Non-contact force is a force between two objects which are not in physical contact.
 Gravitational force, electromagnetic force, strong nuclear force and weak nuclear
force are the four fundamental forces in nature.
 Every object in the universe attracts every other object with a force that is directly
proportional to the product of their masses and inversely proportional to the square
of the distance between them. This is known as Newton’s law of gravitation.
 Newton's first law of motion states that a body continues its state of rest or of uniform
motion with the same constant velocity, unless acted upon by some net external
force.
 The property of a body to maintain its state of rest or of uniform motion is called
inertia.
 The second law of motion states that when a net force acts upon a body, it produces
an acceleration in the direction of force and the magnitude of acceleration is directly
proportional to the force and is inversely proportional to the mass.
 The third law of motion states that to every action there is an equal but opposite
reaction.
 Action and reaction do not act on the same body but act on two different bodies.
 Mass of a body is the quantity of matter in it. It determines the magnitude of
acceleration produced when a force acts on it. Mass of a body does not vary. It is a
scalar quantity and its unit is kilogram (kg).
 The weight of an object is equal to the force with which the Earth attracts a body
towards its centre.
 Force meter is a scientific instrument that measures force in newtons (N).
 Friction is the force that tends to prevent the bodies from sliding over each other.
 The resisting force between the two surfaces before the motion starts is called the
static friction. The maximum value of the static friction is called a limiting friction.
 The friction during motion is called kinetic friction.
 When a body moves with the help of wheels, the friction in this case is known as
rolling friction. Rolling friction is much less as compared to the sliding friction.
 Energy is wasted in doing work against friction that appears in the form of heat.
 When upward air resistance balances the downward force of gravity on a falling
object, it falls down with constant (safe) velocity, it is called terminal velocity.
 The product of mass and velocity of a moving body is called momentum.
 The principle of conservation of momentum states that if no external force acts on an
isolated system, the final total momentum of the system is equal to the initial total
momentum of the system.
 Impulse is defined as the product of F × Δ t = m × ΔV = total change in momentum.

75
 EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
3.1. When we kick a stone, we get hurt. This is due to:
(a) inertia (b) velocity (c) momentum (d) reaction
3.2. An object will continue its motion with constant acceleration until:
(a) the resultant force on it begins to decrease.
(b) the resultant force on it is zero.
(c) the resultant force on it begins to increase.
(d) the resultant force is at right angle to its tangential velocity.
3.3. Which of the following is a non-contact force?
(a) Friction (b) Air resistance
(c) Electrostatic force (d) Tension in the string
3.4. A ball with initial momentum p hits a solid wall and bounces back with the
same velocity. Its momentum p after collision will be:
/

(a) p = p (b) p = – p (c) p = 2 p (d) p = –2 p

/ / /

3.5. A particle of mass m moving with a velocity v collides with another particle
of the same mass at rest. The velocity of the first particle after collision is:
(a) v (b) –v (c) 0 (d) –1/2
3.6. Conservation of linear momentum is equivalent to:
(a) Newton's first law of motion (b) Newton's second law of motion
(c) Newton's third law of motion (d) None of these
3.7. An object with a mass of 5 kg moves at constant velocity of 10 m s−¹. A
constant force then acts for 5 seconds on the object and gives it a velocity
of 2 m s–¹ in the opposite direction. The force acting on the object is:
(a) 5 N (b) –10 N (c) –12 N (d) –15 N
3.8. A large force acts on an object for a very short interval of time. In this case,
it is easy to determine:
(a) magnitude of force (b) time interval
(c) product of force and time (d) none of these
3.9. A lubricant is usually introduced between two surfaces to decrease
friction. The lubricant:
(a) decreases temperature (b) acts as ball bearings
(c) prevents direct contact of the surfaces (d) provides rolling friction

76
 B Short Answer Questions
3.1. What kind of changes in motion may be produced by a force?
3.2. Give 5 examples of contact forces.
3.3. An object moves with constant velocity in free space. How long will the
object continue to move with this velocity?
3.4. Define impulse of force.
3.5. Why has not Newton's first law been proved on the Earth?
3.6. When sitting in a car which suddenly accelerates from rest, you are pushed
back into the seat, why?
3.7. The force expressed in Newton's second law is a net force. Why is it so?
3.8. How can you show that rolling friction is lesser than the sliding friction?
3.9. Define terminal velocity of an object.
3.10. An astronaut walking in space wants to return to his spaceship by firing a
hand rocket. In what direction does he fire the rocket?

C Constructed Response Questions

3.1 Two ice skaters weighing 60kg and 80 kg push off against each other on a
frictionless ice track. The 60 kg skater gains a velocity of 4 m s−¹. Considering
all the relevant calculations involved, explain how Newton's third law
applies to this situation.
3.2 Inflatable air bags are installed in the vehicles as safety equipment. In terms
of momentum, what is the advantage of air bags over seatbelts?
3.3 A horse refuses to pull a cart. The horse argues, “according to Newton’s
third law, whatever force I exert on the cart, the cart will exert an equal and
opposite force on me. Since the net force will be zero, therefore, I have no
chance of accelerating (pulling) the cart.” What is wrong with this
reasoning?
3.4. When a cricket ball hits high, a fielder tries to catch it. While holding the ball
he/she draws hands backward. Why?
3.5. When someone jumps from a small boat onto the river bank, why does the
jumper often fall into the water? Explain.
3.6. Imagine that if friction vanishes suddenly from everything, then what could
be the scenario of daily life activities?

77
D Comprehensive Questions
3.1. Explain the concept of force by practical examples.
3.2. Describe Newton's laws of motion.
3.3. Define momentum and express Newton's 2nd law of motion in terms of
change in momentum.
3.4. State and explain the principle of conservation of momentum.
3.5. Describe the motion of a block on a table taking into account the friction
between the two surfaces. What is the static friction and kinetic friction?
3.6. Explain the effect of friction on the motion of vehicles in context of tyre
surface and braking force.

E Numerical Problems
3.1. A 10 kg block is placed on a smooth horizontal surface. A horizontal force of
5 N is applied to the block. Find:
(a) the acceleration produced in the block.
(b) the velocity of block after 5 seconds. (0.5 m s−², 2.5 m s−¹)
3.2. The mass of a person is 80 kg. What will be his weight on the Earth? What
will be his weight on the Moon? The value of acceleration due to gravity of
Moon is 1.6 m s . (800 N, 128 N)
−2

3.3. What force is required to increase the velocity of 800 kg car from 10 m s−¹ to
30 m s−¹ in 10 seconds? (1600 N)
3.4. A 5 g bullet is fired by a gun. The bullet moves with a velocity of 300 m s−¹. If
the mass of the gun is 10 kg, find the recoil speed of the gun. (−0.15 m s−¹)
3.5. An astronaut weighs 70 kg. He throws a wrench of mass 300 g at a speed of
3.5 m s . Determine:
−1

(a) the speed of astronaut as he recoils away from the wrench.

(b) the distance covered by the astronaut in 30 minutes.
(–1.5 × 10−² m s−1, 27 m)
3.6. A 6.5 × 103 kg bogie of a goods train is moving with a velocity of 0.8 m s−1.
Another bogie of mass 9.2×103 kg coming from behind with a velocity of
1.2 m s collides with the first one and couples to it. Find the common
−1

velocity of the two bogies after they become coupled. (1.03 m s−1)
3.7. A cyclist weighing 55 kg rides a bicycle of mass 5 kg. He starts from rest and
applies a force of 90 N for 8 seconds. Then he continues at a constant speed
for another 8 seconds. Calculate the total distance travelled by the cyclist.
(144 m)
78
3.8. A ball of mass 0.4 kg is dropped on the floor from a height of 1.8 m. The ball
rebounds straight upward to a height of 0.8 m. What is the magnitude and
direction of the impulse applied to the ball by the floor?
(4 N s, upward)
3.9. Two balls of masses 0.2 kg and 0.4 kg are moving towards each other with
velocities 20 m s−1 and 5 m s−1 respectively. After collision, the velocity of
0.2 kg ball becomes 6 m s . What will be the velocity of 0.4 kg ball?
−1

(2 m s−1)

79
 Chapter 4
Turning Effects of Force
Student Learning Outcomes

After completing this chapter, students will be able to:

• [SLO: P -09 - B -44] Differentiate between like and unlike parallel forces.
• [SLO: P -09 - B -45] Analyse problems involving turning effects of forces [Student
should know that moment of a force = force × perpendicular distance from the pivot
and be able to use this in simple problems and give examples and applications of
turning effects in real life]
• [SLO: P -09 - B - 46] State what is meant by centre of mass and centre of gravity.
• [SLO: P -09 - B - 47] Describe how to determine the position of the centre of gravity
of a plane lamina using a plumb line
• [SLO: P -09 - B - 35] Describe and identify states of equilibrium. [This includes the
types, conditions and states of equilibrium and identifying their examples from daily
life.]
• [SLO: P -09 - B - 48] Analyse, qualitatively, the effect of the position of the centre of
gravity on the stability of simple objects
• [SLO: P-09-B-49] Propose how the stability of an object can be improved [by
lowering the centre of mass and increasing the base area of the object]
• [SLO: P-09-B-50] Illustrate the applications of stability physics in real life [Such as this
concept is central to engineering technology such as balancing toys and racing cars
• [SLO: P-09-B-51] Predict qualitatively the motion of rotating bodies [Describe
qualitatively that, analogous to Newton's 1st law for transnational motion (, an object
that is rotating will continue to do so at the same rate unless acted upon by a resultant
moment (in which case it would begin to accelerate or decelerate its rotational
motion)]
• [SLO: P-09-B-52] Describe qualitatively motion in a circular path due to a centripetal
force. (Use of the formula F = mv )
2

c r
• [SLO: P-09-B-53] Identify the sources of centripetal force in real life examples [e.g.,
tension in a string for a stone being swirled around, gravity for the Moon orbiting the
Earth]

As we know, a force is a vector quantity, so it acts in a particular direction.

We observe various effects of forces. Some forces produce acceleration or
decelerating in a body, some tend to turn it around a point and some forces
balance each other acting in opposite directions.
All those forces which act parallel to one another are known as parallel
forces. The points of application of such forces may be different.
80
 4.1 Like and Unlike Parallel Forces
If the parallel forces are acting in the same
direction, then they are called like parallel forces and F1 FF22
if their directions are opposite to one another, they
are called unlike parallel forces. Three forces F1, F2
and F3 are shown in Fig. 4.1 acting on a rigid body at
different points. Here, the forces F1 and F2 are like F3
parallel forces but F2 and F3 are unlike parallel forces. Fig. 4.1
4.2 Addition of Forces
In chapter 2, we have learnt about vectors and their representation.
Remember that the resultant is the same for any order of addition of vectors. As
forces are vectors, so forces can also be added by head-to-tail rule.
To determine the resultant of two or more forces acting in a plane, the
following example will explain its method.
Example 4.1
Let us add three force vectors F1, F2 and F3 having magnitudes of 200 N,
300 N and 250 N acting at angles of 30O, 45O, 60O with x-axis. By selecting a
suitable scale 100 N = 1 cm, we can draw
the force vectors as shown in Fig. 4.2(a). F₃
To add these vectors, we apply
y
head-to-tail rule as shown in Fig. 4.2(b). O
60

F₂

F₂
F₃
45O
60
O

45O F₁ F₁
43O
30
O
30O
x x x x
O O
Fig. 4.2 (a) y Fig. 4.2 (b)
y

Measured length of resultant force is 7.1 cm. According to selected scale, magnitude
of the resultant force F is 710 N and direction is at an angle 43O with x-axis.

81
 4.3 Turning Effect of a Force
We have learnt so far that a net force affects the liner motion of an object
by causing it to accelerate. Since rigid objects can also rotate, so we need to
extend our concept to the turning effect of a force. When we open or close a
door, we apply force. This force rotates the door about its hinge. This is called
turning effect of force. Similarly, we use turning effect of force when we open or
close a water tap. Let us define some terms used in the study of turning effect of a
force.
If the distance between two points of the body remains the same under
the action of a force, it is called a rigid body. Axis of rotation
z
During rotation, all the particles of the rigid body A Rigid
rotate along fixed circles as shown in Fig. 4.3. The straight B body
line joining the centres of these circles is called the axis of
y
rotation. In this case, it is OZ. To observe the turning effect o
x Fig. 4.3
of a force, let us perform an activity.
Activity 4.1
Take your class to play ground where Pivot
a see-saw is available. Let a lighter child sits
on the left side and the heavier one on the Moment arm Moment arm
right side of the see-saw. The distances of
both the children from the pivot should be equal. The force exerted by each child is equal to his
weight acting downward. Does the heavier child move down? Yes, because he is exerting
larger force. Now move the heavier child nearer to the pivot and the lighter child away from
the pivot as shown in the figure. Ask the students what do they observe?

You will see that the see-saw tilts to the opposite direction and the lighter
child moves down. This shows that the turning effect of a force does not depend
only on its magnitude but also on the location where it acts. Therefore, we can
say that the greater the force, the greater is its turning effect. Moreover, the
larger the perpendicular distance of the force from the axis of rotation, the
greater is its turning effect.
The line along which the force acts is
called the line of action of the force.
The perpendicular distance of the line of action of a force from the axis
of rotation is known as moment arm of the force or simply moment arm.

The moment arms of both the children are shown in the figure of
activity 4.1. There are many other examples to observe the turning or rotational
effect of a force. It is harder to open a door by pushing it at a point closer to the
82
hinge as compared to push it at the handle (Fig. 4.4). That is why, door or window
handles are always installed at larger distances from hinges to
produce larger moment of force by applying less force. This makes
the doors be opened or closed more easier. Similarly, it requires
greater force to open a nut by a spanner if you hold it closer such as
point A than point B (Fig. 4.5). F
F’
A B
Nut
Fig. 4.4
Fig. 4.5
Moment of Force
F
The turning effect of a force is measured by a
quantity known as moment of force or torque. O r=ℓ P
axis
Moment of a force or torque is defined as the
product of the force and the moment arm. Fig. 4.6

The magnitude of torque is given by Do You Know?

Momentof force is
τ = F×..................(4.1) applicable in the working
Where τ (tau) is the torque and is of bottle opener. A small
the moment arm. In Fig. 4.6, the line of force applied at longer
moment arm produces
action of a force F is perpendicular to r, more torque while
therefore, moment arm = r. Remember opening a bottle.
that the torque of a force is zero when the line of action of a force passes through
the axis of rotation, because its moment arm becomes zero. The torque is
positive if the force tends to produce an anticlockwise rotation about the axis,
and it is taken as negative if the force tends to produce a clockwise rotation. The
SI unit of torque is newton metre (N m).
In many cases, the line joining the axis of rotation and point P where the
force F acts, is not perpendicular to the force F. Therefore, OP will not be the
moment arm for F. In such cases, we have to find a component of force F
perpendiculars to OP = (Fig. 4.7), or we can find r the component of that is
perpendicular to the (line of action) force F (Fig. 4.8).
F sinθ
F F

O O ℓ
ℓ θ θ
θ
P P

Fig. 4.7 Fig. 4.8

83
For this, we need to know the method of finding rectangular components of a
force or any vector. This is also called as resolution of Forces.
Couple
A couple is a special type of torque. We observe at many situations in our
daily life, when two equal and opposite parallel forces produce torque. For
example, while opening or closing a water tap,
F2
turning key in the lock, opening the lid of a jar and
A r1 O r2
turning steering wheel of a motor car, we apply a B
F1
pair of equal forces in opposite directions. The
torque produced in this way in known as couple. Fig. 4.9

When two equal and opposite parallel forces act at two

different points of the same body, they form a couple.
Steering wheel of vehicles
While turning a vehicle, a couple is applied on the steering
wheel. It is interesting to know that now-a-days, steering
wheels of smaller diameter are installed in vehicles. The reason
is that, most of the fvehicles are provided with power steering
in which a pump pushes hydraulic fluid to reduce the force
needed to turn the wheels, resulting in effortless steering.

Example 4.2
A spanner 25 cm long is used to open a nut. If a force of 400 N is applied at
the end of a spanner shown in Fig. 4.10, what is the torque acting on the nut?
Solution
Length of Spanner = 25 cm = 0.25 m F
Force = F = 400 N
Torque τ=? Fig. 4.10
From Eq. (4.1), τ=F×
Putting the values, τ = 400 N × 0.25 m =100 N m

4.4 Resolution of Vectors

By head-to-tail rule, two or more vectors can be added to give a resultant
vector. Its reverse process is also possible, i.e., a given vector can be divided into
two or more parts. These parts are called as components of the given vector. If
these components are added up, their resultant is equal to the given vector. To
divide a force into its components is known as resolution of a force.
84
 Usually, a force is resolved into two Beam of light
components which are perpendicular to
each other. These are called its perpendicular
or rectangular components of the force. y
C
Let us resolve a force F into its B
perpendicular components. A force F acting
on a body at an angle θ with x-axis is shown in F
Fy
Fig. 4.11(a). Imagine a beam of light is placed
above the vector F. As the light falls
perpendicularly to the x-axis, it will cast a
ᶿ x
O Fx A
shadow OA of vector F onto x-axis. We call y Fig. 4.11(a)
this shadow as x-component of vector F. In C
the same way, if light is thrown perpendicular B

to y-axis, the shadow OB of vector F on y-axis

is the y-component of F. F Fy

A component of a vector is its

O
ᶿ Fx
x
effective value in a given direction. A
Fig. 4.11(b)

The x and y components can be practically drawn simply by dropping

perpendiculars from the tip of vector F onto x and y-axes respectively. The
x-component of force F is denoted as Fx and y-component as Fy.
From Fig. 4.11(b), it is evident that F is the resultant vector of components
Fx and Fy. Moreover, Fx and Fy are perpendicular to each other. Therefore, Fx and Fy
are called perpendicular components of vector F.
The magnitudes of the perpendicular components can be found from the
right angled triangle OAC in Fig. 4.11(b). Do You Know?

OA
= cosθ
OC
Fx
Putting the values, = cos θ
F
or Fx = F cosθ …… (4.2)
AC
Similarly, = sinθ
OC
Fy A tight rope walker balances himself
= sinθ
F by holding a bamboo stick. This is an
application of principle of moments.
or Fy = F sinθ … …. (4.3)
85
 For Your Information!
C
Trigonometric Ratios
Trigonometric is a branch of mathematics that

Perpendicular
deals with the properties of a right angled triangle. A right
angled triangle ABC is shown in the figure. Angle A is
denoted by θ (theta) called the angle of the right angled
θ
triangle. The side AB is called the base, the side BC is called A Base B
the perpendicular and the side AC is called as hypotenuse. θ sinθ cosθ tanθ
The ratio of any two sides is given the names as below:
0° 0 1.0 0
Perpendicular BC 1 1
= = sine θ 3
Hypotenuse AC 30° 2 2 3
= 0.5 = 0.866 = 0.577
Base AB
= = cosine θ 1 1
Hypotenuse AC 45° 2 2 1.0
Perpendicular BC = 0.707 = 0.707
= = tangent θ 3 1
Base AB 2 3
60° 2
= 0.866
For simplicity, sine θ, cosine θ and tangent θ are = 0.866 = 0.5
written as sin θ, cos θ and tan θ respectively. Values of ∞
90° 1.0 0
these ratios for some frequently used angles are given in Unlimited
the table.

4.5 Determination of a Force from its

Prependicular Components
The magnitude and direction of a force can be found if its perpendicular
components are known. Applying Pythagorean theorem to the right angled
triangle OAC (Fig. 4.11-b).
(OC) = (OA) + (AC)
2 2 2

or F = Fx + Fy
2 2 2

F = F x2 + F y2 .......(4.4)

Hence, using Eq. (4.4) the magnitude F of the required vector F can be
determined. The direction of F is given by
Fy
tan θ =
...............
(4.5)
Fx
or Fy
θ = tan-1( )
Fx
By using table of trigonometric ratios or calculator, the value of θ can be
determined.
86
Example 4.3
A force of 160 N is acting on a wooden box at an angle of 60° with the
horizontal direction. Determine the values of its x and y components.
Solution
y
Magnitude of force F = 160 N
Angle θ = 60°
Using calculator, sin θ = sin 60° = 0.866 F
F sinθ
cos θ = cos 60° = 0.5
x-component is given by Eq. (4.2)
Fx = F cos θ 60°
x
Putting the values, Fx = 160 N × 0.5 = 80 N O F cosθ

y-component is given by Eq. (4.3) Fig. 4.12

Fy = F sin θ
Putting the values, Fy = 160N × 0.866 = 138.6 N

4.6 Principle of Moments

To understand the principle of moments, let us perform an activity.
Activity 4.2
Balance a metre rule on a wedge at its centre of gravity such that the rule stays
horizontal. Suspend two weights w 1 and w 2 on one side of the metre rule at distance and
2
from the centre and a third weight w 3 on the other side at distance until the rule is again
balanced.
1 3

CG
w1 w2 3

The weights w1 and w2 tend to rotate the rod anticlockwise about CG and the
weight w3 tends to rotate it clockwise. The values of the moments of the weights are
w1 × 1 , w × 2 and w × 3. When the metre rule is balanced, then
Total anticlockwise moments = Total clockwise moments

w1 × 1 + w2 2 = w3 × 3 … .......................... (4.6)
This is known as principle of moments, which is stated as:

When a body is in balanced position, the sum of clockwise moments about

any point equals the sum of anticlockwise moments about that point.

87
 Example 4.4
A metre stick is pinned at its one end O on a table so that it can rotate
freely. One force of magnitude 18 N is applied perpendicular to the length of the
stick at its free end. Another force of magnitude 60N is acting at an angle of 30O
with the stick as shown in the figure 4.13(a). At what 60 N
distance from the end of stick that is pinned should
the second force act such that the stick does not d 30O
O
rotate? 1.0 m

Solution Fig 4.13(a) 18 N

Weight of the stick does not affect in the horizontal plane. Resolving
force F of magnitude = 60 N into rectangular components that act at distance
d from point O: 60 N
Fx = 60 N × cos 30 = 60 N × 0.866 = 51.96 N
O
Fy F
Fy = 60 N × sin 30O = 60 N × 0.5 = 30 N O d 30O
As the component F
Fx
x passes through the axis
d’=1.0 m
of rotation, its torque is zero. Torque τ1 of 30 N is Fig 4.13(b) 18 N
positive and τ2 of 18 N force is negative. The stick will not rotate when these two
torques balance each others, i.e τ 1= τ2 or F y × d= F ‘× d‘
30 N × d = 18 N × 1 m
d = 18 N × 1 m = 0.6 m
30 N
4.7 Centre of Gravity and Centre of Mass
An object is composed of a large number of small particles. Each particle is
acted upon by the gravitational force directed towards the centre of the
Earth (Fig. 4.14-a). As the object is small as compared to the Earth, the value of g
can be taken as uniform over all particles. Therefore, each particle experiences
the same force mg. Since all these forces are parallel and act in the same
direction, so their resultant as shown in Fig. 4.14(b) will be equal to the sum of all
these forces .i.e,

Fig. 4.14(a) Fig. 4.14(b)

Gravitational force acting Resultant gravitational force
on various particles
88
 We know that the sum of the gravitational forces acting on all particles is
equal to the total weight of the object w = Mg Where M = ∑ m = mass of the
object.
Centre of gravity is that point where total
weight of the body appears to be acting.
If a body is supported at its centre of gravity, it stays there without
rotation. The centre of gravity of an object of regular shape lies at its geometrical
centre. Centre of gravity of some geometrical shapes is given in Table 4.1.

Table 4.1
Object Centre of Gravity
Square, Rectangle Point of intersection of the diagonals
Triangle Point of intersection of the medians
Round plate Centre of the plate
Sphere Centre of the sphere
Cylinder Centre of the axis
Metre rule Centre of the rod

Centre of Gravity of a Plane Lamina

For an irregular shaped plane lamina, the centre of gravity can be found
by suspending it freely through different points (Fig. 4.15-a). Each time the object
is suspended, its centre of gravity lies on the Points of
vertical line drawn from the point of suspension
suspension with the help of a plumbline. The CG
exact position of the centre of gravity is at the
point where two such lines cross each other as
shown in the Fig 4.15(b). The centre of gravity
can exist inside a body or outside the body as
Fig. 4.15(a) Fig. 4.15(b)
is in case of a cup.
Irregular shaped plane lamina
Centre of Mass
For your information!
Newton’s second law of motion is applicable to
single particle or system of particles. Even when the
parts of a system have different velocities and CG

acceleration, there is still one point in the system whose

acceleration could be found by applying second law. Centre of gravity of a bowl
is outside the material.
This point is called the centre of mass of the system.
89
 The centre of mass of a body is that point where the
whole mass of the body is assumed to be concentrated.
Hence, the centre of mass behaves as if all the mass of the body or system
is lying at that point. In the (Fig. 4.16) given below, a rotating wrench slides along
a frictionless floor. There is no resultant force on the wrench. Therefore, its centre
of mass, shown by a yellow dot, follows a linear path with constant speed.

Fig. 4.16: Rotating wrench sliding along a frictionless floor

On the surface of the Earth, where g is almost uniform, the centre of mass
of an object coincides with its centre of gravity.

4.8 Equilibrium
We have learnt how translatory and rotational motion can be caused due
to the application of external forces. Now, we shall see how external forces can be
balanced to produce no translational or Do You Know?
rotational effects.
We know that if a number of forces act on a
body such that their resultant is zero, the body
remains at rest or continues to move with
uniform velocity if already in motion. This state
of the body is known as equilibrium, which can This is a fascinating
be stated as: scene of equilibrium.

A body is said to be in equilibrium if it has no acceleration.

There are two types of equilibrium:

(i) Static equilibrium (ii) Dynamic equilibrium
A body at rest is in static equilibrium whereas a body moving with uniform
velocity is in dynamic equilibrium.

An example of static equilibrium is a book lying on the table as shown in

the Fig. 4.17. Only two forces are acting on it. One is its weight w = mg acting
90
downward and the other is Fn the normal force that the
table exerts upward on the book. Since the book is at rest
so, it has zero acceleration. Therefore, the sum of all the
forces acting on the book should be zero, so that the
book is said to be in equilibrium. Hence

Fn − w = 0 Fig. 4.17
or Fn = w Book is in static equilibrium

This means that forces can act on a body without

accelerating it, provided these forces balance each Rope

other. Wall

An electric bulb hanging from the ceiling of a Beam

room, a man holding a box, a beam held horizontal
against a wall with the help of a rope and a hanging Fig. 4.18 Weight
weight (Fig. 4.18), are all examples of static equilibrium. A beam projected from a wall
is also in static equilibrium
A good example of dynamic equilibrium is a
paratrooper (Fig. 4.19). In a few second after the free
fall, the parachute opens and a little later, the
paratrooper starts descending with a uniform velocity.
In this state, the force of gravity acting vertically
downward on the paratrooper is balanced by the
resistance of air on the parachute acting upward. Fig. 4.19

4.9 Conditions of Equilibrium A paratrooper is in dynamic equilibrium

Fascinating Freefall
There are two conditions of equilibrium:
First Condition of Equilibrium
By Newton’s second law of motion, F = ma
If the body is in translational equilibrium, then a = 0,
therefore, net force F should be 0 or ∑F=0 ........ (4.7)
This is the mathematical form of the first
condition of equilibrium which states that: A group of paratroopers making
in a formation-an example of
dynamic equilibrium.

A body is said to be in translational equilibrium only if the vector

sum of all the external forces acting on it is equal to zero.
In case a number of coplanar forces F1, F2, F3, .... having their resultant
equal to F, are acting on a body, these can be resolved into their rectangular
91
components, and first condition of equilibrium can be then written as:
Along x-direction, F 1x + F 2x + F +…… = 0
or ∑ Fx = 0 …… (4.8)
Similarly, along y-direction,
F 1y + F 2y + F + …… = 0
or ∑ Fy = 0 ……(4.9)
Thus, first condition of equilibrium can also be stated as:

The sum of all the components of forces along x-axis should be zero and
the sum of all the components of forces along y-axis should also be zero.

Second Condition of Equilibrium

The second condition of equilibrium implies to the rotational equilibrium
which means that the body should not rotate under the action of the forces.
Consider the example of a rigid body in Fig.4.20. Two forces F1 and F2 of
equal magnitude are acting on it. In case (a), both the forces act along the same
line of action.
F2 B
F2 A o B
o
F1
A F1
(a) Fig. 4.20 (b)

In case (b), the lines of action of the two forces are different. Since
magnitude of F1 and F2 are equal, so the resultant force is zero in both the cases.
Thus, first condition of equilibrium is satisfied. But you can observe that in case
(b), the forces are forming a couple which can apply torque to rotate the body
about point O. Therefore, for a body to be completely in equilibrium, a second
condition is also required. That is, no net torque should be acting. This is the
second condition of equilibrium which can be stated as:
The vector sum of all the torques acting on
a body about any point must be zero.
Mathematically, we can write: ∑τ=0 ……(4.10 )
Hence, a body will be in complete equilibrium when,

{
∑ Fx = 0
∑ Fy = 0
And ∑τ=0

92
 Solving Problems by Applying Conditions of Equilibrium
The following steps will help to solve problems by Do You Know?
applying conditions of equilibrium.
1. First of all, select the objects to which Eqs. (4.8)
and (4.9) are to be applied. Each object should
be treated separately.
2. Draw a diagram to show the objects and
forces acting on them. Only the forces acting Most balancing toys
on the objects should be included. The forces have a low centre of mass.
which the objects exert on their environment should not be included.
3. Choose a set of x, y axes such that as many forces as possible lie directly
along x-axis or y-axis, it will minimize the number of forces to be resolved
into components.
4. Resolve all the forces which are not parallel to either of the axes, in their
rectangular components.
5. Apply Eqs. (4.8) and (4.9) by putting ∑ Fx = 0 and ∑ Fy = 0 to get two
equations.
6. If needed, apply Eq. (4.10) by putting ∑τ = 0 to get another equation.
7. The equations can be solved simultaneous to find out desired unknown
quantities.
Example 4.5
A picture is suspended by means of two T1 T2
20 cm O 20 cm
vertical strings as shown in Fig 4.21. The A B
weight of the picture is 5 N, and it is acting at
its centre of gravity. Find the tension T1 & T2 in
the two strings.

Solution
Total upward force = T1 + T2
Total downward force = w = 5 N Fig. 4.21
Tensions in the strings, T1 = ? , and T2 = ? w
Since, there is no horizontal force, so ∑ Fx = 0
Already ∑ Fx = 0
Putting ∑ Fy = 0
T1 + T2 −w = 0 ................................ (i)
Apply ∑ τ = 0, selecting point B as point of rotation. Here, torque τ1 of T1 is
93
negative whereas torque τ2 of w is positive about point B. T2 produces zero
torque as it passes through the point of rotation. Hence,
τ2 − τ1 = 0
or w × BO − T1 × AB = 0
putting the values, w × 0.2 m − T1 × 0.4 m = 0
or 5 N × 0.2 m − T1 × 0.4 m = 0
5 N × 0.2 m
or T1 = = 2.5 N
0.4 m
Putting the value of T1 and w in Eq. (i), we have
2.5 N + T2 − 5 N = 0
or T2 = 2.5 N
4.10 States of Equilibrium
An object is balanced when its centre of mass and its point of support lie on
the same vertical line. Then forces on each side are balanced, and the object is
said to be in equilibrium. There are three states of equilibrium in connection with
stability of the balanced bodies.
Stable Equilibrium
A body is said to be in a state of stable equilibrium, if
after a slight tilt, it comes back to its original position.
Stable equilibrium occurs when the torques arising from the rotation (tilt) of
the object compel the body back towards its equilibrium position.
The cone shown in Fig 4.22(a) is in the state of stable equilibrium. Its weight w
acting downward at the centre of gravity
G and the reaction of the floor Fn acting
upward, lie on the same vertical line. nF
nF G
Since these forces are equal and in G
opposite direction, so they balance each w
w

other and both the conditions of (a) (b)

Fig. 4.22
equilibrium are satisfied.
As you try to push over the cone slightly, its centre of gravity is raised but it
still remains above the base of the cone. The weight w and the normal force Fn do
not remain in the same line but act like two unlike parallel forces. The cone does
not remain in equilibrium. Unlike parallel forces produce a clockwise torque
which brings the cone back to its original position. It is worth noting that the
body remains in equilibrium as long its centre of mass lies within the base.

94
 Unstable Equilibrium
Try to balance the cone on its tip. It is balanced for a moment because w and
Fn lie along the same line. Even it is slightly tilted, it will not come back to its
original position by itself. Rather it will fall downward, because its centre of mass
no longer remains above the base. It
topples over, because line of action of w no
longer lies inside the base O (Fig. 4.23). In G G

this case, centre of gravity is lowered on w w

tilting and continues to fall further. It O O

cannot r ise up again because the (a) F
n
(b) F n

Fig. 4.23
anticlockwise torque produced by w
moves it further downward.
A body is said to be in a state of unstable equilibrium if, after a slight
tilt, it tends to move on further away from its original position.
Neutral Equilibrium
A cylinder resting on a horizontal surface (Fig. 4.24) shows the neutral
equilibrium. If the cylinder is rotated slightly, there is no force or torque that
brings it back to its original position or moves it away. As the F n

cylinder rotates, the height of the centre of mass remains G

unchanged. In any position of the cylinder, its weight and
reaction of the ground lie in the same vertical line. w Fig. 4.24

A body is in neutral equilibrium if it comes to rest in its new

position after disturbance without any change in its centre of mass.
Other examples of neutral equilibrium are a ball rolling
on a horizontal surfaces, or a cone resting on its curved
surface (Fig.4.25). Fig. 4.25
4.11 Improvement of Stability
It is our daily life observation that a low armchair is more stable than a high
chair because of its low centre of gravity. The Interesting Information!
position of centre of gravity is very important when
we are talking about stability. A bus can be stable or
unstable depending on how it is loaded. If the heavy
loads are placed on the floor of the bus, its centre of
gravity will be low. Now if it is disturbed slightly, a
A double decker bus is being
torque will bring it back to its original position. tilting to test its stability.
95
 In this case, the bus is in stable equilibrium. If the same bus is loaded with
steel sheets on the top, the centre of gravity be raised. It is now near to a state of
unstable equilibrium. A couple will turn it over if it is slightly tilted. The same is the
case of ships and boats. We can improve the stability of a system either by
lowering the centre of gravity or by widening the base.
Interesting Information!
An unstable equilibrium is illustrated in this
figure. A chair in normal position is quite
G G
stable (Fig. a) but it has been turned into an
unstable position by tilting it back on its legs w w
(Fig. b). In this tilted position, a couple is
formed by its weight w and reaction Fn of the
ground. This clockwise couple tends to
Fn
overturn chair backward. (a) (b)

4.12 Application of Stability in Real Life

The concept of stability is widely applied to engineering technology
especially in manufacturing racing cars and balancing toys.
As the racing cars are driven at very high speeds and also there are sharp
turns in the track, therefore, the chances of the cars to topple over increase. To
enhance the stability of racing cars, their centres of mass are kept as low as
possible. There base areas are also increased by keeping the wheel outside of
their main bodies. Balancing toys are also very interesting for both children and
elders. Look at some balancing toys shown belows.

(a) (b) (c)

Fig. 4.26: Balancing toys
The physics behind these types of toys is that stability is built in with
balancing toys. These toys are basically in completely stable state and their
centres of gravity always remain below the pivot point. If the toys are disturbed in
any direction, the centre of gravity is raised and it becomes unstable for a
moment. It comes back to its initial stable position by lowering its centre of
gravity.
96
 The kids learn from these toys about stable systems and how they return to
their state of initial rest position after being disturbed. Educational games on the
basis of balancing toys have also been developed for the kids as
shown in Fig 4.27.
Interesting Information!
To enhance the
stability of a
racing car, its
centre of mass is
kept as low as
possible. Its
base area is also increased by keeping its
wheels outside of its main body.
Fig. 4.27
Rotational Motion Versus Translatinal Motion
Counterparts of velocity, acceleration, force and momentum in
translational motion are angular velocity, angular acceleration, moment of force
(torque) and angular momentum respectively in rotational motion. It suggests
that the torque plays the same role in the rotational motion that is played by the
force in the translational motion. Therefore, we are justified to predict that
analogous to Newton's first law of motion, a rotating object will continue to do
so with constant angular velocity unless acted upon by a resultant moment
(torque). However, if a resultant torque is applied to rotating object, it will
accelerate depending on the direction of the torque relative to the axis of
rotation.
This fundamental principle enhances our understanding how objects
move and interact with their environment whether in linear or rotational motion
scenarios.
Motion in a Circle
When a body is moving along a circular path, its
velocity at any point is directed along the tangent
v
drawn at that point. Figure 4.28 shows that the direction
of tangent at each point on a circle is different, F
therefore, the velocity of an object moving with uniform
speed in a circle is changing constantly. Hence, a force
perpendicular to the direction of motion is always Fig. 4.28

required to keep the object moving with uniform speed in a circular path.

97
 It should be noted that F is essentially perpendicular to v. For an instance,
if it is not perpendicular to v, the force F will have a component in the direction of
v. This will change the magnitude of velocity. As the body moves with constant
speed, so it is possible only if the component of force along v is F cos 90° = 0.

4.13 Centripetal Force

We have studied above that an object can move in a circular path with
uniform speed only if a force perpendicular to its velocity is acting constantly on
it. This force is always directed towards the centre of the circle. It is called
centripetal force and can be defined as:
The force that causes an object to move in a circle at
constant speed is called the centripetal force.

For an object of mass m moving with uniform speed v in circle of radius r,

the magnitude of centripetal force Fc acting on it can be calculated by using the
relation:
mv2
Fc = r . .......... (4.11)

Example 4.5
A 150 g stone attached to a string is whirled in a horizontal circle at a
constant speed of 8 m s-1. The length of string is 1.2 m. Calculate the centripetal
force acting on the stone. Neglect effects of gravity.
Solution
Mass of stone = m = 150 g = 0.15 kg
Speed of stone = v = 8 m s -1
Radius of circle = r = 1.2 m
Centripetal force = Fc= ?

Fc= mv
2

Using Eq.4.11,
r
0.15 kg × (8 m s-1)2
Putting the values, Fc= =8N
1.2 m

Sources of Centripetal Force

We have learnt that centripetal force has to be
supplied if the body is to be maintained in its circular (a)
path. What could be the sources of centripetal force? Fig. 4.29

A stone whirled in a circle by a string

98
 If we tie a stone to one end of a string and whirl it from the other end, we
will have to exert a force on the stone through the string (Fig 4.29-a). If we release
the string when it is at any point P, the stone will fly Q
off along the tangent (PQ) to the circle. Then, it will v
P
move along the same straight line with constant
velocity unless an unbalanced force acts upon it. T
In fact, the tension T in the string was O
providing the stone the necessary centripetal force
to keep it along the circular path (Fig 4.29-b).
When we release the string we stop applying force
on the stone and hence it moves in a straight line. Fig. 4.29 (b)

Now consider the case of the moon which

moves around the Earth at constant speed. The
gravity of the Earth provides the necessary
centripetal force to keep it in its orbit. Same is the
case of satellites orbiting the Earth in circular paths
with uniform speed. The gravitational pull of the Fig. 4.30
Earth provides centripetal force. A satellite orbiting the Earth

One of the real life examples is a washing

machine dryer. A dryer is a metallic cylinderical
drum with many small holes in its walls. Wet clothes
are put in it. When the cylinder rotates rapidly,
friction between clothes and drum walls provides
necessary centripetal force. As the water molecules
are free to move, so they cannot get the required Fig. 4.31
centripetal force to move in circular paths and Washing machine
escape from the drum through the holes. This
results into quick drying of clothes.

Another interesting example is that of a

cream separator. In a cream separator, milk is
whirled rapidly.

Cream seperator
Fig. 4.32
99
 The lighter particles of cream experience less centripetal force and gather
in the central part of the machine. The heavier particles of milk need greater
centripetal force to keep their circular motion in circles of small radius r. In this
way, they move away towards the walls.

KEY POINTS
 If the parallel forces are acting in the same direction, then they are called like parallel
forces and if they are acting in opposite directions, they are called unlike parallel forces.
 A force which is equal to the sum of all the forces is known as resultant force.
 The line along which the force acts is called the line of action of the force.
 The perpendicular distance of the line of action of a force from the axis of rotation is
known as moment arm of the force.
 The torque or moment of a force is defined as the product of the force and the moment
arm.
 When two equal and opposite, parallel forces act at two different points of the same body,
they form a couple.
 The centre of gravity is a point inside or outside the body at which the whole weight of the
body is acting.
 The centre of mass of a body is that point where the whole mass of the body is assumed to
be concentrated.
 A body is said to be in equilibrium if it has no acceleration.
 A body will be in translational equilibrium only if the vector sum of all the external forces
acting on it is equal to zero. This is called first condition of equilibrium. The vector sum of
all the torques acting on a body about any axis should be zero. This is second condition of
equilibrium.
 When a body is in equilibrium, the sum of clockwise moments about any point equals the
sum of anticlockwise moments about that point.
 A body is said to be in a state of stable equilibrium, if after a slight tilt, it comes back to its
original position.
 A body is said to be in a state of unstable equilibrium if, after a slight tilt, it tends to move
on further away from its original position.
 A body is in neutral equilibrium if it comes to rest in its new position after disturbance
without any change in its centre of mass.
 Analogous to Newton's first law of motion in a straight line, a rotating object will continue
to do so with constant angular velocity unless acted upon by a resultant moment of force.
 The force that causes an object to move in a circle at constant speed is called the
centripetal force.

100
 EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
4.1. A particle is simultaneously acted upon by two forces of 4 and 3 newtons.
The net force on the particle is:
(a) 1 N (b) between 1 N and 7 N (c) 5 N (d) 7 N
4.2. A force F is making an angle of 60º with x-axis. Its y-component is equal
to:
(a) F (b) F sin60° (c) F cos60° (d) F tan60°
4.3. Moment of force is called:
(a) moment arm (b) couple (c) couple arm (d) torque
4.4. If F1 and F2 are the forces acting on a body and τ is the torque produced in
it, the body will be completely in equilibrium, when:
(a) ∑ F = 0 and ∑ τ = 0 (b) ∑ F = 0 and ∑ τ ≠ 0
(c) ∑ F ≠ 0 and ∑ τ = 0 (d) ∑ F ≠ 0 and ∑ τ ≠ 0
4.5. A Shopkeeper sells his articles by a balance having unequal arms of the
pans. If he puts the weights in the pan having shorter arm, then the
customer:
(a) loses (b) gains (c) neither loses nor gains (d) not certain
4.6. A man walks on a tight rope. He balances himself by holding a bamboo
stick horizontally. It is an application of:
(a) law of conservation of momentum
(b) Newton’s second law of motion
(c) principle of moments
(d) Newton’s third law of motion
4.7. In stable equilibrium the centre of gravity of the body lies:
(a) at the highest position (b) at the lowest position
(c) at any position (d) outside the body
4.8. The centre of mass of a body:
(a) lies always inside the body
(b) lies always outside the body
(c) lies always on the surface of the body
(d) may lie within , outside or on the surface
101
4.9. A cylinder resting on its circular base is in:
(a) stable equilibrium (b) unstable equilibrium
(c) neutral equilibrium (d) none of these
4.10. Centripetal force is given by:
(c) mv mv
2
(a) rF (b) rFcosθ (d)
r r
B Short Answer Questions
4.1. Define like and unlike parallel forces.
4.2. What are rectangular components of a vector and their values?
4.3. What is the line of action of a force?
4.4. Define moment of a force. Prove that τ = rFsinθ, where θ is angle between
r and F.
4.5. With the help of a diagram, show that the resultant force is zero but the
resultant torque is not zero.
4.6. Identify the state of equilibrium in each case in the figure given below.

(a) (b) (c)

4.7. Give an example of the body which is moving yet in equilibrium.

4.8. Define centre of mass and centre of gravity of a body.
4.9. What are two basic principles of stability physics which are applied in
designing balancing toys and racing cars?
4.10. How can you prove that the centripetal force always acts perpendicular to
velocity?
C Constructed Response Questions
4.1. A car travels at the same speed around two curves with different radii. For
which radius the car experiences more centripetal force? Prove your
answer.
4.2. A ripe mango does not normally fall from the tree. But when the branch of
the tree is shaken, the mango falls down easily. Can you tell the reason?
4.3. Discuss the concepts of stability and centre of gravity in relation to objects
toppling over. Provide an example where an object’s centre of gravity

102
 affects its stability, and explain how altering its base of support can
influence stability.
4.4. Why an accelerated body cannot be considered in equilibrium?
4.5. Two boxes of the same weight but different heights are lying on the floor
of a truck. If the truck makes a sudden stop, which box is more likely to
tumble over? Why ?
D Comprehensive Questions
4.1. Explain the principle of moments with an example.
4.2. Describe how could you determine the centre of gravity of an irregular
shaped lamina experimentally.
4.3. State and explain two conditions of equilibrium.
4.4. How the stability of an object can be improved? Give a few examples to
support your answer.

E Numerical Problems

4.1 A force of 200 N is acting on a cart at an angle of 30O with the horizontal
direction. Find the x and y-components of the force.
(173.2 N, 100 N)
4.2 A force of 300 N is applied perpendicularly at the
knob of a door to open it as shown in the given
figure. If the knob is 1.2 m away from the hinge,
what is the torque applied? Is it positive or
negative torque? 1.2 m
F
(360 N m, positive)
4.3 Two weights are hanging from a metre rule at
the positions as shown in the given figure. If the
rule is balanced at its centre of gravity (C. G), find
the unknown weight w. (3 N)

40 cm 30 cm

C.G

w
4N

103
4.4 A see-saw is balanced with two children sitting near either end. Child A
weighs 30 kg and sits 2 metres away from the pivot, while child B weighs
40 kg and sits 1.5 metres from the pivot. Calculate the total moment on
each side and determine if the sea-saw is in equilibrium. (60 N)
4.5 A crowbar is used to lift a box as shown in
the given figure. If the downward force of
250 N is applied at the end of the bar, F
how much weight does the other end
bear? The crowbar itself has negligible 30 cm
5 cm
weight. (1500 N)

4.6 : A 30 cm long spanner is used to open the nut of a car. If the torque
required for it is 150 N m, how much force F should be applied on the
spanner as shown in thefigure given below.
F

(500 N)

4.7 : A 5 N ball hanging from a rope is pulled to the right 60°

by a horizontal force F. The rope makes an angle of
60° with the ceiling, as shown in the given figure. T
Determine the magnitude of force F and tension T
in the string. F

(2.9 N, 5.8 N)
4.8 : A signboard is suspended by means of two steel T1 T2
2m 2m
wires as shown in the given figure. If the weight of
the board is 200 N, what is the tension in the Signboard
strings? (100 N, 100 N)

4.9 : One girl of 30 kg mass sits 1.6 m from the axis of a 200 N
see-saw. Another girl of mass 40 kg wants to sit on
the other side, so that the see-saw may remain in
equilibrium. How far away from the axis, the other
girl may sit? 60°

(1.2 m)

4.10 : Find the tension in each string of the as shown in

the given figure, if the block weighs 150 N.
150 N
(86.6 N, 173.2 N)
104
 Work, Energy And Power
Chapter
5
Student Learning Outcomes
After completing this chapter, students will be able to:
[SLO: P-09-B-59] Define work done.
[SLO: P-09-B-60] Use the equation work
done = force × distance moved in the
direction of the force W = F × d to solve
problems
[SLO: P-09-B-61] Define energy as the
ability to do work
[SLO: P-09-B-62] Explain that energy may
be stored [Such as in gravitational potential,
c h em ic a l, e l astic ( s t r a in ), nuc lea r,
electrostatic, and internal ( thermal)
energies]
[SLO: P-09-B-63] Prove that Kinetic
Energy= 12 mv2 [use of equations of motion
not needed; proof through kinematic graphs
will suffice]
[SLO: P-09-B-64] Prove and use the formula for gravitational potential energy
[SLO: P-09-B-65] Use the formulas for kinetic and gravitational potential energy to solve
problems involving simple energy conversions [make use of the conversion of energy from
one form to the other, including cases involving loss of energy to the surroundings]
[SLO: P-09-B-66] Describe how energy is transferred and stored during events and processes
[e.g. work done during transfer by mechanical work done, electrical work done, and heat]
[SLO: P-09-B-67] State and apply the principle of the conservation of energy
[SLO: P-09-B-68] Justify why perpetual energy machines do not work
[SLO: P-09-B-69] Differentiate between and list renewable and non-renewable energy
sources
[SLO: P-09-B-70] Describe how useful energy may be obtained from natural resources
[including the cases of (a) chemical energy stored in fossil fuels, (b) chemical energy stored in
biofuels, (c) hydroelectric resources, (d) solar radiation, (e) nuclear fuel, (f) geothermal
resources, (g) wind, {h) tides, (i) waves in the sea while including references to a boiler, turbine
and generator where they are used]
[SLO: P-09-8-71] Describe advantages and disadvantages of methods of energy generation
[limited to whether it is renewable, when and whether it is available, and its impact on the
environment]
[SLO: P-09-8-72] Define and calculate power [As work done per unit time and also as energy
transferred per unit time. This also includes applying the equations: (a) power= work
done/time taken P = W/t (b) power = energy transferred/time taken
[SLO: P-09-B-73] Define and calculate efficiency [including: (a) (%) efficiency = (useful energy
output)/(total energy input) ( x 100%) (b) (%) efficiency = (useful power output)/(total power
input) ( x 100%)]
[SLO: P-09-B-74] Apply the concept of efficiency to simple problems involving energy
transfer
[SLO: P-09-B-75] State that a system cannot have an efficiency of 100% due to unavoidable
energy losses that occur.

105
 Work and energy are important
concepts in physics as well as in our everyday
life. Commonly the word ‘work’ covers all sort
of activities whether mental or physical. If a
girl is studying (Fig. 5.1) or a man is standing
(Fig. 5.2) with a load of bricks on his head, we
say that they are doing work. But according to
physics, work has a specific definition. Work is Fig. 5.1
said to be done when a force acts on an object
and moves it through some distance.
The concept of energy is closely associated with that of
work, when work is done by one system on another,
energy is transferred between the two systems.
In this chapter, we will define work, energy, power
and efficiency and show how they are related to one
another.

5.1 Work Fig. 5.2

Force and distance are two essential elements of work. When a constant force
acting on a body moves it through some distance, we say that 'the force has done
work'.
Work is defined as the product of magnitude of force
and the distance covered in the direction of force.
Consider a block of wood lying on a
table (Fig. 5.3). If we exert a force F on the
block to move it through a distance S in the F F
direction of force, then the work W done by
the force is: S
Work = Magnitude of force × Distance Fig. 5.3
or W = F × S.....................(5.1)
From Eq. (5.1), it can be concluded that if some force is
acting on a body but there is no displacement, then no
work is done. For example, a man is pushing hard a wall
but the wall remains fixed in its place. In this case, the man
is doing no work (Fig. 5.4).
Similarly, if a force acting on the body is zero and the body
is moving with uniform velocity, work will be zero.
As F = 0 so W=0×S=0 Fig. 5.4

106
What will be the work done when a force is
F F
acting on a body making an angle θ with the
θ θ
direction of motion? In this case, work is done
due to the component of force which is acting F cosθ
S
along the direction of motion (Fig. 5.5). Fig. 5.5
Resolving the force F into its components, we have
the component F cosθ that acts in the direction of motion. Therefore,
W = (Fcosθ) S
or W = FS cos θ …… (5.2)
If θ is zero, cos 0° = 1, then
W = FS (1) = FS

This is the case when force and distance covered

are in the same direction. Now if θ = 90°, then Force
F
cos 90° = 0 which means the force has zero
component in the direction of motion. Thus, θ 90O

Displacement
W = FS (0) = 0 S
This is the case when force is perpendicular
to the displacement. Look at Fig. 5.6, it suggests
that if a person carries a bag to some distance, this
work is zero, because the force applied to hold the Fig. 5.6
load is upward which is perpendicular to the displacement.
The work done to push an object is the same whether the object moves
north to south or east to west, provided the magnitude of force and the distance
moved are not changed. Work does not convey any directional information, so it
is a scalar quantity.

Calculation of Work Done by Graph

When a constant force F acts through a distance S, P Q

the event can be plotted on a force-distance graph as Shaded area

shown in Fig. 5.7. If the force and distance covered are in F work done
the same direction, the work done is F × S. Force
Clearly the shaded area in the figure is also F × S. O
Dis tance R
Hence the area under a force distance curve can be taken S
to represent the work done by that force. Fig. 5.7

107
Units of Work
The SI unit of work is joule (J).
One joule work is done when a force of one newton acting on a body
moves it through a distance of one metre in its own direction.
From Eq. (5.1)
1J=1N×1m
or 1J=Nm
Bigger units are also used like 1 kJ = 10 J and 1MJ = 106 J
3

Example 5.1
A person does 200 J of work in pushing a carton through a distance of
5 metres. How much force is applied by him?
Solution
Work done W = 200 J
Distance S = 5m
Force F =?
W
From Eq. (5.1) W = F × S or F =
S
Putting the values, we get
200 J
F= = 40 N
5m
Example 5.2
Find the work done by a 65 N force in pulling the suitcase (Fig. 5.8) for a
distance of 20 metres.
Solution
Force applied F = 65 N
Distance covered S = 20 m
30
O

Angle from the figure θ = 30o

Work W= ?
Using Eq. 5.2,
Fig. 5.8
W = FS cos 30o
W = 65 N × 20 m × 0.866
W =1125.8 N m = 1125.8 J

108
5.2 Energy For Your Information!
Our body cannot move unless we have energy
from food. A car would not run without the energy it
obtains from burning fuel. Machines in the factories
cannot run without consuming energy supplied by
electricity. Any change in motion requires energy. When
we say that a certain body has energy, we mean that it
has the ability of doing work.
A stretched bow stores
Energy can be defined as the ability of a body to do work. energy, which is
transferred to the arrow
When someone does work, energy of the body as it is shot. Some bows
has to be spent. In fact, energy is transferred to the body store enough energy
to shot an arrow even
on which work is done. In other words, the energy is
1 km away.
transferred from one system to another. For example,
when you do work pushing a swing, chemical energy in your body is transferred
to the swing and appears as energy of the motion of the swing.
Like work, energy is a scalar quantity. Its SI unit is joule (J).

When one joule work is done on a body, the amount of energy spent is one joule.
There are many forms of energy. Electrical energy, chemical energy, nuclear
energy, heat energy and light energy are some well-known forms which we shall
study later on. There are two basic forms of energy:
(i) Kinetic energy
(ii) Potential energy

The combination of these two types of energies is called mechanical energy.

Kinetic Energy
The kinetic energy of a body is the energy
that a body possesses by virtue of its motion.
To find out how much kinetic energy a moving body possesses, an opposite
force can be applied on the body to stop its motion. Then the work done by
the force will be equal to the kinetic energy of the body. i.e., Kinetic energy
(E k ) = Work done (W)
Suppose a body of mass m is moving with velocity v. An opposing force F acting
on the body through a distance S brings it to rest. Then,

109
E k = work done = F × S
v v
As F = ma and S = v a × time =( v + 0
2 )t = × t
2
vt 1 velocity
Hence, E k = ma × 2 = 2 ma × vt (m s−1)
Using velocity-time graph (Fig 5.9), the acceleration t
O
time (s)
‘a’ is given by its slope.
v Fig. 5.9
Hence, a =
t , the slope is negative as the velocity and force are in opposite
direction.
Thus E =1 m (v vt
k 2 t
1
or E k = mv - -------- (5.3)
2

2
For Your Information!
Example 5.3 • The work done by the
A truck of mass 3000 kg is moving on a road with uniform single beat of human
velocity of 54 km h−¹. Determine its kinetic energy. heart is 0.5 J.
• The energy content of
Solution thenuclear bomb
dropped on Hiroshima,
Mass of the truck m = 3000 kg Japan, in the second
Velocity v = 54 km h−¹=15 m s−¹ world war was 8.0 × 1013J.
Kinetic energy Ek = ? • The energy output of a
power station in one
Putting the values, year is 1016 J.
E k = 1 mv2 = 1 × 3000 kg × (15) m s
2 2 −2

2 2
E k = 337500 J = 337.5 kJ
Potential Energy
In the previous section, we have seen that the work done on a body is used
to increase its kinetic energy. Sometimes, the work done on a body does not
increase its kinetic energy, rather it is stored in the body as potential energy.
Potential energy is defined as the energy that a body Do You Know?

possesses by virtue of its position or deformation.

Forms of Potential Energy:
There are many forms of potential energy. As
mentioned above, the energy possessed by an object
by virtue of its position relative to the Earth is known The train is changing
potential energy every
as gravitational potential energy. moment in the roller coaster

110
 The energy stored in a compressed or stretched spring is called elastic
potential energy and the potential energy in the chemicals of a battery is called
chemical potential energy, which is changed to electrical energy by chemical
reactions. Thermal or internal energy is released by burning fossil fuels i.e. coal,
oil or gas through chemical reactions.
Nuclear energy is the hidden energy in the nuclei of atoms. When they
are broken, energy is released in the form of heat and some other radiations. This
is called nuclear fission.
If the block shown in Fig. 5.10 is lifted to a height
h above the ground, then the block would have F
potential energy in that raised position. Therefore, it h
has the ability to do work whenever it is allowed to fall.
How should potential energy be measured? Because Fig. 5.10
w
work is done on the block to put it into the position where it has potential energy,
therefore, we can say that the work done is stored in it as potential energy. Thus,
potential energy Ep is given by
E p = Work done to put the block in elevated position
The applied force necessary to lift the block with constant velocity is equal
to weight w of the block and since w = mg, therefore, potential energy of the
block at height h becomes,
E p = wh
or E p = mgh ....................... (5.4)
The most obvious example of
gravitational potential energy is a waterfall
(Fig. 5.11), water at the top of the fall has
potential energy. When the water falls to the
bottom, it can be used to run turbines to Fig. 5.11 Waterfall
produce electricity and thus can do work.
For Your Information!
According to Einstein’s theory of
Example 5.4 relativity, matter and energy are
interchangeableunder certain
A ball of mass 180 g was thrown vertically
conditions. The loss of some mass in
upward to a height of 12 m. Find the nuclear reactions may transform into
potential energy gained by the ball. energy production and similarly energy
may be converted into material
Solution p a r t i c l es . H enc e, now we have
Mass of ball m = 180 g = 0.18 kg conservation of mass and energy rather
Height h = 12 m that conservation of each separately.
111
P.E. gained Ep = ?
g = 10 m s−2
From Eq. (5.4) Ep = mgh
Putting the values
E p = 0.18 kg × 10 m s−2 × 12 m = 21.6 J

5.3 Conservation of Energy

The study of various forms of energy and the transformation of one kind
of energy into another has led to a very important principle known as the
principle of conservation of energy. Formally, it is stated as:

Energy cannot be created or destroyed. It may be transformed from

one form to another, but the total amount of energy never changes.
During energy transfer process, some energy seems to be lost and not
accounted for in calculations. This loss of energy is due to work done against
friction of the moving parts in the process. This energy appears as heat and is
dissipated in the environment. This energy does not remain available for doing
some useful work and may be called waste energy.
A process of energy conversion and conservation can be described with
the given example.
Let a body of mass m be at rest at a point A above the
A
height h from the ground (Fig.5.12). Its total energy is P.E is mgh,
E p = mgh
and Ek = 0 B h
Then the body is allowed to drop to point B at a height x from the
ground. The body lose potential energy and gains kinetic energy x
as it gets speed while falling down. Assuming air resistance C
negligible. Fig. 5.12
E p= mg (h − x)
The loss of potential energy will appear as the gain in kinetic energy, hence, at
point B
Ek= mgx
Total energy at B E = mg (h − x) + mgx = mgh
Just before hitting the ground at point C, the whole of potential energy is
changed into kinetic energy. Thus,
E p= 0 and E = mgh
Thus, total energy remains the same as mgh. On hitting the ground, this
energy is dissipated as heat and sound in the environment.
112
5.4 Sources of Energy For Your Information

Fossil Fuel Energy

Fossil fuel energy comes out from burning of oil,
coal and natural gas. These materials are known as fossil
fuels. The burning of these fuels gives out heat which is
used to generate steam that runs the turbines to
produce electricity. A block diagram of the process Before electricity was
going on in electricity generation by fossil fuels is given discovered, one of the
in Fig. 5.13. primary functions of
fossil fuels was to
provide light.

Steam line Turbine Do You Know?

Generator
Transmission Thermal energy
lines
from coal burning
Coal was a major
supply
source used in the
boilers of steam
engines to drive
Condenser locomotives in the
Water supply Transformer past.

Fig. 5.13
Hydroelectric Generation Transmission
towe Transformer

Hydroelectric generation
Water reservoire
is the electricity generated from
the power of falling water. Water Water intake
Generator
in a high lake or reservoir Turbine
Tunnel
possesses gravitational potential Bed rock

energy stored in it. When water is Water discharge

(canal)
allowed to fall from height, the
potential energy is changed into Fig. 5.14

kinetic energy (Fig. 5.14). Tunnels are made for water to flow from the reservoir to
a lower place. Such a construction is known as dam.
The kinetic energy of running water rotates the turbine which in turn runs the
electric generator.

113
Solar Energy
Sun is the biggest source of energy. The energy obtained from sunlight is
referred to as solar energy. Solar energy can be used in two ways. Either it can be
used for heating system or can be converted to electricity. In one way, solar
panels absorb heat of the Sun. They consist of large metal plates which are
painted black (Fig. 5.15). Heat can be used for warming houses or running water
heating system. If solar radiation is concentrated to a small surface area by using
large reflectors or lenses, reasonably high temperature can be achieved.

Fig. 5.15 Fig. 5.16

Solar panels installed on the roof Solar cells panels

At this high temperature, water can be For Your Information!

boiled to produce steam that can run the turbine
of an electric generator. In this way, electricity can
be produced.
In the second method, sunlight is directly
transformed to electricity through the use of solar
Solar powered car which won
cells. Solar cells are also known as photo voltaic the world solar challenge race
cells. The voltage produced by a single voltaic cell in Darwin, Australia in 1993.
is very low. In order to get sufficient high voltage
for practical use, a large number of such cells are
connected in series to form a solar cell panel as
shown in Fig. 5.16.
Solar calculators are also available which Earth satellites get solar energy
work by using the electrical energy provided by through their solar panels.

solar cells. Large solar panels are also used to

power satellites.
114
 For Your Information!
Nuclear Energy
Geothermal energy is currently
Nuclear energy is released in the form of used in Japan, Russia, Iceland,
heat when an atomic nucleus breaks. Nuclear Italy, New Zealand and USA.
More than 85% of Icelanders use
power stations make use of nuclear fuels such as geothermal energy to warm
uranium and plutonium. their homes. The cost of heating
These materials release huge amount of is only one-third of the cost of
burning oil to power electric
energy as the nuclei of their atoms break during
heaters.
nuclear fission. The process is done in a nuclear
reactor. Heat produced by the fuel is used to make steam that runs the turbines
of electric generators. Pakistan also runs nuclear power stations at Karachi and
Chashma.

Geothermal Energy
In some parts of the world, hot rocks
are present in the semi molten form deep Turbine Generator

under the surface of the Earth. They are

Transmission
heated by energy released due to decay of lines

radioactive elements. The temperature of

these rocks is about 250°C. This energy is
known as geothermal energy which can be Hot rocks
Steam Water
extracted to run electric generators. A out in

typical geothermal power plant is shown in Fig. 5.17 Geothermal power plant

Fig. 5.17.

To make use of the heat of the rocks, two

holes are drilled up to the rocks. Cold water
is pumped down through one of the holes. It
is heated up by the hot rocks and starts
boiling. Steam is produced that comes out
through the other hole. The steam runs the
generator which produces electricity. Where
there is water already present over the hot Fig. 5.18
rocks, it comes out of the surface of the Earth in the form of hot springs and
geysers. Such a geyser is shown in Fig. 5.18.

115
Wind Energy
For thousands of years, people have
been using windmills to draw water from the
well or to grind grains into flour. The modern
windmill is used to run generators that
produce electricity. Wind generators make
electricity in the same way as steam generators
in power stations. For large scale power
generation, a 'wind farm' with a hundred or
more windmills is needed. A windmills farm
is shown in Fig. 5.19. Fig. 5.19 Windmills farm

Energy from Tides

The gravitational force for the moon gives rise to tides in the seas. The tide
raises the water level near the sea shore twice a day. The rise and fall of water can
be utilized to turn on turbine for electricity generation. The water at high tides
can be trapped at a suitable location, a basin, by building a dam. The water is
then released in a controlled way at low tide to drive the turbines for producing
electricity. At next high tide, the dam is filled again and the incoming water also
drives turbines.

Energy from Waves in Sea

The tides and winds blowing over the surface of the sea produce strong
water waves.
Their energy can be used to generate Duck floats
Balance float
electricity. The method to harness wave
energy is to use large floats which move up
and down with the waves. One such device
invented by Prof. Salter is known as Salter's
duck (Fig.5.20). It consists of two parts. Waves

Fig. 5.20
(i) Duck float (ii) Balanced float
The energy of the water waves causes duck float to move relative to the balance
float. The relative motion of the duck float is used to drive the electricity
generators.

116
 Do You Know?
Biofuel Energy
The radioactive fallout from the 1986
It is that energy which is obtained from the Chernobyl nuclear accident in Russia
biomass. Biomass consists of organic (1986) affected people, livestock and
materials such as plants, waste foods, crops. Although only 31 people died
from direct exposure, about 600,000
animals dung, sewage, etc. Sewage is that
people were significantly exposed to
dirt which is left over after staining dirty the fallout.
water. The material can itself be used as fuel
or can be converted into other types of fuels.
Direct combustion is a method in which
biomass, commonly known as solid waste, is
burnt to boil water and produce steam. The
steam can be used to generate electricity. In
another process, the rotting of biomass in a
closed tank called a 'digester' produces
methane rich biogas (Fig. 5.21). In this
process, micro-organisms break down
Fig. 5.21 Biogas digester
biomass material in the absence of oxygen.
Biogas produced in the tank is piped out and
Economic, Social and Environmental
can be used for heating and cooking like Impact of Various Energy Sources
natural gas. Fossil fuels is a common source of
Biofuel such as ethanol (alcohol) can also be energy but it is very expensive. It also
obtained from the biomass. It is a replacement produces pollution that affects the
of petrol. In this case, bacteria converts it into human health badly. On the other
hand, hydroelectric energy is the
ethanol.
cheapest source of energy. It does not
5.5 Renewable and produce pollution. It has only one
negative point that it may cause water
Non-Renewable Sources logging by raising the water table
The resources of energy which are replaced under the nearby lands.
The use of solar energy, wind energy,
by new ones after their use are called
tidal energy, etc. is pollution free. Only
renewable energy source. On the other hand, the initial cost is high in the use of these
non-renewable sources are those, which are sources.
depleted with the continuous use. Once they Nuclear energy is very desirable source.
run out, they are not easily replaced by new It is cheaper and can meet the
increasing demands of energy easily.
ones. Sources such as hydroelectricity, solar
energy, wind energy, tidal energy, wave energy and geothermal energy are
renewable. These are replaced by new ones. For example, snow fall and rain fall

117
are continuous processes. Therefore, water supply to the reservoirs of dams for
generation of hydroelectric power will never end up. Likewise, solar energy will
remain available forever. Same is the case with wind and tidal energy. These are
not going to run out in future.
Non-renewable sources include fossil fuels and nuclear energy. The remnants of
plants and animals buried under the Earth took millions of years to change into
fossil fuels. These fuels are in limited quantity. Once they are used up, it will take
further millions of years to form new ones. Similarly, fuels for the nuclear energy
are also limited.
As the need for energy is increasing day by day, there is need to develop other
non- traditional renewable energy sources.

5.6 The Advantages and Disadvantages

of methods of Energy production
The production of hydroelectric
power is more economical and
pollution free. The solar power, wind,
tidal and wave power need more
initial cost but they do not produce
pollution and are also economical as
well. On the other hand, power
generation by fossil fuels and nuclear
fuel adds to the pollution of
environment. Burning of fossil fuels Fig. 5.22
produces smoke, carbon dioxide gas Do You Know?
and heat (Fig. 5.22). They enhance Burning fossil fuels release five billion tonnes of
direct pollution to atmosphere. carbon dioxide into the atmosphere every year.
Wind-mills are very noisy. Some people think that wind turbines spoil the beauty
of landscape.
Nuclear power generators are also run by steam produced by nuclear
heat energy. Heat itself is a form of pollution. Moreover, there is always danger of
leakage of the radioactive radiation which is harmful to living bodies. People
living around nuclear plants are always at risk. The disposal of nuclear waste is
another problem for the nuclear power generation. However, any form of waste
energy ends up as thermal energy that goes to the environment. Thus, thermal
pollution is increasing day by day causing global warming.

118
5.7 Power
In many cases, the time to do work is as important as the amount of work
done. Suppose you walk up to a height ‘h’ through upstairs (Fig. 5.26). You do
work, because you are lifting your body up the stairs. If you run up, you can reach
the same height in a shorter time interval.

height (h)

Fig. 5.26
The work done is the same in either case, because the net result is that you lifted
up the same weight w to the same height h. But you know that if you run up the
stairs, you would be more tired than you walked up slowly. In fact, there is a
difference in the rate at which work is done. We say that you expend more energy
when you go up the stairs rapidly than when you go slowly.
The concept of power can also be explained with another example of an electric
motor or a water pump. A bigger motor draws more water during the same
interval of time as compared to a smaller one. It is said that the power of bigger
motor is greater than that of smaller one.

Power is defined as the time rate of doing work.

Mathematically,
Power = Work
Time
If W is the work done in time t, then
P = W................ (5.5)
t
Power of any agency can also be defined as energy transferred per unit time.
119
Units of Power
Since both work and time are scalar quantities, so according to Eq.(5.5)
power is also a scalar quantity. The SI unit of powers is watt (W).

One watt is the work done at the rate of one joule per second.

Do You Know?
1W= 1J or 1Js Av. Power
-1

1 Appliance (watts)
Bigger Units of power are: Energy saver 23
Tube light 40
1 kW = 10 ³ W Electric fan 80
1 MW = 10⁶ W Bulb 100
T.V. 200
In British engineering system, the unit of power used Washing machine 250
Refrigerator 600
is horse-power (hp). The horse power is defined as Electric iron 1000
1 hp = 746 W Toaster 1000
Microwave oven 1200
Example 5.5 Air conditioner 2500

A 1000 kg car moving with an acceleration of 4 m s–2 covers a distance of

50 m in 5 seconds. What is the power generated by its engine?
Solution
Mass of car m = 1000 kg
Acceleration a = 4 m s–2
Distance S = 50 m
Time taken t=5s
Power P=?
First, we shall determine the force applied by Newton's second law.
F = ma = 1000 kg × 4 m s = 4000 N
–2

From Eq. (5.1), Work, W = FS For Your Information!

The watt is named in
Or W = 4000 N × 50 m = 2.0 × 105 J honour of James Watt
From Eq. (5.5), P = W (1736-1819), a Scottish
engineer who perfected
t
the steam engine.
Putting the values of W and t, we have

P = 2.0 × 10 J
5
= 4 × 104 W = 40 kW
5s

120
5.8 Efficiency Do You Know?
Average
Activity
The efficiency of a working system tells us Efficiency (%)
Diesel engine 35
what part of the energy can be converted into the Petrol engine 25
required useful form of energy and what part is Electric motor 80
wasted out of the energy available. Bicycle 15
The available energy for conversion is usually
called the input energy and the energy converted For Your Information!
into the required form is known as the output A machine with it's output
energy. equal to input is called an
The efficiency of a system is defined as: idealmachine with
efficiency 100%
The ratio of useful output energy and the total input
energy is called the efficiency of a working system.

Useful output energy

or Efficiency =
Total input energy
Efficiency is often multiplied by 100 to give percentage efficiency. Thus,
Useful output energy
Percentage Efficiency = × 100
Total input energy
It can also be given as:
Useful power output
Percentage Efficiency = × 100 .......... (5.6)
Total power input
It is found that the energy output is always less than the energy input. During any
conversion of energy, some energy is wasted in the form of heat. No device has
yet been invented that may convert all the input energy into required output.
That is why a system cannot have an efficiency of 100 %. As the energy losses are
inevitable in the working of a machine, hence, an ideal or perpetual machine
cannot be constructed.
Perpetual Energy Machines
It is a hypothetical machine that can do work indefinitely, without any
external source of energy. A perpetual machine would have to generate more
energy than it consumes, effectively producing energy from nothing, which is
impossible. In any real mechanical system, some energy is always lost as heat due
to friction between moving parts and air resistance etc. Thus, making it
impossible for a machine to keep moving without an external source of energy.
Infact, it is a consequence of the principle of conservation of energy that a
perpetual energy machine is not workable.

121
Example 5.6
A block weighing 120 N is dragged up a slope with a force of 100 N to lift it up a
height of 10 m. If the slope is 20 m long, calculate the efficiency of the system.
Solution
Weight of block W = 120 N
Force applied F = 100 N
Distance S = 20 m 10 m
Height h = 10 m
% Efficiency = ?
Work done to lift the block up is:
W = F × S = 100 N × 20 m = 2000 J
Now, total input energy = work done on the block = 2000 J
Useful output energy = Gravitational potential energy gained = wh
= 120 N × 10 m = 1200 J
Useful output energy
Percentage Efficiency = × 100
Total input energy
1200 J
= × 100 = 60%
2000 J
KEY POINTS
 Work is defined as the product of the magnitude of force and the distance covered in
the direction of force.
 Work will be one joule if a force of one newton moves a body through a distance of
one metre in the direction of the force.
 Energy is the ability of a body to do work. Its unit is also joule.
 Kinetic energy is the energy of a body by virtue of its motion.
 Gravitational potential energy is defined as the energy that a body possesses by virtue
of its position in the gravitational field.
 The potential energy stored in a compressed or stretched spring is known as elastic
potential energy.
 Fossil fuel energy is the energy that is released by burning of oil, coal and natural gas.
 Hydroelectric generation is the electricity generated by using the kinetic energy of
the falling water.
 Solar energy is the energy of the Sunlight that can be converted into electricity.
 The energy released by breaking the nucleus of an atom is known as nuclear energy.
 Geothermal energy is the heat energy of the hot rocks present deep under the surface
of the Earth.
 Wind energy is the electrical energy produced by using the kinetic energy of the fast-
blowing wind.
 Biofuel energy is that energy which is obtained by fermentation of organic materials
in the form of biogas or ethanol.
 Power is defined as the time rate of doing work.
 Power will be one watt, if one joule of work is done in one second.
 The ratio of useful output energy to the total input energy is called the efficiency of a
working system.
122
 EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
5.1. Work done is maximum when the angle between the force F and the
displacement d is:
(a) 0° (b) 30° (c) 60° (d) 90°
5.2. A joule can also be written as:
(a) kg m s–2 (b) kg m s–1 (c) kg m2s–3 (d) kg m2s–2

5.3. The SI unit of power is:

(a) joule (b) newton (c) watt (d) second
5.4. The power of a water pump is 2 kW. The amount of water it can raise in
one minute to a height of 5 metres is:
(a) 1000 litres (b) 1200 litres
(c) 2000 litres (d) 2400 litres
5.5. A bullet of mass 0.05 kg has a speed of 300 m s−1. Its kinetic energy will be:
(a) 2250 J (b) 4500 J (c) 1500 J (d) 1125 J
5.6. If a car doubles its speed, its kinetic energy will be:
(a) the same (b) doubled
(c) increased to three times (d) increased to four times
5.7. The energy possessed by a body by virtue of its position is:
(a) kinetic energy (b) potential energy
(c) chemical energy (d) solar energy
5.8. The magnitude of momentum of an object is doubled, the kinetic energy
of the object will:
(a) double (b) increase to four times
(c) reduce to one-half (d) remain the same
5.9. Which of the following is not renewable energy source?
(a) Hydroelectric energy (b) Fossil fuels
(c) Wind energy (d) Solar energy

123
B Short Answer Questions
5.1. What is the work done on an object that remains at rest when a force is
applied on it?
5.2. A slow-moving car may have more kinetic energy than a fast-moving
motorcycle. How is this possible?
5.3. A force F₁ does 5 J of work in 10 s. Another force F2 does 3 J of work in 5 s.
Which force delivers greater power?
5.4. A woman runs up a flight of stairs. The gain in her gravitational potential
energy is 4500 J. If she runs up the same stairs with twice the speed, what
will be her gain in potential energy?
5.5. Define work and its SI unit.
5.6. What is the potential energy of a body of mass m when it is raised through a
height h?
5.7. Find an expression for the kinetic energy of a moving body.
5.8. Define efficiency of a working system. Why a system cannot have 100%
efficiency?
5.9. What is power? Define the unit used for it.
5.10. Differentiate between renewable and non-renewable energy sources.

C Constructed Response Questions

5.1. Can the kinetic energy of a body ever be negative?
5.2. Which one has the greater kinetic energy; an object travelling with a
velocity v or an object twice as heavy travelling with a velocity of ½ v?
5.3. A car is moving along a curved road at constant speed. Does its kinetic
energy change?
5.4. Comment on the statement. “An object has one joule of potential energy.”
5.5. While driving on a motorway, tyre of a vehicle sometimes bursts. What may
be its cause?
5.6. While playing cricket on a street, the ball smashes a window pane. Describe
the energy changes in this event.
5.7. A man rowing boat upstream is at rest with respect to the shore. Is he doing
work?
5.8. A cyclist goes downhill from the top of a steep hill without pedalling and
takes it to the top of the next hill.
(i) Draw a diagram of what happened.

124
 (ii) Analyse this event in terms of potential and kinetic energy.
Label your diagram using these terms.
5.9. Is timber or wood renewable source of heat energy? Comment.

D Comprehensive Questions
5.1. What is meant by kinetic energy? State its unit. Describe how it is
determined.
5.2. State the law of conservation of energy. Explain it with the help of an
example of a body falling from certain height in terms of its potential
energy and kinetic energy.
5.3. Differentiate between renewable and non renewable sources of energy.
Give three examples for each.
5.4. Explain what is meant by efficiency of a machine. How is it calculated?
Why there is a limit for the efficiency of a machine?
5.5. Describe the process of electricity generation by drawing a block diagram
of the process in the following cases.
(i) Hydroelectric power generations (ii) Fossil fuels
E Numerical Problems
5.1. A force of 20 N acting at an angle of 60° to the horizontal is used to pull a
box through a distance of 3 m across a floor. How much work is done?
(30 J)
5.2. A body moves a distance of 5 metres in a straight line under the action of a
force of 8 newtons. If the work done is 20 Joules, find the angle which the
force makes with the direction of motion of the body.
(60o)
5.3. An engine raises 100 kg of water through a height of 80 m in 25 s. What is
the power of the engine?
(3200 W)
5.4. A body of mass 20 kg is at rest. A 40 N force acts on it for 5 seconds. What
is the kinetic energy of the body at the end of this time?
(1000 J)
5.5. A ball of mass 160 g is thrown vertically upward. The ball reaches a height
of 20 m. Find the potential energy gained by the ball at this height.
(32 J)
5.6. A 0.14 kg ball is thrown vertically upward with an initial velocity of 35 m s¹.
Find the maximum height reached by the ball.
(61.25 m)
125
5.7. A girl is swinging on a swing. At the lowest point of her swing, she is 1.2 m
from the ground, and at the highest point she is 2.0 m from the ground.
What is her maximum velocity and where?
(4 m s-1, at the lowest position)

5.8. A person pushes a lawn mower with a force

of 50 N making an angle of 45° with the
horizontal. If the mower is moved through a
distance of 20 m, how much work is done?
(707 J)

5.9. Calculate the work done in

(i) Pushing a 5 kg box up a frictionless
inclined plane 10 m long that makes an h
angle of 30° with the horizontal.
(250 J) 30O

(ii) Lifting the box vertically up from the ground to the top of the inclined
plane.
(250 J)
5.10. A box of mass 10 kg is pushed up along a ramp 15 m long with a force of
80 N. If the box rises up a height of 5 m, what is the efficiency of the
system?
(41.7%)
5.11. A force of 600 N acts on a box to push it 5 m in 15 s. Calculate the power.

(200 W)
5.12. A 40 kg boy runs up-stair 10 m high in 8 s. What power he developed.

(500 W)
5.13. A force F acts through a distance L on a body. The force is then increased
to 2F that further acts through 2L. Sketch a force-displacement graph and
calculate the total work done.
(5FL or 5 units)

126
 Chapter
6 Mechanical
Properties of Matter
Student Learning Outcomes

After completing this chapter, students will be able to:

[SLO: P-09-B-54] Illustrate that forces may
produce a change in size and shape of an
object.
[SLO: P-09-B-55] Define and calculate the
spring constant [apply the equation, spring
constant = force/extension k = F/x to solve
problems involving simple springs]
[SLO: P-09-B-56] Sketch, plot and interpret load–
extension graphs for an elastic solid and
describe the associated experimental procedures.
[SLO: P-09-B-57] Define and use the term 'limit of proportionality' for a load-extension
graph [Including identifying this point on the graph (an understanding of the elastic limit is
not required)]
[SLO: P-09-B-58] Illustrate the applications of Hooke's law [Such as that it is the
fundamental principle behind engineering many measurement instruments such as the
spring scale, the galvanometer, and the balance wheel of the mechanical clock.]
[SLO: P-09-B-76] Define and calculate density.
[SLO: P-09-B-77] Define and calculate pressure [As force per unit area. Use the equation
pressure = force/area P= F/ A to solve simple problems]
[SLO: P-09-B-78] Describe how pressure varies with force and area in the context of
everyday examples
[SLO: P-09-B-79] Describe how pressure at a surface produces a force in a direction at right
angles to the surface [can make reference to experiments to verify this principle]
[SLO: P-09-B-80] Justify that the atmosphere exerts a pressure.
[SLO: P-09-B-81] Describe that atmospheric pressure decreases with the increase in height
above the Earth's surface.
[SLO: P-09-B-82] Explain that changes in atmospheric pressure in a region may indicate a
change in the weather.
[SLO: P-09-B-83] Analyse the workings and applications of a liquid barometer
[SLO: P-09-B-84] Justify and analyse quantitatively how pressure varies with depth in a
liquid
[SLO: P-09-B-85] Describe the working and applications of a manometer
[SLO: P-09-B-86] Define and apply Pascal's law [Apply Pascal's law to systems such as the
transmission of pressure in hydraulic systems with particular reference to the hydraulic press
and hydraulic brakes on vehicles.]

127
 You have learnt in lower classes that every thing around us is made up of
matter. The matter normally exists in solid, liquid and gaseous states. These
states are due to attractive force that exist between the atoms and molecules. We
have already studied some basic properties of matter. In this chapter, we will
discuss mechanical properties of matter that are of vital importance for use of a
material for various useful purposes in technology and engineering. The main
contents included in this chapter are: deformation of solids due to some applied
force, density and pressure.
6.1 Deformation of solids
We have observed that an external force applied
on an object can change its size or shape. Such a force is
known as deforming force. For example, an appropriate
force applied to a spring can increase its length called
extension or cause compression thus reducing its
length. If this force is removed, the spring will restore its
original size and shape. Similarly, stretched rubber strip
or band comes to its original shape and size on
removing the applied force.
When a tennis ball is hit by a racket, the shapes of tennis Fig. 6.1
ball and also racket strings are distorted or deformed
(Fig. 6.1). They regain their original shape after
For Your Information!
bouncing of the ball by the racket. An object is said to
Some materials such as
be elastic, if after removal of the deforming force, it
clay dough or plasticine
restores to its original size and shape. This property of do not return to their
the material is known as elasticity. Due to this property, original shape after the
we can determine the strength of a material and the r e m o v a l o f t h e
deformation produced under the action of a force. deforming force. They
Most of the materials are elastic up to a certain are known as inelastic
materials.
limit known as elastic limit. Beyond the elastic limit, the
change becomes permanent. The object or material does not regain its original
shape or size even after the removal of the deforming force.

6.2 Hooke’s law

If force F is applied on a spring to stretch or compress it, the extension or
compression x has been found directly proportional to the applied force within
the elastic limit. Thus, F∝x F .............
or or k= (6.1)
F = kx
x
128
where k is the constant of proportionality and is known as spring constant. In fact,
it is a measure of stiffness of the spring. The greater the value of spring constant,
the greater will be the stiffness or strength of the
A
spring. Its unit is N m-1. Elastic limit
A graph of force against extension is a straight
line passing through the origin. If the applied force or F
load exceeds the elastic limit of the spring, it is (N)
permanently deformed and its graph will no longer O x
remain linear. The gradient or slope of force-extension (m)
graph is a measure of spring constant k.
Fig. 6.2
Hooke’s law also holds when a force is applied to a straight thin wire or a
rubber band within its elastic limit.
Activity 6.1

The teacher will arrange a helical spring with an

attached pointer, slotted weights, half metre rule or
scale, iron stand and will facilitate to perform this activity
as per instructions. Note that a spring of helical or spiral
shape is called helical spring. Its length should be greater
than its diameter.
(i) Suspend a helical spring with the stand.
(ii) Adjust the pointer so that it does not touch the
scale but can move up and down freely along
the scale.
(iii) Place a slotted weight say 50 g in the hanger and
note the position of pointer on the scale.
(iv) Repeat this step for five times, each time
increasing the load in equal amount.
(v) Draw a graph between force F along y-axis and
extension along x-axis.
(vi) What is the shape of the graph?
(vii) What does it show?
(viii) Find the slope of the straight line. What does it
represent?

Quick Quiz
1. If the above experiment is repeated with a stiffer spring (high value of k), what will be the
effect on the graph?
2. How can you find the value of unknown weight using this experiment?

129
Applications of Hooke's Law
Hooke's law serves as the basic principle in wide range of applications. In
the field of technology and engineering, springs in many devices rely on Hooke's
law for their functions such as spring scales, balance wheel of the mechanical
clocks, galvanometer, suspensions system in vehicles and motorbikes, door
hinges, mattresses, material testing machines, etc.
However, Hooke's law applies within a
specific range of forces. Exceeding the range or
limit results in permanent deformation and no
longer follows Hooke's law. Some of the uses are
elaborated below:
1. Spring scales
Springscalesusethe extension or Fig. 6.3 Spring scales
compression of a spring to determine the weight
of objects. In a common spring balance the Balancing
spring
extension or elongation produced is a measure of
the weight. In compression balance, the spring is
compressed by the load (force) and the Fig. 6.4
compression produced is measured by means of a
pointer moving over a scale. Weighing machine usually use this type of balance.
2. Balance wheel of mechanical clocks
The balance wheel in mechanical clocks use spring to control the back and
forth motion that regulates the speed of the hands of a clock (Fig. 6.4).
3. Galvanometer
Galvanometer is a current detecting
device. It makes use of a tiny spring called hair
spring (Fig. 6.5) which provides electrical
connections to the galvanometer coil and also
restores the pointer back to zero position. The
deflection of the pointer is proportional to the
current flowing through it within the range.
6.3 Density Inside of a
Galvanometer
If you take equal volumes of different Fig. 6.5
substances and weigh them by a balance, you will

130
find that each of them has a different mass. That is, one centimetre cube of wood
may weigh only 0.7 g but made of iron will weigh 8.0 g. Why is it so? You know
that all substances are composed of molecules. The molecules of different
substances are different in size and mass. The inter-molecular spacing is also
different.
The mass of equal volume of various substances actually is the mass of the
total number of molecules present in that volume. Naturally, the substance
whose molecules are densely packed and also which are heavy will weigh more
than others.
Density of a substance is defined as its mass per unit volume.
Mass
Density = Volume . .......... (6.2) For Your Information!
Packing foam or polythene
The SI unit of density is kg m-3. Other unit also
has a very low density.
in use is g cm-3. Table 7.1 shows the density of some
substances. Table 7.1
The architects and engineers take special Substance Density (kg m-3)
care of the density of the building material to be Air 1.3
used in designing and constructing roads, bridges Patrol 800
and buildings. The density of building material is Water 1000
essential for estimating the strength required in Concrete 2400
foundations and supporting pillars. Aluminum 2700
Example 6.1 The length, breath and thickness of Steel 7800
Lead 11400
an iron block are 3 cm, 2 cm, 2 cm respectively.
Gold 19300
Calculate the density of iron if the mass of block is
Osmium 22600
94 g.
Solution For Your Information!
Given Length = 3 cm, Breath = 2 cm, Immiscible liquids of
Thickness = 2 cm, Mass = 94 g, Density = ? different densities
Mass form layers when
Density = they are mixed.
Using Eq. 6.2 Volume
Quick Quiz
where volume = Length × Breadth × Thickness How will you measure the
= 3 cm × 2 cm × 2 cm = 12 cm3 volume if the object is lighter
than the liquid?
94 g
Hence, Density = = 7.8 g cm–3
12 cm 3 For Your Information!
Thus, density of iron = 7800 kg m–3 Density is a test to know the
purity of a substance.

131
Density Measurement Quick Quiz
By which property can you
Density of a substance can be determined by identify a silver spoon and a
measuring its mass and volume. The mass can be stainless steel spoon?
easily measured by a physical balance.
If the substance is solid and has a regular shape, its volume can be found
by measuring its dimensions. For example, if the substance is in the form of a
sphere, its diameter can be measured by a Vernier Callipers and volume is
thereby calculated. Knowing mass and volume, the density can be found out. If
the solid has not a geometrical shape, its volume is determined by the following
activity:
Activity: 6.2
Teacher should facilitate to help the groups to pour some
water in a measuring cylinder. If the substance is soluble in water,
then use a liquid in which the substance is insoluble. Note the level
of the liquid in the cylinder. Now gently drop the substance into
the cylinder. The rise in the level gives the volume of the substance.

6.4 Pressure
If a wooden rod has a flat end, it will be very For Your Information!
difficult to push it into ground. On the other hand, if
it has a pointed end, it can be easily pushed into the
ground. In the first case, the applied force is spread
over a large area, whereas in the second case, the
force is concentrated on a small area. The force
applied on the rod will exert greater pressure in the
The force in both the pictures is
second case than in the first one. same, equal to weight of the
bag. In right hand picture, the
Pressure is defined as the force exerted
area of contact is the greater
normally on unit area of an object. than in the left hand picture.
We say that the pressure is less
If F is the force acting normally on a surface
in the right hand picture.
of area A, then pressure P on the surface is given by
F ..............
P= (6.3)
For Your Information! A
Sports boots for football and hockey have studs on their soles.
They reduce the area in contact between your feet and the
ground. This increases the pressure and your feet grip the surface
more firmly.
132
 The area A on which the force acts is usually referred as contact area.
Equation (6.3) shows that for a certain force, the pressure can be very large if the
contact area A is small.
In the system international, the unit of pressure is N m-2 and is called
pascal (Pa).
Daily Life Examples
1. The edge of the blade of a chopper is made
very sharp. When we apply force on the
handle of the chopper to cut an object, the
pressure on the object, at the contact
surface, due to its small area becomes very Fig. 6.6 Chopper
high and the object is easily cut (Fig. 6.6).
2. The top of a thumb pin is flat but the end of
the pin is very sharp. So, the contact area is
very small. When we apply a force at the top,
the pressure at the end of pin is so high that
it pierces into the wooden board (Fig. 6.7).
3. When we walk on ground, we exert a force
on it due to which we experience a reaction Fig. 6.7 Thumb pin
force. When the ground is flat, this reaction Brain Teaser!
force is spread over the whole area of the Why a bulldozer has large pillar
foot and the pressure due to reaction force tracks instead of wheels?
is not painful. But when we walk on pebbles,
the contact area is reduced. Then the
pressure due to reaction force becomes so
high that it becomes painful.
4. Heavy animals like elephant have thick legs
and large flat feet so that due to large
contact area, pressure becomes less
otherwise, their bones would not tolerate the pressure.

6.5 Pressure in Liquids

We have learnt in the lower classes that liquids exert pressure in all
directions. Moreover, liquid pressure increases with depth.
Let us determine the pressure at a certain depth of a liquid. Figure. 6.8
shows a container of liquid. Consider an area A in the liquid at depth h. The force
acting on this area is equal to the weight of the liquid column over surface A. The
volume of this liquid is V = Ah. If ρ is the density of liquid, then mass m of the
liquid column will be:
m = ρV = ρAh
133
Therefore, force acting on area A will be
F = mg = ρ Ahg
The pressure P at area A will be,
F ρAhg
P =A =
A
Or P = ρgh ...........................(6.4)
P
Equation 6.4 shows that pressure in a h
mg
liquid increases with depth. The value of pressure A
depends on the depth and density of the liquid.
Pressure produces force at right angle to
the surface. A force or its component that is
parallel to the surface, does not contribute to
pressure. The pressure, by definition, is only Fig. 6.8 Pressure in a liquid

contributed by the normal component of the force. That is, the forces in a liquid
that push directly against the surface and add up to a net force is perpendicular
to the surface. If there is a hole in the surface of the liquid container, the liquid
spurts at right angle to the surface before curving downward due to gravity.

Example 6.2
Calculate the pressure of column of mercury 76 cm high. Density of
mercury is 13.6 × 103 kg m-3.

Solution
For Your Information!
Density ρ = 13.6 × 103 kg m-3 Some liquids under pressure
Height h = 76cm =76 ×10-2m can dissolve more gas than a
g = 10 m s-2 liquid at a lower pressure. When
we open a bottle of soda water,
Pressure = ρgh the pressure in the bottle is
P =13.6 × 103 kg m-3 × 10 m s-² × 76 × 10-2 m decreased. The liquid can no
P = 1.034 × 105 kg m-³ × m s-² × m longer hold as much gas. The
dissolved gas comes out of the
P = 1.034 × 105 N m -2 solution and rises to the surface
P = 1.034 ×105 Pa of the liquid in the form of
bubbles.
Example 6.3
A cylindrical water tank 2 m deep has been built on the top of a building
20 m high. What will be the pressure of water at the ground floor when the tank is
full? Density of water is 1000 kg m-3. Take g = 10 m s-2.
134
Solution
Height h = 2 + 20 = 22 m
Density ρ = 1000 kg m-3
g =10 m s-2
P = ρgh = 22 m × 1000 kg m-3 × 10 m s-2
= 220000 Pa = 2.2 ×105 Pa
Activity 6.3
Teacher should help the students to perform this
activity and initiate discussion as per instructions:
i. Make three small holes at different heights in the side of a
container as shown in the given figure.
ii. Fill the container with water.
iii. Observe the water streams flowing out of the holes. It is
initially normal to the surface.
iv. Which one of the streams hits the ground at larger
distance?
v. At which position the liquid has more pressure?
You will observe that the stream from each hole, initially flows out normal to the surface before
curving down due to gravity and the lowest hole has more pressure. It shows that liquid pressure
increases with depth.

Activity 6.4
Teacher should demonstrate or help the students to
perform by following the instructions given below:
(i) Fill a polythene shopping bag with water.
(ii) Poke several holes by using a pin on the bag.
(iii) Squeeze the bag gently.
(iv) What do you observe?
Squeezing the top of bag causes the water to squirt on
in all directions. It means the pressure is transmitted equally
throughout the liquid.

6.6 Atmospheric Pressure

The Earth is surrounded by a layer of air which we call atmosphere. We
know that air is a mixture of gases. Their molecules are always in motion. They
collide with one another and with all other objects coming in their way. Thus, they
exert force on the objects. This force per unit area is the atmospheric pressure.
Since the molecules of air have random motion, therefore, atmospheric pressure
acts equally in all directions.
The atmosphere exerts pressure on the surface of the Earth and on
everything on the Earth. This pressure is called atmospheric pressure.

135
 Atmospheric pressure extends up to a Do You Know?
height of about 100 kilometres. The density of air is The pressure of 1 atmosphere
is equivalent to placing a
not the same in the atmosphere. It decreases 1.0 kg mass (10 N weight) on
continuously with altitude. an area of 1 cm².

We live at the bottom of the Earth's atmosphere which is a fluid that exerts
pressure on our bodies. At sea level, the value of atmospheric pressure is about
1.013 × 10 Pa. This value is referred to as standard atmospheric pressure. It is an
5

enormous pressure which can crush anything. We do not feel it because

practically all the bodies have air inside them. As atmospheric pressure acts in all
directions, so it balances the pressure inside.

Evidence of Atmospheric Pressure

We can observe the force of the atmospheric pressure if we remove the
inside air from a vessel as shown in the following activity.

Activity 6.5

The teacher should perform this activity in the

class following the instructions given.
Boil some water in a tin can. When it is full of
steam, remove it from the burner and close its mouth by
an air tight cork. Then pour cold water over it. The can
crumples as shown in the given figure. Why does the tin
crumples?

Variation of Atmospheric Pressure with Height

We have studied that pressure in a liquid increases with depth. At depth h,
the pressure of liquid is given by
P = ρgh
This formula is applicable to all the fluids. As the gases of the atmosphere
are also fluid, therefore, the atmospheric pressure should be maximum on the
ground at sea level. As we go up in the air, atmospheric pressure decreases. At a
height of about 5 km, it falls to 55 kPa and at a height of 30 km it falls to 1 kPa. By
measuring the atmospheric pressure at a point in air, altitude of that point can be
determined. The lower the atmospheric pressure, the greater is the altitude.
136
6.7 Measurement of Atmospheric Pressure
Atmospheric pressure is usually measured by
Glass
the height of mercury column which it can support. tube
Vacuum

Instruments which measure the atmospheric

pressure are called barometers. A simple mercury Scale
barometer consists of a glass tube about one metre
long that is closed at one end. It is completely filled Air
Pressure
with mercury, then it is inverted vertically in a dish of
mercury. A metre scale is placed by the side A B
of the tube to measure the height of mercury column
(Fig. 6.9). The space in glass tube over the top of the
mercury is completely empty. The pressure is almost
zero. Fig 6.9 Barometer

The pressure P, at point A in the

mercury column is the same as at point B at For Your Information!
the surface of mercury in the dish because
both the points are at the same level. This is
equal to the atmospheric pressure P = ρgh
acting at the surface of mercury in the dish.

For Your Information!

Air pressure guage which is used to measure the A Fortin's Barometer is used in
pressure in motor car tyres. l a b o r a t o r ie s to m easu re the
atmospheric pressure.

If we put P = 1.013 × 10 Pa at sea level, Quick Quiz

5

Would you exert more,

ρ = 13.6 × 10³ kg m-³ for mercury, the height of
same or less pressure on
mercury column comes out to be 760 mm. By using the ground if you stand
this instrument atmospheric pressure at any altitude on one foot instead of
in the air can be measured in terms of height of two feet?
mercury column.
137
Changes in Atmospheric Pressure as Weather Indicator
The atmospheric pressure does not always Quick Quiz
remain uniform but flactuates. By observing the Can we use water in place
variation, the meteorologists can forecast the of mercury to construct a
weather conditions. barometer? Explain why.
Atmospheric pressure depends upon the
density of air. At high altitudes, where the air is less dense, the atmospheric
pressure falls down. Similarly, increase in the quantity of water vapours also
decreases the density. Thus, atmospheric pressure becomes low in cloudy
regions. Weather casters use this knowledge to predict rains. A fall in pressure
often means that rain clouds are on the way and the rain is to follow.
6.8 Measurement of Pressure by Manometer
A simple manometer consists of a
U-shaped glass tube which contains mercury. In
the beginning, the atmospheric pressure at the
two open ends of the tube is the same and
hence, mercury level in the two arms remains
same (Fig. 6.10). If on connecting a gas cylinder
with short arm keeping the longer arm of the
tube open, the mercury level in short arm is
lower than that in the long arm (Fig. 6.11), then
the unknown pressure is more than the
atmospheric pressure. If the mercury level in the
short arm is more than the long arm (Fig.6.12), Fig. 6.10 manometer
then the unknown pressure is less than the
atmospheric pressure.

Air pressure Gas cylinder

h
h

Fig. 6.11 Fig. 6.12

138
6.9 Pascal’s Law
When we inflate a balloon, we blow air Some Typical Pressures
in it with a certain pressure but the balloon Location Pressure (Pa)
blows uniformly from all sides. It means that Sun's centre 2 × 1016
the pressure applied at its mouth has been Earth's centre 2 × 1011
transmitted uniformly in all directions. Deepest ocean trench 1.1 ×1018
Similarly, when a motorbike tyre is inflated, A motor tyre 2 × 105
air pressure is applied at one point but the Standard atmospheric 1.013 × 105
tyre is uniformly inflated from all sides. This Blood pressure 1.6 × 104
indicates that pressure is transmitted to each On mount Everst 4 × 104
part of the tyre. On mars 7 × 102

Let us perform a very interesting activity with a liquid. Take water in a flask
with piston and having a few side tubes fixed at different positions. If such flask is
not available you can join a syringe at the mouth of a pet bottle. For side tubes,
bendable transparent drinking straws can be glued on the holes punched on
sides of the bottle.
You will observe that the level of water in all the side tubes is the same. This
is because a liquid seeks its own level and rises to
the same height at all points. Now push the piston Side
Piston
tubes
through some distance.
The level of water in all the side tubes rises
to the same height. Why does this happen? This is
because the pressure applied at one point of the
liquid is transmitted equally to every point of the
liquid. Since gases (air) and liquids are termed as
fluids so the above activities prove that:

When pressure is applied at one point in

an enclosed fluid, it is transmitted Flask Water
equally to all parts of fluid without loss. Fig. 6.13

This is the statement of Pascal's law.

The technology of hydraulic systems is based on Pascal's law. Its main
advantages are:
(I) Liquids do not absorb any of the supplied energy.
(ii) They are capable of moving much heavy loads and providing great forces
due to incompressibility.
Some useful hydraulic systems are:
1. Hydraulic press
2. Car lift at service stations
3. Hydraulic brakes of vehicles
139
Hydraulic Press
Consider a specially designed container as shown in Fig. 6.14. In this
container there are two cylinders joined by means of a pipe. The cross-sectional
area of the smaller cylinder is A 1 F1
and that of the larger one is A 2. F2
The cylinders are filled with some
incompressible liquid.
Suppose that the small piston is Piston
A1 area
pressed down by applying a
force F1. The pressure P = F1 / A1 A2
Piston area
produced by small piston is
transmitted equally to the large
piston. Liquid
Pipe
Due to this pressure P, a force F2,
will act on A2 , which is given by Fig. 6.14
F =PA
2 2

Putting the value of P,

F1
2F = A2 ...................................................(6.5)
A1
Since A₂ > A1, therefore, F₂ > F₁. The result indicates that a small force
applied on the smaller piston, results into a large force on the larger piston. Such
a system is known as force multiplier.
A hydraulic press works on this principle. Cotton bale or any other object
to be compressed is placed over the larger piston. A force F₁ is applied on the
smaller piston. The pressure P produced by smaller piston is transmitted equally
to the larger piston. A much greater
force F2 acts on it. This force lifts the
larger piston and compresses the
cotton bale.
This principle is also used at
service stations to lift cars for
washing (Fig. 6.15).

Example 6.4 Fig. 6.15

The diameters of the pistons of a hydraulic press are 5 cm and 25 cm

respectively. A normal force of 160 N is applied on the smaller piston, what will be

140
the pressure exerted by this force on the bigger piston? How much weight can be
lifted by the other piston?
Solution
Let the areas of cross-sections of the pistons be A 1 and A and their radii be
r 1 and r respectively.
25
Putting the values of r = 5 cm = 2.5 × 10-2 m r = cm = 12.5 × 10 m
-2

1
2 2
2
A1 = π r and A2 = π r 2
2

Force on the smaller piston F₁ = 160 N. Its pressure on the piston is

F F
P= 1 = 1
A1 π r 12
If the weight lifted by the bigger piston is w, then according to the Pascal's law.
F1 w
A1 =
A2
F 1πr 2 F1 × r
2
F1 2
or w = = =
A1 πr 12 r12

Putting the values,

w =160 N × (12.5 × 10-2 m)² / (2.5 × 10-2 m)² = 4000 N = 4 kN
So, we can lift 4000 N weight by applying a force of 160 N on smaller piston.
Hydraulic Brakes
The brakes of some vehicles
work on Pascal's law. In such type Larger
brake
of brakes, cylinders with pistons are Brake
cylinder
pads
attached to the wheels. The brake
brake
pedal is attached to a master fluid

cylinder having smaller area of

cross-section. Master cylinder is Smaller
Brake piston
connected to all the larger line
Master
cylinders attached to the wheel cylinder Brake
through pipes as shown in pedal

Fig. 6.16. Oil is filled in this system.

When pedal is pushed down, the
piston applies pressure on the
liquid in the master cylinder. The Tyre
liquid pressure is transmitted Fig. 6.16 Hydraulic brake system
141
equally to all the larger pistons of other cylinders. This pressure causes these
pistons to move outward pressing the brake pads towards brake discs or brake
drums. Force of friction between the pads and discs or drums slows down the
vehicle. When pressure is released from the pedal, the springs pull back the brake
pads and wheels again turn freely.

Activity 6.6 Plunger

moving out
The teacher should facilitate the groups to
follow the instructions given below.
i. Fill a syringe with water and insert its nozzle
into a thin plastic tube.
ii. Press the syringe to fill the tube with water.
iii. Half fill the second syringe with water and Plunger
insert its nozzle to the other end of the tube. pressed in
iv. Press one plunger in through some distance.
v. Is the second plunger pushed out through the
same distance?
vi. Is the pressure transmitted to the second
plunger by the liquid? Water
vii. What is your inference?
Plastic tube

KEY POINTS
 Elasticity is the property of solids by which they come back to their original
shape when deforming force ceases to act.
 Within the elastic limit of a helical spring, the extension or compression in it is
directly proportional to the applied force. This is known as Hooke's law.
 Density is defined as mass per unit volume.

Pressure is the force that acts normally on unit area of a surface. Its SI unit is
pascal = 1 N m-2
 Atmospheric pressure is the force exerted by the atmosphere acting on unit area
of the Earth’s surface.
 Atmospheric pressure is measured by the column of mercury which the
atmospheric pressure can support.
 If pressure is exerted on a liquid, the liquid transmits it equally in all directions.
This is known as Pascal's law.

142
 EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
6.1. A wire is stretched by a weight w. If the diameter of the wire is reduced to
half of its previous value, the extension will become:
(a) one half (b) double
(c) one fourth (d) four times
6.2. Four wires of the same material are stretched by the same load. Their
dimensions are given below. Which of them will elongate most?
(a) Length 1 m, diameter 1 mm (b) Length 2 m, diameter 2 mm
(c) Length 3 m, diameter 3 mm (d) Length 4 m, diameter 0.5 mm
6.3. Two metal plates of area 2 and 3 square metres are placed in a liquid at the
same depth. The ratio of pressures on the two plates is:
(a) 1:1 (b) 2 : 3
(c) 2:3 (d) 4:9
6.4. The pressure at any point in a liquid is proportional to:
(a) density of the liquid
(b) depth of the point below the surface of the liquid
(c) acceleration due to gravity
(d) all of the above
6.5. Pressure applied to an enclosed fluid is:
(a) increased and applied to every part of the fluid
(b) diminished and transmitted to the walls of container
(c) increased in proportional to the mass of fluid and then transmitted to
each part of the fluid
(d) transmitted unchanged to every portion of the fluid and walls of
containing vessel
6.6. The principle of a hydraulic press is based on:
(a) Hooke's law
(b) Pascal's law
(c) Principle of conservation of energy
(d) Principle of conservation of momentum
6.7. When a spring in compressed, what form of energy does it possess?
(a) Kinetic (b) Potential (c) Internal (d) Heat
6.8. What is the force exerted by the atmosphere on a rectangular block
surface of length 50 cm and breadth 40 cm? The atmospheric pressure is
100 kPa.
(a) 20 kN (b) 100 kN (c) 200 kN (d) 500 kN
143
B Short Answer Questions
6.1. Why heavy animals like an elephant have a large area of the foot?
6.2. Why animals like deer who run fast have a small area of the foot?
6.3. Why is it painful to walk bare footed on pebbles?
6.4. State Pascal's law. Give an application of Pascal's law.
6.5. State what do you mean by elasticity of a solid.
6.6. What is Hooke's law? Does an object remain elastic beyond elastic limit?
Give reason.
6.7. Distinguish between force and pressure.
6.8. What is the relationship between liquid pressure and the depth of the
liquid?
6.9. What is basic principle to measure the atmospheric pressure by a simple
mercury barometer?
6.10. State the basic principle used in the hydraulic brake system of the
automobiles.
C Constructed Response Questions
6.1. A spring having spring constant k hangs vertically from a fixed point. A
load of weight L, when hung from the spring, causes an extension x, the
elastic limit of the spring is not exceeded.
Some identical springs, each with spring constant k, are arranged as
shown below:
For each arrangement, complete the table by determining:
(i) the total extension in terms of x.
(ii) the spring constant in terms of k.
Spring constant (k) of
Arrangement Total Extension x the arrangement

144
6.2. Springs are made of steel instead of iron. Why?
6.3. Which of the following material is more elastic?
(a) Iron or rubber (b) Air or water
6.4. How does water pressure one metre below the surface of a swimming
pool compare to water pressure one metre below the surface of a very
large and deep lake?
6.5. What will happen to the pressure in all parts of a confined liquid if pressure
is increased in one part? Give an example from your daily life where such
principle is applied.
6.6. If some air remains trapped within the top of the mercury column of the
barometer which is supposed to be vacuum, how would it affect the
height of the mercury column?
6.7. How does the long neck
is not a problem to a
giraffe while raising its
neck suddenly?

6.8. The end of glass tube used in a simple barometer is not properly sealed,
some leak is present. What will be its effect?
6.9. Comment on the statement, “Density is a property of a material not the
property of an object made of that material.”
6.10. How the load of a large structure is estimated by an engineer?
D Comprehensive Questions
6.1. What is Hook’s law? Give three applications of this law.
6.2. Describe the working and applications of a simple mercury barometer
and a manometer.
6.3. Describe Pascal’s Law. State its applications with examples.
6.4. On what factors the pressure of a liquid in a container depend? How is it
determined?
6.5. Explain that atmosphere exerts pressure. What are its applications. Give at
least three examples.

145
 E Numerical Problems
6.1 A spring is stretched 20 mm by a load of 40 N. Calculate the value of spring
constant. If an object cause an extension of 16 mm, what will be its
weight?
(2 kN m , 32 N)
-1

6.2 The mass of 5 litres of milk is 4.5 kg. Find its density in SI units.
(0.9 × 103 kg m-3)
6.3 When a solid of mass 60 g is lowered into a measuring cylinder, the level
of water rises from 40 cm³ to 44 cm³. Calculate the density of the solid.
(15 × 103 kg m-3)
6.4 A block of density 8 x 103 kg m-3 has a volume 60 cm3. Find its mass.
(0.48 kg)
6.5 A brick measures 5 cm × 10 cm × 20 cm. If its mass is 5 kg, calculate the
maximum and minimum pressure which the brick can exert on a
horizontal surface.
(1 × 10 Pa, 25 × 10 Pa)
4 2

6.6 What will be the height of the column in barometer at sea level if mercury
is replaced by water of density 1000 kg m-3, where density of mercury is
13.6 × 10 kg m
3 -3

(10.3 m)
6.7 Suppose in the hydraulic brake system of a car, the force exerted normally
on its piston of cross-sectional area of 5 cm² is 500 N. What will be the
pressure transferred to the brake oil? What will be the force on the second
piston of area of cross-section 20 cm2?
[1.0 × 106 N m-2, 2000 N]
6.8 Find the water pressure on a deep-sea diver at a depth of 10 m, where the
density of sea water is 1030 kg m-3.
(1.03 × 105 N m-2)
6.9 The area of cross-section of the small and large pistons of a hydraulic
press is respectively 10 cm2 and 100 cm². What force should be exerted on
the small piston in order to lift a car of weight 4000 N?
(400 N)
146
6.10 In a hot air balloon, the following data was recorded. Draw a graph
between the altitude and pressure and find out:
(a) What would the air pressure have been at sea level?
(b) At what height the air pressure would have been 90 kPa?
Altitude Pressure
(m) (kPa)

150 99.5
500 95.7
800 92.4
1140 88.9
1300 87.2 (a). 1.01 × 105 Pa
1500 85.3 (b). 1.02 km

6.11 If the pressure in a hydraulic press is increased by an additional 10 N cm-2,

how much extra load will the output platform support if its cross-sectional
area is 50 cm ?
2

(500 N)

6.12 The force exerted normally on the hydraulic brake system of a car, with its
piston of cross sectional area 5 cm2 is 500 N. What will be the:
(a) pressure transferred to the brake oil?
(b) force on the brake piston of area of cross section 20 cm2?
[(a) 1.0 × 106 N m-2, (b) 2000 N)]

147
 Thermal Properties
Chapter
7
of Matter
Student Learning Outcomes

After completing this chapter, students will be able to:

[SLO: P-09-C-01] Describe, qualitatively, the
particle structure of solids, liquids and gasses
[Including and relating their properties to the
forces and distances between particles and
to the motion of the particles (atoms,
molecules, ions and electrons)].
[SLO: P-09-C-02] Describe plasma as a
fourth state of matter [In which a significant
portion of the material is made up of ions or
electrons e.g. in stars, neon lights and
lightning streamers].
[SLO: P-09-C-03] Describe the relationship between the motion of particles and temperature
[including the idea that there is a lowest possible temperature (approx.-273°C), known as
absolute zero, where the particles have least kinetic energy]
[SLO: P-09-C-04] State that an increase in the temperature of an object increases its internal
energy
[SLO: P-09-C-05] Explain, with examples, how a physical property which varies with
temperature may be used for the measurement of temperature
[SLO: P-09-C-06] Justify the need for fixed points in the calibration of thermometers
[including what is meant by the ice point and steam point.]
[SLO: P-09-C-07] illustrate what is meant by the sensitivity, range and linearity of
thermometers.
[SLO: P-09-C-8] Differentiate between the structure and function of liquid-in-glass and of
thermocouple thermometers
[SLO: P-09-C-9] Discuss how the structure of a liquid in-glass thermometer affects its
sensitivity, range and linearity

Heat or thermal energy has always been the necessity of human beings,
animals and plants in this world. Without heat, their existence would not have
been possible. In the beginning, the Sun was the only source of light and heat.
With the discovery of fire, a new era was started. The uses of heat produced from
fire were increased day by day and contributed greatly to the comforts and
facilities for the human being. Initially, the hot and cold objects were sensed by
touching which was not a good standard to measure the degree of hotness of an
148
object. So, man evolved different methods to measure it. After the invention of
standard measuring devices, the temperature was also included in the list of
basic physical quantities like mass, length and time.
This chapter begins with the introduction of kinetic molecular theory of
particles of matter. It is due to the fact that temperature and heat or internal
energy are associated with the motion of particles in the matter.
7.1 Kinetic Molecular Theory of Matter
According to this theory, matter is composed of very small particles called
molecules which are always in motion. Their motion may be vibrational,
rotational or linear. There exists a mutual force of attraction between the
molecules known as intermolecular force. This force depends upon the distance
between the molecules. It decreases with increasing distance between them.
The molecules possess kinetic energy due to motion and potential energy
due to force of attraction. When a substance is heated, its temperature rises and
its molecular motion becomes more vigorous which increases the kinetic energy
of the molecules. Thus, the temperature of the substance depends upon the
average kinetic energy of its molecules. In general, matter exists in three states
solids, liquids and gases as shown in Fig. 7.1.

Solid Liquid Gas

Fig. 7.1
Most of the properties of solids, liquids and gases
can be explained on the basis of kinetic molecular theory of
matter. In case of solids, the intermolecular forces are so
strong that they keep the molecules bound. So, the
molecules are held at fixed positions but still they show
vibrational motion about their fixed points (Fig. 7.2). This is
why, the solids have a definite shape and a definite volume.
In case of liquids, intermolecular force is so weak that
it cannot hold the molecules at fixed positions and the Fig. 7.2
molecules can slide over each other in random directions. A liquid, therefore,
possesses a definite volume but has no definite shape. Due to flow of the
molecules, it acquires the shape of the containing vessel.
Gas molecules are relatively far away from one and another. Due to which,
gas neither posseses a definite volume nor a definite shape.
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Plasma
The plasma is a gas in which most of the atoms
are ionized containing positive ions and electrons
(Fig. 7.3-a). They are freely moving in the volume of the
gas. Due to presence of positive ions and free electrons,
plasma is the conducting state of matter. It allows
electric current to pass through it. Since the gas in
plasma state has properties which are quite different
from ordinary gas, therefore, plasma is known as fourth Fig. 7.3(a) Plasma
state of matter. The Sun and the most of other stars are in plasma state. Plasma is
also found in plasma TV and in gas discharge tubes (Fig. 7.3-b) when electric
current passes through them. The plasma state also occurs during the early
stages of lightning formation known as lightning streamers which are the
conducting paths through the atmosphere due to ionized air molecules.

Fig. 7.3(b) Gas discharge tube

7.2 Temperature and Heat

When we touch ice, we feel cold. When we dip Ice cubes
our fingers in warm water, we feel hot. Thus, by sense of
touch we can tell which of the bodies is colder or hotter.
A hotter body is said to be at higher temperature as
compared to a colder body.
Temperature of a body is defined as degree
of its hotness or coldness.
It is our common experience that when we heat a
body, its temperature rises. Process of heating provides
heat or thermal energy to the body which is the cause Warm water
of the rise in temperature. Fig. 7.4
The following activity will help to define temperature.
Activity 7.1
The teacher should arrange hot water in some tea cups, thermometers and metal spoons.
Make groups of the students. Each group will put the spoon in the hot water and stir it. Ask
them what do they feel. Does the other end of the spoon also become hot?
150
 Do they observe that the spoon also gets hotter? It means heat is being transferred from the
hot water to the spoon because the temperature of the water was higher than that of the
spoon.
Thus
Temperature can be defined as a physical quantity which
determines the direction of flow of thermal energy.
This means that thermal energy is transferred from one object to another
due to temperature difference of the two bodies. Therefore, we can define heat
as follows:
Heat is the energy which is transferred from one object to another due to
difference of temperature between the two bodies.

Temperature and Internal Energy

We know that matter is composed
of molecules which are always in
motion. Molecules of a solid are
vibrating about their fixed positions.
The molecules of a liquid are sliding
one over the other and those of gases
are randomly moving. The molecules
possess kinetic energy on account of Fig. 7.5 The internal energy of air
their motion. Potential energy is also inside a hot-air balloon increases as
the temperature increases.
associated with molecules because of
their attractive forces.
The sum of kinetic and potential energies of the
molecules of an object is called its internal energy.
When we heat a substance, its molecular motion becomes more vigorous
which means an increase in its internal energy. As a result, temperature of the
substance rises. The heat energy transferred to a body increases the internal
energy of its molecules due to which its temperature rises.
Remember that, it is not true to say that a substance contains heat. The
substance contains internal energy. The word heat is used only when referring to
the energy actually in transit from hot to cold body.

7.3 Thermometers
Our sense of touch can tell us whether an object is hot or cold. It gives an
idea about the object's temperature but we cannot measure the actual
151
temperature of the body just by touching it. For the exact measurement of the
hotness of a substance, we require an instrument called a thermometer.
Thermometers use some property of a substance, which changes
appreciably with the change of temperature.
Basic Thermometric Properties
Some basic thermometric properties for a material suitable to construct
a thermometer are the following:
1. It is a good conductor of heat.
2. It gives quick response to temperature changes.
3. It has uniform thermal expansion.
4. It has high boiling point.
5. It has low freezing point.
6. It has large expansivity (low specific heat capacity).
7. It does not wet glass.
8. It does not vapourize.
9. It is visible.
Liquid-in-Glass Thermometer
We know that liquids expand on heating. So, expansion in the volume of a
liquid can be used for the measurement of temperature. This is known as
liquid-in-glass thermometer. One such liquid which is commonly used in
thermometers is mercury. Figure 7.6 shows a mercury thermometer. It is made of
glass. It has a bulb at one end filled with mercury.
Capillary tube
Mercury Linear scale
°C

Measured temperature = 38°C Glass stem

Fig. 7.6
When the temperature rises, the mercury expands and moves up through
the narrow capillary tube in the form of a mercury thread. As shown in the given
figure 7.6, the position of the end of thread reads the temperature. Mercury is
opaque and can be easily seen due to its silvery colour. Alcohol is also a choice for
the thermometric liquid, but it must be coloured to make it visible.
Point to Ponder! Brain Teaser!
Could we make mercury (a) Why the walls of the
thermometer if expansion thermometer bulb are thin?
of glass would have been (b) Why the inner bore must be
greater than mercury? narrow?

152
Temperature Scales
For Your Information!
For the measurement of temperature, a The pressure of a given mass of gas
scale is to be constructed which requires two increases with temperature. So,
reference temperatures called two fixed points. pressureofa gas is also a
One is the steam point slightly above the thermometric property which is used
boiling of water at standard atmospheric in gas thermometers. The resistance
of a given length of wire also
pressure. This corresponds to upper fixed point depends upon temperature. It
of the scale. The second fixed point is the increases with the increase in
melting point of pure ice or simply ice point. It is temperature. So, the resistance of a
called the lower fixed point. Different scales of wireisalsoa thermometric
temperature have been constructed by substance and is used in platinum
resistance thermometer.
assigning different numerical values to these °F °C K
fixed points. Three different scales are:
(i) Celsius or centigrade scale

210 220 °F
(ii) Fahrenheit scale

100 °C
212°F 100°C 373 K

373
(iii) Kelvin scale Steam

363
In Celsius or centigrade scale, the point

90
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
numerical values assigned to lower and upper

353
80
fixed points are 0 and 100. As the difference

343
70
between these values is 100, so the space
between these points is divided into 100 equal

333
60
parts. Each part is known as 1°C.

323
100 divisions
180 divisions

100 divisions
50

In Fahrenheit scale, the lower fixed point

is labelled as 32 and upper as 212. As the
313
40

difference between these two numbers is 180, 303

30

so in this scale the space between these points

293
20

is divided into 180 equal parts. Each part is

283

known as 1°F. Celsius and Fahrenheit scales are Ice

10

point
generally used in ordinary life. 32°F 0°C 273 K
273
0

There is a third scale of temperature

-10

known as Kelvin scale or Absolute temperature

scale. It is used in scientific measurements. In
Kelvin scale, the lower and upper fixed points
are labelled as 273 and 373. As the difference
between these values is 100, so the width of 1 K Comparison of
is the same as that of 1°C. The zero point of this three scales of temperature
scale is the temperature at which the molecules Fig. 7.7
153
of a substance cease to move. Their average kinetic energy becomes zero. This is
known as absolute zero. Its value is -273.15 °C. For calculations, it is simply taken
as -273 °C. Absolute zero is the lowest possible temperature even to be in the
whole universe. The matter does not exist below absolute zero temperature.
Conversion of Temperature from One Scale to Another
If the temperature of a body is Tc on Celsius scale, TF on Fahrenheit scale
and Tk on Kelvin scale, then these readings are related by the following formulae:
(I) Conversion of Celsius (centigrade) to
Fahrenheit scale: For Your Information!
9
TF = × TC + 32 ……. (7.1)
5 Inside hot stars 10 9

(ii) Conversion of Fahrenheit to 10 8

Celsius scale:
5 Inside the Sun 10 7

TC = (T – 32) ……. (7.2)

9
F
10 6

Nuclear explosion

(iii) Relationship between Kelvin and 105

Celsius scales: Stellar nebulae 104

Melting point of iron
Tk = TC + 273 ……. (7.3) 103
Melting point of ice (°0 C)
Example 7.1 Highest known transition temperature
for a superconductor
Nitrogen liquefies
102

Hydrogen Liquefies 101

How much 30°C temperature Outer space
4
He becomes superfluid
would be on Fahrenheit and Kelvin 100 - 1 K

scales? 10–1

10–2
He becomes superfluid
3

Solution 3
10–3 - 1 mK

Lowest temperature obtained for He, 10–4

Temperature TC = 30°C
9 Lowest temperature for
10–5

Using TF = × TC + 32° electrons in a metal

5 10–6 - 1 μK

9 10–7
= × 30°C+ 32°=86°F
5 10–8
Lowest temperature obtained
Using Tk = TC +273 for nuclei in a solid
absolute zero 10–9 - 1 nK
= 30°C + 273 = 303K
Thermocouple Thermometer
This type of thermometer consists of two wires of different materials such
154
as copper and iron. Their ends are joined together to For Your Information!
form two junctions. If the two junctions are at different Thermo-electric current is
a thermometric property
temperatures, a small current flows across them. This in a thermocouple
current is due to the potential difference produced
across the two junctions as the two wires Thermocouple
have different resistance to the flow of Hot Metal A Voltage
current. The greater is the difference of junction
V
temperatures, the greater is the potential
Metal B
difference or voltage produced across Cold junction
the junctions. If one end of the junction is Fig. 7.8

kept at a fixed lower temperature, say by placing it in an ice bath at 0OC for
reference, the temperature of other junction at a higher temperature can be
measured using a millivolt meter by a calibrated scale on it (Fig. 7.8).
This type of thermometer is particularly useful for very high temperatures
and also rapidly changing temperature as there is only a small mass of metal
(the junction) to heat up.
7.4 Sensitivity, Range and Linearity of Thermometers
A thermometer is evaluated by its three key characteristics that are
sensitivity, range and linearity. They help determine the suitability of the
thermometer for specific use ensuring accurate and reliable measurement of
temperature.
Sensitivity
Sensitivity of a thermometer refers to its ability to detect small changes in
the temperature of an object. For example, the minimum division on the scale of
a thermometer is 1°C. The accuracy of its temperature measurement will be 1°C.
On another thermometer the marks are 0.1°C apart. Hence, its accuracy will be
up to 0.1°C and said to be more sensitive. Its measurement will be more precise
than the measurement by a thermometer with an accuracy of 1°C.
Range
This refers to the span of temperature, from low to high, over which the
thermometer can measure accurately. For example, a clinical thermometer
designed for human body temperature has a narrow or short range, say from
35°C to 45°C. A long-range thermometer is usually used for science experiments
in the laboratory with markings from −10°C to 110°C. The choice of liquid for

155
thermometers put a lower and upper limit for the range of a thermometer. For
example, Mercury freezes at -39°C and boils at 357°C. Hence, we can construct
mercury in glass thermometers within this range. The marking scale depends on
desired range of measurement. For extremely low temperatures, alcohol is used.
Alcohol has a much lower freezing point about -112°C which increases its lower
limit for the range but it has lower upper limit as it boils at 78 °C.
Linearity
This refers to a direct proportional relationship between the temperature
and scale reading across entire range of measurement. A good linear
thermometer should measure equal increments on the scale corresponding to
equal change in the temperature. It means that marking on the scale should be
evenly spaced over the whole range. High linearity means more consistent and
proportional scale readings over the entire range to ensure accuracy of
measurement.
7.5 Structure of A Liquid-in-Glass Thermometer
A liquid-in-glass thermometer has a narrow and uniform capillary tube
having a small bulb filled with mercury or alcohol at its lower end. The thin wall of
the glass bulb allows quick conduction through glass to the liquid from a hot
object whose temperature is to be measured. Mercury being metal is a good
conductor and hence responds quickly to the change in temperature. The small
amount of liquid also responds more quickly to a change in temperature. The
quick response makes the device sensitive. Use of mercury is quite sensitive for
normal measurements. For greater accuracy, alcohol can be used as its
expansivity is six times more than mercury but it has range limitation to higher
temperature measurements due to its low boiling point (78°C).
The uniformity of the narrow tube or bore ensures even expansion of the
liquid required to make the linear measuring scale. The choice of mercury allows
to use it over a long-range temperature due to its low freezing point and high
boiling point. It provides a fairly long range of measurement of temperature.
Mercury Thick glass stem Range from
-10°C to 110°C
-10 0 10 20 30 40 50 60 70 80 90 100 110°C

Bulb with thin Scale, usually in 1º divisions Fine-bore,

glass wall but can read to 0.1°C on very uniform
long, fine-bore tubes evacuated tube
Fig. 7.9 Labelled diagram of a laboratory thermometer
156
 KEY POINTS
 According to kinetic molecular theory of matter, the matter is composed of molecules
which are in motion. The molecules possess a mutual force of attraction. The molecules
have kinetic energy due to their motion and potential energy due to the force of
attraction.
 Plasma consists of ionized atoms of a gas containing equal amount of positive and
negative charges.
 Temperature is the degree of hotness or coldness of a body and it determines the
direction of flow of heat when two bodies are brought in thermal contact.
 Heat is the form of energy which is transferred from one body to the other due to the
difference in temperature.
 A body does not contain heat. It contains internal energy which is the sum of kinetic and
potential energy of the total molecules of an object.
 Temperature is the degree of hotness of an object. According to particle theory of matter,
it is a measure of the average kinetic energy of the molecules of an object.
 Thermometer is a device used to measure the temperature of a body.
 Conversion of temperature from one scale to the other:
a. Relationship between Kelvin (TK) and Celsius (TC) temperature TK = TC + 273
b. Relationship between Celsius (TC) also known as centigrade to Fahrenheit
temperature (TF)
TF = 9 × TC + 32
5 5
c. Relationship between Fahrenheit (TF) to Celsius (TC) TC = 9 (TF – 32)
 Thermocouple thermometer is based on the flow of electric current between two
junctions of two wires of different materials due to difference of temperatures at the
junctions.

EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
7.1. How do the molecules in a solid behave?
(a) Move randomly
(b) Vibrate about their mean positions
(c) Rotate and vibrate randomly at their own positions
(d) Move in a straight line from hot to cold ends.
7.2. What type of motion is of the molecules in a gas?
(a) Linear motion (b) Random motion
(c) Vibratory motion (d) Rotatory motion

157
7.3. Temperature of a substance is:
(a) the total amount of heat contained in it
(b) the total number of molecules in it
(c) degree of hotness or coldness
(d) dependent upon the intermolecular distance
7.4. Heat is the:
(a) total kinetic energy of the molecules
(b) the internal energy
(c) work done by the molecules
(d) the energy in transit
7.5. In Kelvin scale, the temperature corresponding to melting point of ice is:
(a) zero (b) 32 (c) -273 (d) +273
7.6. The temperature which has the same value on Celsius and Fahrenheit
scale is:
(a) -40 (b) +40 (c) +45 (d) -45
7.7. Which one is a better choice for a liquid-in-glass thermometer?
(a) Is colourless (b) Is a bad conductor
(c) Expand linearly (d) Wets glass
7.8. One disadvantage of using alcohol in a liquid-in-glass thermometer:
(a) it has large expansivity (b) it has low freezing point (-112°C)
(c) it wets the glass tube (d) its expansion is linear
7.9. Water is not used as a thermometric liquid mainly due to:
(a) colourless (b) a bad conductor of heat
(c) non-linear expansion (d) a low boiling point (100°C)
7.10. A thermometer has a narrow capillary tube so that it:
(a) quickly responds to temperature changes
(b) can read the maximum temperature
(c) gives a large change for a given temperature rise
(d) can measure a large range of temperature
7.11. Which thermometer is most suitable for recording rapidly varying
temperature?
(a) Thermocouple thermometer
(b) Mercury-in-glass laboratory thermometer
(c) Alcohol-in-glass thermometer
(d) Mercury-in-glass clinical thermometer

158
B Short Answer Questions
7.1. Why solids have a fixed volume and shape according to particle theory of
matter?
7.2. What are the reasons that gases have neither a fixed volume nor a fixed
shape?
7.3. Compare the spacing of molecules in the solid, liquid and gaseous state.
7.4. What is the effect of raising the temperature of a liquid?
7.5. What is meant by temperature of a body?
7.6. Define heat as ‘energy in transit’.
7.7. What is meant by thermometric property of a substance? Describe some
thermometric properties.
7.8. Describe the main scales used for the measurement of temperature. How
are they related with each other?
7.9. What is meant by sensitivity of a thermometer?
7.10. What do you mean by the linearity of a thermometer?
7.11. What makes the scale reading of a thermometer accurate?
7.12. What does determines the direction of heat flow?
7.13. Distinguish between the heat and internal energy.
7.14. When you touch a cold surface, does cold travel from the surface to your
hand or does energy travel from your hand to cold surface?
7.15. Can you feel your fever by touching your own forehead? Explain.
C Constructed Response Questions
7.1. Is kinetic molecular theory of matter applicable to the plasma state of
matter? Describe briefly.
7.2. Why is mercury usually preferred to alcohol as a thermometric liquid?
7.3. Why is water not suitable for use in thermometers? Without calculations,
guess what is equivalent temperature of 373 K on Celsius and Fahrenheit
scales?
7.4. Mention two ways in which the design of a liquid-in-glass thermometer
may be altered to increase its sensitivity.
7.5. One litre of water is heated by a stove and its temperature rises by 2°C. If
two litres of water is heated on the same stove for the same time, what will
be then rise in temperature?
7.6. Why are there no negative numbers on the Kelvin scale?
7.7. Comment on the statement, “A thermometer measures its own
temperature.”
159
7.8. There are various objects made of cotton, wood, plastic, metals etc. in a
winter night. Compare their temperatures with the air temperature by
touching them with your hand.
7.9. Which is greater: an increase in temperature 1°C or one 1°F?
7.10. Why would not you expect all the molecules in a gas to have the same
speed?
7.11. Does it make sense to talk about the temperature of a vacuum?
7.12. Comment on the statement: “A hot body does not contain heat”.
7.13. Discuss whether the Sun is matter.
D Comprehensive Questions
7.1. Describe the main points of particle theory of matter which differentiate
solids, liquids and gases.
7.2. What is temperature? How is it measured? Describe briefly the
construction of a mercury-in-glass thermometer.
7.3. Compare the three scales used for measuring temperature.
7.4. What is meant by sensitive, range and linearity of thermometers? Explain
with examples.
7.5. Explain, how the parameters mentioned in question 7.4 are improved in
the structure of glass-in-thermometer.
E Numerical Problems
7.1 The temperature of a normal human body on Fahrenheit scale is 98.6°F.
Convert it into Celsius scale and Kelvin scale.
(37°C, 310 K)
7.2 At what temperature Celsius and Fahrenheit thermometer reading would
be the same? (- 40O)
7.3 Convert 5°F to Celsius and Kelvin scale. (-15°C, 258 K)
7.4 What is equivalent temperature of 25°C on Fahrenheit and Kelvin scales?
(77°F, 298 K)
7.5 The ice and steam points on an ungraduated thermometer are found to
be 192 mm apart. What temperature will be on Celsius scale if the length
of mercury thread is at 67.2 mm above the ice point mark?
(35°C)
7.6 The length between the fixed point of liquid-in-glass thermometer is
20 cm. If the mercury level is 4.5 cm above the lower mark, what is the
temperature on the Fahrenheit scale? (72.5°F)

160
 Chapter
8 Magnetism
Student Learning Outcomes
After completing this chapter, students will be able to:
[SLO: P-09-E-01] Describe the
forces between magnetic poles
and between magnets and
magnetic materials [Including
the use of the terms north pole
(N pole), south pole (S pole),
a ttr ac t ion and r epu lsion ,
magnetized and unmagnetized]
[SLO: P-09-E-02] Describe
induced magnetism
[SLO: P-09-E-03] Differentiate
betweentemporaryand
permanent magnets
[SLO: P-09-E-04] Describe magnetic fields [as a region in which a magnetic pole experiences
a force]
[SLO: P-09-E-05] State that the direction of the magnetic field at a point is the direction of
the force on the N pole of a magnet at that point
[SLO: P-09-E-06] State that the relative strength of a magnetic field is represented by the
spacing of the magnetic field lines
[SLO: P-09-E-7] Describe uses of permanent magnets and electromagnets
[SLO: P-09-E-8] Explain qualitatively in terms of the domain theory of magnetism how
materials can be magnetized and demagnetize [stroking method, heating, orienting in
north-south direction and striking, use of a solenoid]
[SLO: P-09-E-9] Differentiate between ferromagnetic, paramagnetic and diamagnetic
materials [by making reference to the domain theory of magnetism and the effects of
external magnetic fields on these materials]
[SLO: P-09-E-10] Analyse applications of magnets in recording technology [and illustrate
how electronic devices need to be kept safe from strong magnetic fields]
[SLO: P-09-E-11] State that soft magnetic materials (such as soft iron) can be used to
provide shielding from magnetic fields

Almost all of us are familiar with a magnet because of its interesting

properties. In lower, classes we have studied some of the properties. You might
have also enjoyed a magnet attracting small pieces of iron.
161
8.1 Magnetic Materials
Magnetism is a force that acts at a distance upon magnetic materials.
These materials are attracted to magnets. These materials are called magnetic
materials. Let us perform an activity to test such materials.
Activity 1

The teacher should divide the students into

groups and provide them permanent magnets to
perform this activity.
Each group should collect some items made
of different materials such as copper wire, nickel ring,
glass bottle, paper clips, iron nail, eraser, wooden
ruler, plastic comb, etc. Place them on a table as shown
in figure. Bring the permanent magnet close to each
item one by one and observe which items are
attracted by the magnet and which are not. Make a list of magnetic and non magnetic
materials.
Materials such as iron, nickel and cobalt will be attracted by the magnet. They are
magnetic materials. The materials such as brass, copper, wood, glass and plastic are not
attracted by the magnet. They are called non-magnetic materials.
We will discuss different types of materials in detail later in this chapter.
For Your Information!
Over 1000 years ago, the Greeks discovered a rock called lodestone or
magnetite that could attract materials that contained iron. Also, if suspended
from a string to rotate freely, it would always settle in north-south direction.
This unique property led to form the basis of compass which was later on
used for navigation on land and at sea.

Activity 2
The teacher should facilitate each group to perform
this activity as per instructions.
1. Place some iron filings scattered on the
top of a card paper or a sheet of glass. (b) Iron filings
2. Move a magnet beneath the card paper, attracted
glass or a plastic sheet as shown in the by magnet
figure. (a) Scattered Iron
filings on a glass s heet
3. What do you observe? Describe briefly.

You must have seen the the iron

iron filings
filings following
following the
the magnet.
movement Magnetic
of the
force account
magnet. for force
Magnetic these accounts
movements. This movements.
for these activity also This
shows that
activity
also shows that magnets can attract objects containing iron, etc. evenin
magnets can attract objects containing iron etc. even if they are not if
directare
they contact
not inwith them.
direct contact with them.

162
8.2 Properties of Magnets
The property of attracting magnetic materials by the magnets has been
discussed above. The magnets also exhibit the following properties.

1. Magnetic Poles North

West
I f a bar magnet is suspended East

horizontally through a string and allowed to South

come to rest, it will point in north-south
direction. The end of the magnet that points
north is called the north magnetic pole (N)
Fig. 8.1
and rhe end that points south is the south
magnetic pole (S) as shown in Fig. 8.1.

2. Attraction and Repulsion of Magnetic Poles

When two freely suspended bar magnets are
placed close to each other, the two north poles will
repel each other (Fig. 8.2). So will the two south Fig. 8.2
poles (Fig. 8.3).
However, if the north pole of one is placed
near the south pole of the other, the poles will
Fig. 8.3
attract (Fig. 8.4 & Fig. 8.5). We can say that Like
poles repel and unlike poles attract.

3. Identification of a Magnet Fig. 8.4

To identify whether an object is a magnet or

simply a magnetic material, we can bring its one end
close to any pole of a suspended bar magnet. If it is
attracted, then we can conclude that the end of the Fig. 8.5

object is either of opposite pole to that of the

suspended magnet or it is simply a magnetic material. Then we should bring the
same end of the object close to the other end of the suspended magnet. If the
object is again attracted, it is not a magnet but it is a magnetic material.
If it is repelled by the other end of the suspended magnet, then the object is a
magnet.
The repulsion between the like poles is
a real test to identify a magnet.

163
4. Is Isolated Magnetic Pole Possible?
If we break a bar magnet into two equal
pieces, can we get N-pole and S-pole separately? N S
No, it is not possible. Each piece will have its two
N S N S N S N S
poles, i.e., N-pole and S-pole. Even if a magnet is
divided into thousands pieces, each piece will be a Fig. 8.6
complete magnet with its N, and S-poles (Fig.8.6).

8.3 Induced Magnetism

Magnetic material such as iron or steel can be made a magnet. This is
known as magnetization. In other words, we can say that magnetism has induced
in it. You can perform an activity to observe this fact.
Activity 3
The teacher should facilitate each group to perform this activity as per instructions.
1. Take a magnetic compass. Put it on a table and see which end of its needle points north.
The N-pole of the needle is usually coloured red.
2. Place a bar magnet on the table. Bring the compass near to its N-pole. In which direction
does the N-pole of the needle stay?

3. Put the compass near to the S-pole of the bar magnet. In which direction does the N-pole
of the needle stay this time?
4. Now place an iron nail having its head in contact with any pole of the bar magnet.

N S

5. Put the compass near to the pointed end of an iron nail. Observe the direction in which
N-pole of the needle settles. Has the nail become a magnet? Has magnetism been
induced in it?
6. Take the bar magnet away from the nail. Again check the behaviour of the nail by bringing
compass near to its ends. Does the magnetism vanish?
From the above activity, we conclude that the S-pole of the true magnet induces N-pole
in the near end of the piece of iron (nail) while the far end of the iron piece becomes S-
pole as shown in the figure.
It should be noted that the induced magnetism vanishes as the true magnet is
removed.

164
8.4 Temporary and Permanent Magnets
Temporary magnets are the magnets that work in the presence of a
magnetic field of permanent magnets. Once the magnetic field vanishes, they
lose their magnetic properties. You have learnt something about a magnetic field
in lower classes. In the next chapter, we will study it in detail.
Usually, soft iron is used to make temporary magnets. Paper clips, office
pins and iron nails can easily be made temporary magnets. Electromagnets are
also good examples of temporary magnets. You have already learnt different
uses of electromagnets.
Permanent magnets retain their magnetic properties forever. These are
either found in nature or artificially made by placing objects made of steel and
some special alloys in a strong magnetic field for a sufficient time. There are
many types of permanent magnetic materials. For example cobalt, alnico and
ferrite.

Activity 4

The teacher should facilitate the groups to

provide each a bar magnet, a stand with clamp, some
small nails made of iron and also some nails of steel. He
should further supervise them to perform the activity as
per instructions.
1. Clamp the bar magnet horizontally on the stand.
2. Touch the head of an iron nail to anyone end of the
magnet. It will be attracted and stick to the magnet.
Touch another iron nail to the lower end of the first
one, does it stick to it?
Yes, it will, because the upper nail has become a
magnet itself. Go on hanging iron nail one by one to
make a chain until no more nails stay attached to the
chain.
3. Try to hang steel nails at the other end of the bar
magnet to form a similar chain.
4. Remove the chain of iron nails by pulling the topmost nail. Does the chain collapse?
5. Remove the chain of steel nails in the same way. Does this collapse?
You will observe that the chain of iron nails immediately collapses but the steel nails
remain attached to each other for some time. This shows that the magnetism induced in
the iron nails is temporary while that in the steel nails is permanent.

165
8.5 Magnetic Fields
When a magnet attracts a certain magnetic
material, it exerts some force to do so. Similarly, when it
attracts or repels a magnetic pole of another magnet, it
exerts a force on it. This force can be observed up to a
certain distance from the magnet that can be explained
by the concept of magnetic field around the magnet.

A magnetic field is the region around a magnet where

an other magnetic object experiences a force on it.

The pattern of a magnetic field around a bar

magnet can be seen very easily by a simple experiment. Fig. 8.7
If iron filings are sprinkled on a thin glass plate placed over a bar magnet,
the filings become tiny magnets through magnetic induction. Now if the glass
surface is gently tapped, the filings form a pattern. This pattern is known as the
magnetic field pattern (Fig.8.5). This pattern can be better shown by lines that
correspond to the path of the filings. These lines are called magnetic lines of
force.
Magnetic lines of Force
The magnetic lines of force around
a bar magnet can be drawn by using a
small compass. The needle of the compass
will move along the magnetic lines of force.
Figure. 8.8 shows the magnetic lines of
force around a bar magnet drawn by this
Fig. 8.8
method.Thecompass needle is
symbolized by an arrow being the north
pole (Fig. 8.9).
The magnetic field at a point has both
a magnitude and a direction. Fig. 8.9

The direction of the magnetic field at any point in space

is the direction indicated by the N-pole of a magnetic
compass needle placed at that point.

166
 Figure. 8.8 also shows that the field lines appear to originate from the
north pole and end on the south pole. Actually, the magnetic field extends in
space all around the magnet but the figure shows the field in one plane only.

Strength of the Magnetic Field

The strength of the magnetic field is proportional to the number of
magnetic lines of force passing through unit area placed perpendicular to the
lines. Thus, the magnetic field is stronger in regions where the field lines are
relatively close together and weaker where these are far apart. For example in
Fig. 8.10, the lines are closest together near north and south poles indicating that
the strength of the magnetic field is stronger in these regions. Away from the
poles, the magnetic field becomes weaker.

Fig. 8.10 Fig. 8.11 Fig. 8.12

In case the two magnets are placed close to each other, their combined
magnetic field can also be drawn by using the compass needle. Figure. 8.10 and
Fig. 8.11 show the patterns of the combined magnetic field of two magnets
lying with different orientations. In Fig. 8.11, point 'x' is called a neutral point
because the field due to one magnet cancels out that due to the other magnet.
Figure. 8.12 represents the field pattern of a horse-shoe magnet. The field is
almost uniform between the poles except near the edges.

8.6 Uses of Permanent Magnets

There are many uses of permanent magnets such as:
1. They are the essential parts of D.C motors, A.C and D.C electric generators.
2. Permanent magnets are used in the moving coil loud-speakers.
3. These are very commonly used in door catchers.
4. Magnetic strips are fitted to the doors of refrigerators and freezers to
keep the door closed tightly.
5. They are commonly used to separate iron objects from different mixtures.
Flourmills use permanent magnets to remove iron nails, etc. from the
grains before grinding.
167
6. In the medical field, they are used to remove iron splinters from the eyes.
7. A piece of permanent magnet is used to reset the iron pointer in a
maximum and minimum thermometer.

Applications of Permanent Magnets

Let us see, how some of the following devices use permanent magnets.

A.C Generator Slip rings

When a coil is rotated between the

I
poles of a permanent magnet, the
magnetic field through the coil changes Carbon I
and an emf is induced between the ends of brush Carbon
brush
the coil (Fig.8.13). On connecting these
ends to an external circuit, an alternating I
current (A.C) flows through the circuit. B
N S
Electric motor is the reverse process of I
electric generator. When an A.C is made to
pass through the coil between the poles of Coil rotated by
a permanent magnet, it starts rotating. Permanent
mechanical means

magnet Fig. 8.13

Moving Coil Loudspeaker
A voice coil attached to the cone of
the speaker is slipped over one pole (N) of Permanent Cone
magnet Voice
the radial permanent magnet as shown in
coil
Fig‫ ۔‬8.14. From a microphone or some other S
sound signals in the form of varying (A.C)
N
current passes through the voice coil that is
inserted in the gap of permanent magnet. S
This A.C interacts with the magnetic field to gap

generate a varying force that pushes and Current

pulls on the voice coil and the attached Fig. 8.14
cone. The cone vibrates back and forth to
produce sound in the air.
8.7 Electromagnets
Electromagnets are also a kind of temporary magnets. The following
activity will show how electromagnets can be made and tested.

168
 Activity 5

The teacher should divide the students into groups and facilitate them
to perform this activity.
Iron
Take a battery of two cells, a Thread Nail
switch, an iron nail, cotton (or Coil
plastic) covered copper wire, thread
and a few paper clips.
Wind the wire over the iron
nail to form a coil. Suspend the coil
by means of thread tied to its centre. Switch Battery
Connect ends of the wire to the
Clips
battery through the switch as shown
in the figure.
Keeping the switch OFF, bring some paper clips near to one end of the
nail. Do they stick to the nail? Now turn the switch ON and again bring the
paper clips near to the end of the nail. Do they stick this time? Does the nail
behave like a magnet? Yes, the nail has become a magnet. Turn the switch OFF
and see what happens to the clips. Do they fall down? What do you conclude
from this activity?

An iron nail or a rod becomes a magnet when an electric current

passes through a coil of wire around it. It is called an electromagnet.

When an electric current passes through the coil of wire, magnetic field is
produced inside the coil that magnetizes the iron nail. As we have observed that
the magnetic properties of an electromagnet are temporary, therefore, iron
object remains a magnet as long as the electric current passes through the coil.
When the current is stopped, it no longer remains a magnet.
If we increase the number of cells in the battery or increase the number of
turns of the coil, we will observe that the strength of the magnetic field in each
case increases. This will be indicated by the more number of clips held by the nail
in these cases.

Uses of Electromagnets
Electromagnets are used in electric bell, telephone receiver, simple
magnetic relay, circuit breaker, reed switches, cranes, tape recorder, maglev
trains and many other devices. Functions of some of them are described below:
169
Magnetic Relay
This is a type of switch which works with an electromagnet. It is an input
circuit which works with a low current for safety purpose. When it is turned ON it
activates another circuit which works with a high current.
The input circuit supplies a small current to electromagnet. It attracts the
iron armature which is pivoted. The other end of the armature moves up and
pushes the metal contacts to join together which turn the high current-circuit
ON (Fig.8.15).
Springy metal
To high Insulator contracts
current circuit
Pivot

Iron armature
Electromagnet

Low current
input circuit Fig. 8.15 Soft iron core

Circuit Breaker
A circuit breaker is designed to pass a certain maximum current through it
safely. If the current becomes excessive, it switches OFF the circuit. Thus, electric
appliances are protected from burning. As shown in Fig.8.16, inside a circuit
breaker, the current flows along a copper strip, through the iron armature and
coil of the electromagnet. The electromagnet attracts the armature. If the current
is large enough, the armature is detached from the copper strip and the circuit
breaks. Armature Pivot Spring
Copper Strip

Current Switch
contacts

Coil
around
iron core
Plastic
frame
Current

Fig. 8.16
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Telephone Receiver Electromagnet
Diaphragm
There is an iron diaphragm in the
receiver under which an electromagnet is
placed (Fig.8.17). The microphone of the
telephone handset on the other side sends
varying electric current in accordance with the
sound signals. When the varying current
Varying
passes through the coil of receiver on this current
side, it causes variation in the force of Fig. 8.17
electromagnet. As a result, the diaphragm over it moves back and forth to
produce sound.
For Your Information!
A wonderful use of
electromagnets can be seen in the
Maglev trains. The maglev stands for a
magnetically levitated train. A maglev
uses forces that arise from induced
magnetism to levitate or float a few
centimetres above the guideway. That is
why, it does not need wheels and faces Guideway Rail
no friction. In Japan, it is known as a Arm

bullet train that can run up to a speed of

400 km per hour. Levitation
As described above, magnetic electromagnet

levitative only lifts the train and does not (a)

Guideway
(b)
move it forward. To push the train
forward, propulsion electromagnets are installed along the guideway and train. By push and
pull of these magnets the train moves forward.

Electromagnetic Cranes
Huge electromagnets are used in
cranes at scrapyards, steel works and on
ships. These are so powerful that they can
lift iron and steel objects such as cars as
shown in Fig.8.18. After moving the heavy
objects to the required position, the
objects are released by just switching OFF
the current of the electromagnet.
Fig. 8.18
171
8. 8 Domain Theory of Magnetism
It is observed that the magnetic
field of a bar magnet is like the field
produced by a solenoid (long coil of wire)
carrying current (Fig. 8.19-a & b). It
suggests that all magnetic effects are due
Fig. 8.19(a)
to moving charges. In case of solenoid,
charges are moving in the wire. The
motion responsible for the magnetism in a
magnet is due to electrons within the
atoms of the material. Current
We know that an electron is a Fig. 8.19(b)
charged particle. Also, each electron in an atom is revolving about the nucleus
and at the same time, it is spinning about an axis through it. The rotation and spin
both give rise to a magnetic field. Since there are many electrons in an atom, their
rotations and spins may be so oriented to strengthen the magnetic effects
mutually or to cancel the effects of one another. If an atom has some resultant
magnetic field, it behaves like a tiny magnet. It is called a magnetic dipole.

Paramagnetic Materials
If the orbital and spin axes of the electrons in an atom are so oriented that
their fields support one another and the atom behaves like a tiny magnet, the
materials with such atoms are called paramagnetic materials such as aluminium
and lithium.

Diamagnetic Materials
Magnetic fields produced by both orbital and spin motions of the
electrons in an atom may add up to Zero. In this case, the atom has no resultant
field. The materials with such atoms are called diamagnetic materials. Some of
their examples are copper, bismuth, water, etc.

Ferromagnetic Materials
There are some solid substances such as iron, steel, nickel, cobalt, etc. in
which cancellation of any type does not occur for large groups of neighbouring
atoms of the order of 10¹⁶ because they have electron spins that are naturally
aligned parallel to each other. These are known as ferromagnetic materials.
172
 The group of atoms in this type of material form a region of about 0.1 mm
size that is highly magnetized. This region is called a magnetic domain. Each
domain behaves as a small magnet with its own north and south poles.
Alignment of Domains
The domains in a ferromagnetic material are
randomly oriented as shown in Fig.8.20 (a). The magnetic
fields of the domains cancel each other so the material Fig. 8.20(a)
does not display any magnetism. However, an
unmagnetized piece of iron can be magnetized by
placing it in an external magnetic field provided by a
permanent magnet or an electromagnet.
The external magnetic field penetrates the Fig. 8.20(b)
unmagnetized iron and induces magnetism in it by causing two effects on the
domains. Those domains whose magnetism is parallel or nearly parallel to the
external magnetic field grow in size at the expense of other domains that are not
oriented. In addition, the magnetic alignment of the other domains rotates and
become oriented in the direction of the external field (Fig.8.20-b). As a result, the
iron is magnetized and behaves like a magnet having its own north and south
poles.
For Your Information!
In soft iron, the domains are easily oriented on
The magnetism induced in a
applying an external field and return to random ferromagnetic material can
position when the field is removed. This is desirable in be surprisingly large in the
an electromagnet and also in transformers. On the presence of weak external
other hand, steel is not so easily oriented to change field. In some cases, induced
order. It requires very strong external field, but once field is a thousand times
stronger than the external
oriented, retains the alignment. That is why, steel is field. That is why, high field
used to make permanent magnets. electromagnets are made
In non-ferromagnetic materials, such as by using cores of soft iron of
aluminium and copper, the formation of magnetic some other ferromagnetic
material.
domains does not occur, so magnetism cannot be
induced into these substances.

8.9 Magnetization and Demagnetization

There are two methods used for magnetizing a steel bar:
1. Stroking
In this method, magnetism is induced in a steel bar by using the magnetic
field of a permanent magnet. The steel bar can be stroked in two ways:
173
(a) Single Touch Method
A steel bar is placed on a horizontal surface. It is
stroked from one end to the other several times Permanent
magnet
in the same direction using the same pole (say
N) of the permanent magnet. Every time the
magnet is lifted up sufficiently high on reaching
the other end of the bar (Fig. 8.21). Fig. 8.21
(b) Double Touch Method Permanent Permanent
In this method, stroking is done from the magnet magnet

centre of the steel bar onwards with the unlike

poles of two permanent magnets at the same
time (Fig. 8.22). This method is more efficient
Steel bar
than the first one. Fig. 8.22
In both the cases, the poles produced at the ends
of magnetized steel bar after stroking are of the
opposite polarity to that of the stroking pole.
2. Making a Magnet using Solenoid
In this method, a steel bar to be
magnetised is placed inside a solenoid (long coil
of wire) as shown in Fig. 8.23. The solenoid - +
Current Current
should have several hundred turns of insulated Fig. 8.23
copper wire. When direct current is passed
through the solenoid, the steel bar becomes a magnet. The polarity of the
magnetised steel bar is found by applying Right hand Grip rule which is
stated as:
Grip the solenoid with the right hand such that fingers
are curled along the direction of current (positive to the
negative terminal of the battery) in the solenoid, then
the thumb points to the N-pole of the bar end.

Demagnetisation of Magnets
1. Heating
Thermal vibrations tend to disturb the order of the
domain. Therefore, if we heat a magnet strongly, the magnet
loses its magnetism very quickly (Fig. 8.24). Fig. 8.24

174
2. Hammering
If we beat a magnet, the domains lose their
alignment and the magnet is demagnetised. It is also
called hammering (Fig. 8.25).
Fig. 8.25

3. Alternating Current
When an alternating current (A.C) is flowing
through a long solenoid, a magnet moved out slowly
from inside of the solenoid is demagnetised (Fig. 8.26). AC
Fig. 8.26

8.10 Applications of Magnets in Recording Technology

Electromagnets have widely used in recording technology of sound,
video and data in the form of electrical signals through magnetization of a
magnetic material. Most common magnetic recording mediums are magnetic
tapes and disk recorders which are used not only to reproduce audio and video
signals but also to store computer data. These materials are usually coated with
iron oxide. Some other recordings mediums are magnetic drums, ferrite cores
and magnetic bubble memory. We will discuss the process of magnetic
recording on tapes and disks in some detail.

Magnetic Tape Recording

Induced magnetism is used in the
process of magnetic tape recording. A.C
Recording and playing head is a coil of wire
wrapped around an iron core. The iron core Recording
has a horse-shoe shape with a narrow gap in head
between its two ends. Audio and video tapes Magnetic Tape
coating travel
are synthetic tapes coated with a layer of
ferromagnetic material. Plastic backing Fringe field penetrates
Sound or picture is converted into magnetic coating

electrical forms as varying currents. These

currents are sent to the head that becomes an N

electromagnet with a N-pole at one end and

S

a S-pole at the other end. The magnetic field Induced

magnetism
lines pass through the iron core and cross the
Fig. 8.27

175
gap. Some of the field lines in the gap curved outward as shown in Fig. 8.27. The
curved part of the magnetic field called as fringe field penetrates magnetic
coating on the moving tape and induces magnetism in the coating. This induced
magnetism is retained when the tape leaves the vicinity of the recording head.
The reverse process changes the varying induced magnetism into varying
current that onward is converted into sound or picture.

Hard Disk Recording

Hard disks are circular flat plates Rotating
made of aluminium, glass or plastic and magnetic Read/write
disk head
coated on both sides with iron oxide. Hard
disks can store terabyte of information.
Voice coil
A magnetic head is a small positioner
electromagnet which writes a binary digit
(1 or 0) by magnetizing tiny spots on the
spinning disk in different directions and
reads digit by detecting the magnetization
direction of spots (Fig. 8.28). The term hard
disk is also used to refer to the whole of a Fig. 8.28
computer's internal data storage.
Magnetic disk devices have an advantage over tapes recorders. A disk unit
has the ability to read or write a recording instantly while locating a desired
information on tape may take many minutes.
Electronic devices can be protected from strong magnetic effects by
enclosing them in the boxes made of soft iron. We will describe it in detail in the
next section.

8.11 Soft Iron as Magnetic Shield

Soft iron casing

Softironhas high magnetic

permeability. The permeability is the ability
of a material to allow the magnetic flux or Sensitive
instrument
lines of force through it when the material is
placed inside a magnetic field. When a piece
of soft iron is put into a magnetic field, it
g e ne ra t es a magnetic fi eld due to
magnetization. External magnetic field

Fig. 8.29

176
 If a sensitive magnetic device is enclosed in a casing of soft iron, the
magnetic flux gets established in the soft iron rather than the device. Thus, the
device is shielded from external magnetic field.
Figure 8.29 can explain this phenomenon well. A soft iron casing (shell) is
placed inside a magnetic field produced by opposite poles of two bar magnets.
Since the magnetic permeability of the iron shell is higher than that of air, so the
magnetic flux is established in the soft iron. As a result, the device is protected
from the magnetic field. Usually, the casing is made with rounded corners to
facilitate the magnetic field line up easily.
Soft iron is generally used in the cores of transformers and
electromagnets because of its high permeability. In case of an electromagnet,
the core of soft iron can be easily magnetized when current is passed around it
and quickly lost when current is stopped. That is why, electromagnets are widely
used in electric bells, loud speakers, picking and releasing iron scraps by the
cranes and in many more appliances. The sensitivity of a moving coil
galvanometer is also increased by placing a soft iron core inside the coil.
KEY POINTS
 Magnets can attract magnetic materials even if they are not in direct contact with them.
 A magnet has two poles; north pole and south pole. Like poles repel and unlike poles
attract each other.
 To get an isolated magnetic pole is not possible.
 Temporary magnets work only in the presence of a magnetic field, whereas permanent
magnets retain their magnetic properties forever.
 A magnetic field is the region around a magnet where a magnetic object experiences a
force on it.
 A magnetic field at a point has both a magnitude and a direction.
 The strength of the magnetic field is proportional to the number of magnetic lines of
force passing through unit area placed perpendicular to the lines.
 Permanent magnets are used in electric motors, electric generators, moving coil
loudspeakers, separating iron objects from different mixtures etc.
 Electromagnets are temporary magnets. They are used in electric bells, magnetic relays,
circuit breakers, telephone receivers, electromagnetic cranes, etc.
 The materials in which fields due to orbital and spins motion of the electrons in the atoms
support each other are called paramagnetic materials.
 The materials in which fields due to orbital and spin motions of the electrons in the atoms
add up to zero are called diamagnetic materials.
 The materials in which large groups of atoms of the order of 1016 have their electrons spin
naturally aligned parallel to each other are called ferromagnetic materials. These groups
are called magnetic domains.
 The external magnetic field penetrates the ferromagnetic material and aligns all the
domains to make it a magnet.
177
  Steel bars are magnetised by stroking, single and double touch sliding with permanent
magnets or keeping them in a very strong magnetic field inside a solenoid through which
large current is passed.
 Magnets can be demagnetised by heating, hitting or drawing through a solenoid in which
A.C current is passed.
 Electromagnets are widely used in recording technology. Such recording mediums are
audio/video magnetic tapes, hard disks of computers and other data storing devices.
 Soft iron is also used to protect sensitive magnetic device from external magnetic fields.

EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
8.1 Which one of the following is not a magnetic material?
(a) Cobalt (b) Iron
(c) Aluminium (d) Nickel
8.2 Magnetic lines of force:
a) are always directed in a straight line
(b) cross one another
(c) enter into the north pole
(d) enter into the south pole
8.3 Permanent magnets cannot be made by:
(a) soft iron (b) steel (c) neodymium (d) alnico
8.4 Permanent magnets are used in:
(a) circuit breaker (b) loudspeaker
(c) electric crane (d) magnetic recording
8.5 A common method used to magnetise a material is:
(a) stroking
(b) hitting
(c) heating
(d) placing inside a solenoid having A.C current
8.6 A magnetic compass is placed around a bar magnet at four points as
shown in figure below. Which diagram would indicate the correct
directions of the field?

N S N S N S N S

(a) (b) (c) (d)

178
8.7 A steel rod is magnetised by double touch stroking method. Which one
would be the correct polarity of the AB magnet?

Permanent Permanent
magnet magnet

N S S N N SS N S NN S

(a) (b) (c) (d)

A B
Steel bar

8.8 The best material to protect a device from external magnetic field is:
(a) wood (b) plastic (c) steel (d) soft iron
B Short Answer Questions
8.1 What are temporary and permanent magnets?
8.2 Define magnetic field of a magnet.
8.3 What are magnetic lines of force?
8.4 Name some uses of permanent magnets and electromagnets.
8.5 What are magnetic domains?
8.6 Which type of magnetic field is formed by a current-carrying long coil?
8.7 Differentiate between paramagnetic and diamagnetic materials.

C Constructed Response Questions

P
8.1 Two bar magnets are stored in a wooden box. Label
the poles of the magnets and identify P and Q
objects.
8.2 A steel bar has to be magnetised by placing it inside
a solenoid such that end A of a bar becomes N-pole
Q
and end B becomes S-pole. Draw circuit diagram of
A B
solenoid showing steel bar inside it. Steel bar

8.3 Two bar magnets are lying as shown in the figure. A compass is placed at
the middle of the gap. Its needle settles in the north-south direction. Label
N and S poles of the magnets. Justify your answer by drawing fields lines.

179
8.4 Electric current or motion of electrons produce magnetic field. Is the
reverse process true, that is the magnetic field gives rise to electric
current? If yes, give an example and describe it briefly.
8.5 Four similar solenoids are placed in a circle
as shown in the figure. The magnitude of
D
current in all of them should be the same.
Show by diagram, the direction of current in
C
each solenoid such that when current in
O
anyone solenoid is switched OFF, the net A
magnetic field at the centre O is directed
towards that solenoid. Explain your answer.
B

D Comprehensive Questions
8.1 How can you identify whether an object is a magnet or a magnetic
material?
8.2 Describe the strength of a magnetic field in terms of magnetic lines of
force. Explain it by drawing a few diagrams for the fields as examples.
8.3 What is a circuit breaker? Describe its working with the help of a diagram.
8.4 A magnet attracts only a magnet. Explain the statement.
8.5 Differentiate between paramagnetic, diamagnetic and ferromagnetic
materials with reference to the domain theory.
8.6 Why ferromagnetic materials are suitable for making magnets?

180
 Nature of Science
Chapter
9
Student Learning Outcomes
After completing this chapter, students will be able to:
[SLO: P-09-G-01] Describe physics as the study of matter, energy, space, time and their
mutual connections and interactions
[SLO: P-09-G-02] Explain with examples that physics has many sub-fields, and in today's
world involves interdisciplinary fields. (Students should be able to distinguish in terms of the
broad subject matter that is studied between the fields:
 Biophysics
 Astronomy
 Astrophysics
 Cosmology
 Thermal Physics
 Optics
 Classical Mechanics
 Quantum Mechanics
 Relativistic Mechanics
 Nuclear Physics
 Particle Physics
 Electromagnetism
 Acoustics
 Computational Physics
 Geophysics
 Climate Physics)
[SLO: P-09-G-03] Explain with examples how Physics is a subset of the Physical Sciences and
of the natural sciences
[SLO: P-09-G-04] Brief with examples that science is a collaborative field that requires
interdisciplinary researchers working together to share knowledge and critique ideas
[SLO: P-09-G-05] Understand the terms 'hypothesis', 'theory' and 'law' in the context of
research in the physics
[SLO: P-09-G-06] Explain, with examples in Physics, falsifiability as the idea that a theory is
scientific only if it makes assertions that can be disproven
[SLO: P-09-G-07] Differentiate the terms 'science', 'technology' and 'engineering' with
suitable examples

181
Science is a collective knowledge about the natural phenomena, processes and
events occurring around us. The process starts with asking a question, how and
why the things in the world behave as such. We try to look orderliness and
regularities among various phenomena apparently of diverse nature. Such study
of nature gave birth to a single discipline, known as Natural Philosophy now
known as science. There was a tremendous increase in the volume of scientific
knowledge at the beginning of nineteenth century. That made it necessary to
classify the study of nature basically into two main disciplines.
(i.) The biological sciences which deal with the living things.
(ii.) The physical sciences which are about the study of non-living things.
Physics is important and basic part of physical sciences beside other
disciplines such as chemistry and geology.
9.1 Scope of Physics Do You Know?
Physics is the fundamental science that deals
with the constituents of the universe, that is, matter,
energy, space, time and their mutual relationships and
interactions. It strives to understand how the universe
works, from the smallest subatomic particles to the
largest star and galaxies. We have studied some of the
basic properties of matter, energy and their mutual This toy which worked
inter-relationship in the earlier chapters of this book. by steam invented by
We will discuss in detail the concept of space and time in Hero, from Alexandria in
the 3rd century.
the higher classes. Briefly, the space is the three- However, the people did
dimensional extent in which all objects and events not think of using such
occur. It provides framework to define positions and things for luxury and
motions of various objects under some force. comfort in those days.
The time measures the sequence and durations of events. It is considered
fourth dimension. For example, oscillating motion such as that of a swinging
pendulum relies on the time interval that determine frequency of oscillations.
Another example is the time dilation which is a phenomenon discussed by
special theory of relativity where time passes slowly for an observer moving at
ultra-high speed compared to one relatively at rest. Physics explores how these
fundamental concepts are inter connected. For example, the theory of relativity
explains how space and time are not absolute quantities but are related to each
other. It describes the relationship between space and time and how they are
influenced by gravity and speed, for example, the bending of light around
182
massive objects like stars. Another branch of physics, the quantum mechanic,
explains the behavior of particles at the atomic and subatomic levels. It is how the
physics has applied its principles to wide variety of phenomena, from everyday
occurrences such as related to motion and heat to the extreme conditions found
in the universe.

9.2 Branches of Physics

Due to expanding scope of research in Physics, it is usually divided into
following branches?

1. Mechanics: It is a study of motion and the

physical effects which influence motion. It is
based on Newton's laws of motion and
gravitation and is often called classical mechanics.

Gears in a mechanical system

2. Heat and thermodynamics: It deal with the

thermal energy possessed by the materials and it is
used when it flows from one body to another.

Heat engine

3. Acoustics: It deals with the nature and

physical aspects of audible sound energy.

Pressure horn

4. Optics: It deal with the physical aspects of

visible light.

Dispertion of light

183
5. Electromagnetism: It is the study of
electromagnetic phenomenon and mutual
relationship between electric current and
magnetic field.
Electric current is produced in a
coil rotated in a magnetic field

6. Quantum Mechanics: It explains the

behavior of particles at the atomic and
subatomic level.

Excited states of atom

7. Relativistic Mechanics: It explains how

space and time are not absolute quantities but
related to observer. It describes the relationship
between them and how they are influenced by
gravity and speed.
Einstein view of gravity
as space time curvature

8. Nuclear Physics: It is the study of the

properties of nuclei of the atoms.

Nuclear atom

9. Particle Physics: It is the study of

subatomic particles and elementary particles
which are basic building blocks of matter.

Quark Structure
of a Neutron

10. Astronomy: It is study of

distribution of celestial bodies like
planets, stars and galaxies.

Extended Universe
184
 11. Cosmology: It explores the
large structure and evolution of the
universe.

Study of exploring universe

12. Solid State Physics: It is the study of

some specific properties of matter in solid
form. Electrical bonding of solids

9.43 Interdisciplinary Nature of Physics

It refers to integration and interaction of Physics with various other fields
of study. Physics, being fundamental science, provides essential principles,
techniques and methods that are applicable across a wide range of disciplines.
Some of these are:
1. Biophysics: Some biological systems and
processes are described using the principles and
technique of physics under this field of Study. Examples
include the mechanics of biological structures, physical
properties of cells, tissues and organs. DNA
Structure
2. Medical Physics: It applies physical
principlestodeveloptechniquesand
technologies for health diagnosis and treatment.
The examples include imaging techniques, such as
X-rays; ultra sound, MRI and CT scan and also
radiation therapy for cancer treatment.
Magnetic Resonance Imaging
(MRI)

3. Astrophysics: It deals with the

physical properties and processes of celestial
bodies and phenomena. For example, the
interaction between the matter and energy in
space to understand the universe as a whole.
Study of celestial bodies
185
 4. Geophysics: It applies physical principle
to the study of internal structure of the Earth, its
magnetic and gravitational fields, seismic
activity (earthquake), volcanoes, etc.

Internal structure of the Earth

5. Climate Physics: It includes the study of

physical process in the environment, including
atmospheric dynamics, climate change and
weather conditions.

A tornado

6. Computation Physics: It is about

the use of computational techniques and
methods to solve complex physical
Computer graphics problems.

9.4 Interdisciplinary Research

Collaboration and interdisciplinary nature of science is essential for
addressing the complex issues and challenges of today. By working together and
sharing knowledge, scientist can achieve more significant breakthrough and
contribute to a deeper understanding of the natural and physical world around
us. It allows us to contribute to advance in technology, healthcare,
environmental issues and many other areas. We need collaborated efforts
because:
(I). Solution of complex issues requires multifacet expertise
Many challenging issues, such as climate change, disease prevention and
treatment, sustainable energy solution are of diverse nature. It is difficult for one
discipline to address them adequately. Such as understanding and mitigating
climate change require knowledge for meteorology, oceanography, physics,
chemistry, biological and environmental sciences. Similarly, the health care
issues such as recent Covid epidemic involved combined efforts of expertise

186
from biology, chemistry, physics, medical technologies and data science to
combat this challenge.
(ii). Interdisciplinary approaches foster innovation
Combined different perspectives and methodologies evolve innovation
or out of box solutions. This approach can lead to novel insight and
breakthroughs that might not emerge working in isolation. For example, nano-
technology is a blend of physics, chemistry, material science and engineering to
create materials and devices at the nano-scale with unique applications in
medical, energy and electronics. In an other field of “artificial intelligence” the
development involves computer science, mathematical logic, neuroscience etc.
The collaboration across these fields enhanced the development of intelligence
systems and their applications.
(iii). Rapid sharing of knowledge and information across the globe
Sharing and collaboration of knowledge across the globe brings rapid
advances in science. The online internet information exchanges, conferences
and workshops provide platforms bringing together researchers from different
fields to share their fresh findings, discussion and brainstorming new
approaches. Collaborated research projects and research journals are also
means of collaborate research.
Interdisciplinary research and collaboration leads to a more holistic
understanding of challenging issues by interacting with different perspectives
such as that of environment and space exploration.

9.5 Scientific Method

Scientific method is a systematic approach used to search for truth of an
issue and problem solving regarding natural and physical world. It is based on
the following steps.
1. Identify or recognize an issue or a problem.
2. Gather information through observations of its various aspects.
3. Propose an explanation or a guess work known as hypothesis.
4. Perform experiment or collect evidences to test the hypothesis.
5. Record, organize and analyze gathered data, plotting and interpreting
graphs to reach at a conclusion which is called a theory.
6. Repeated tests of the theory to wide range of similar issues then lead
towards the formulation of a law.
Some key steps are elaborated here.

187
1. Observation
The first step in scientific method is
to make observations of natural processes
and to collect the data about them. This
maybedone either by ordinary
observations or by obtaining the results
from different experiments. For example, it
is our common observation that shadow of
an opaque object is formed when it is
placed in the path of light coming from the
Sun or a lamp (Fig.9.1). Fig. 9.1

2. Hypothesis
On the basis of the data collected through observations or
experimentation, we can develop a hypothesis. This is done in order to test its
logical results, i.e., it is assumed that nature will act in a particular way under
certain specific circumstances. From the above example, we assume that
shadows of opaque objects are formed when they come in the path of light
because light travels in a straight line.

3. Experiment
Experiment is an organized repeatable process which is used to test the
truth of a hypothesis.
To verify the assumption made in the above example, four card boards,
each with a hole, are placed in a straight line, such that the hole in 1st card is in
front of a torch. When we see through the hole in cards, we can see the light of
the torch (Fig. 9.2-a). If any of these cards is displaced, we cannot see light
passing through (Fig. 9.2-b). Thus, this experiment proves that light travels in a
straight line.

Fig. 9.2 (a)

Fig. 9.2 (b)

188
4.Theory
Observation
After the successful
verification of an assumption and
with the help of careful Hypothesis
experimentation, it becomes a theory
andisapplicable to similar
Experiment
phenomena. With the help of the Lack of
above experiment, the assumption agreement
has been proved that light travels in a Theory
straight line. So it then becomes a
theory.
It is a logical explanation of the Prediction
causes and effects of an issue or an Negative
Positive
event that occurs in nature. result
result

Law

5. Prediction
After the careful analysis of a theory we can make predictions about
certain unknown aspects of nature. To verify the prediction, experiments are
designed to test the theory over and over again. If test result do not agree,
hypothesis is changed or rejected.

6. Falsifiability For Your Information!

It is a concept introduced that suggests a theory

to be considered scientific if it also make predictions
that can be tested and potentially proven false. The
requirement of falsifiability ensures that theories are not
In the 20th century, Albert
based on vague, non-specific or untestable claims. It Einstein declared that
distinguishes scientific theories from false or pretended mass and energy, the two
beliefs that cannot be experimentally tested. concerns of Physics, are
forms of each other. His
theory of relativity altered
man’sviews of the
universe.

189
7. Law
When a theory has been tested many times and generally accepted as
true, it is called a law. The law is such a statement regarding the behaviour of
nature which explains the observations and experiments of the past and can
predict about other aspects of nature. From the fact that light travels in a straight
line, we can predict that shadow of an opaque object, similar in shape, is formed
whenever it is placed in the path of light. For example, the shadow of a ball will be
round whereas the shadow of a rectangular block will be a rectangle After testing
the theory under different situations, this becomes a law of science that light
travels in a straight line.
The theories or laws of physics are man made ideas about the way the
things work. They are liable to be disproved or modified with the future advances
in science which brings fresh facts and new insights about the natural and
physical world.

9.6 Scientific Base of Technologies and Engineering

Science or to be more specific, physics plays a vital role being the core of
each invention based on physical laws and principles. Technology refers to the
methods and techniques developed by using scientific knowledge. It may be a
machine technology or a software programme of information technology. For
example,
(i) Automobile technology is based on the principles of the
thermodynamics.
(ii) Radar technology is based on the detection and reflection principles of
electromagnetic waves.
(iii) Laser technology is based on the principles of atomic physics. It is widely
used in medical diagnosis and treatment, metallurgy, industry,
telecommunication and space exploration.
Engineering is the process of applying various technologies and scientific
principles to design various instruments, tools and build things that help to meet
specific needs in every walk of life. Engineers also consider factors like cost
effectiveness and safety measures when designing various products. Examples
include:
(I) A civil engineer designs a bridge that can withstand strong winds,
earthquakes, intense weather conditions and heavy traffic.

190
8
 (ii) A software engineer designs a user friendly application of a smartphone.
(iii) An aviation engineer looks for lighter material which can withstand
sudden and severe disturbances and extreme weather conditions during
the flight of an aeroplane.
Though the science, technology and engineering fields seem distinct but
they often work together. Scientific discoveries lead to new technologies and
engineers rely on scientific knowledge for our benefits and comforts. They are
the potent for change in the outlook of mankind in shaping life style and
influencing our way of thinking.

KEY POINTS
 Science is a collective knowledge about the natural phenomena and events.
 Physics is the fundamental branch of science which deals with matter, energy, space, time
and their mutual relationships.
 There are many sub fields of physics called its branches such as mechanics, heat, optics,
electromagnetism, etc.
 Interdisciplinary nature of physics refers to integration and interaction of physics with
other disciplines of science. Some of them are biophysics astrophysics, geophysics,
climate physics and computational physics.
 Scientific method is a specific and systematic approach for the search of the truth about a
natural phenomenon or event. Its steps include observation, hypothesis, experiment,
theory, prediction and law.
 The advancement in the science knowledge and its applications through various
technologies and engineering has changed the outlook of mankind and have made our
lives easier and comfortable.

EXERCISE
A Multiple Choice Questions
Tick () the correct answer.
9.1 Physics is a branch of:
(a) Social science (b) Life science
(c) Physical science (d) Biological science
9.2 Which branch of science plays vital role in technology and engineering?
(a) Biology (b) Chemistry (c) Geology (d) Physics

191
8
9.3 Automobile technology is based on:
(a) acoustics (b) electromagnetism
(c) optics (d) thermodynamics
9.4 A user friendly software application of smart phone use:
(a) laser technology (b) information technology
(c) medical technology (d) electronic technology
9.5 The working of refrigeration and air conditioning involves:
(a) electromagnetism (b) mechanics
(c) climate science (d) thermodynamics
9.6 What is the ultimate truth of a scientific method?
(a) Hypothesis (b) Experimentation
(c) Theory (d) Law
9.7 The statement “If I do not study for this test, then I will not get good
grade” is an example of:
(a) theory (b) observation
(c) prediction (d) law
9.8 Which of the following are methods of investigation?
(a) Observation (b) Experimentation
(c) Research (d) All of these
9.9 A hypothesis:
(a) may or may not be testable (b) is supported by evidence
(c) is a possible answer to a question (d) all of these
9.10. A graph of an organized data is an example of:
(a) collecting data (b) forming a hypothesis
(c) asking question (d) analyzing data
9.11. The colour of a door is brown. It is an example of:
(a) observation (b) hypothesis
(c) prediction (d) law

192
B Short Answer Questions
9.1 State in your own words, what is science? Write its two main groups.
9.2 What is physics all about? Name some of its branches.
9.3 What is meant by interdisciplinary fields? Give a few examples.
9.4 List the main steps of scientific method.
9.5 What is a hypothesis? Give an example.
9.6 Distinguish between a theory and a law of physics.
9.7 What is the basis of laser technology?
9.8 What is falsifiabilty concept? How is it important?

C Constructed Response Questions

9.1 Is the theory of science an ultimate truth? Describe briefly.
9.2 Do you think that the existing laws of nature may need a change in future?
Describe briefly.
9.3 Describe three jobs that need the use of scientific knowledge.
9.4 Describe when a theory is rejected or need its modification.
9.5 Comment on the statement. “ A theory is capable of being proved right
but not being proved wrong is not a scientific theory”.
9.6 What has been the general reaction to new ideas about established
truths?
9.7 If a hypothesis is not testable, is the hypothesis wrong? Explain.
9.8 Explain how a small amount of data cannot prove that a prediction is
always correct but can prove it is not always correct.
9.9 What is the relationship between an experiment and a hypothesis?
9.10 Describe why the solution of complex problems need interdisciplinary
research and collaboration.

D Comprehensive Questions
9.1 Describe the scope of physics. What are the main branches of physics?
State briefly.
9.2 What is meant by interdisciplinary fields of physics? Give three examples.
9.3 What is scientific method? Describe its main steps with examples.
9.4 Differentiate the terms, science, technology and engineering with
examples.
9.5 What is the scope of physics in everyday life? Give some examples.

193
 Bibliography Physics Class IX

Name of Book Name of Author/Authors

1. College Physics Vincent P. Colletta
2. Physics Paul A. Tippler
3. Fundamentals of Physics Peter J. Nolan
4. Physics Nuffield Chelsea Curriculum Trust
5. Senior Secondary Physics P.N. Okeke and M.W. Anyakoha
6. IGCSE Physics Tom Duncon and Heather Kennett
7. Coordinated Science Marry Jones and Philip Marchington
8. Physics Zitzewitz Glencoe Macgraw-Hill
9. Principles of Physics F.J. Bueche and David A. Jerde
10. Physics Jerry D. Wilson
11. Physics A. F. Abott
12. Science Insight Michael Dispezio and others
13. Physical Science Prentice Hall Program
14. Balanced Science Jone and Marchington
15. Physics Charles Chew and others
16. Conceptual Physics Paul G. Hawitt
17. Physics Brian Arnold
18. GCSE Physics Steve Witney and others
19. Lower Secondary Science I & II Singapore
20. Integrated Science Holt science and Technology
21. A Textbook of Physics Class-9 Punjab Textbook Board-Edition-2004

194
 Glossary
Acceleration: Rate of change of Density: Mass of unit volume of a
velocity with time. substance.
Accuracy: Relative measurement Derived Quantity: A quantity which is
reflected by the number of significant expressed with reference to base
figures. quantities.
Artificial Satellites: Objects moving in Derived Units: Units which can be
fixed circular orbits around the Earth. derived from base units.
Base Quantity: Such quantity, which Displacement: The shortest distance
can be expressed independently between two points.
without the reference of any other Dynamics: Study of motion of bodies
quantity. under action of forces.
Base Units: The units in System Efficiency: Ratio of output and input.
International, which are seven in Elastic Potential Energy: Energy of a
number. compressed or stretched spring.
Biofuel Energy: Energy obtained from Elasticity: The property of the solids
waste organic materials. because of which they restore their
Centre of Gravity: The point of body original shape when external force
where its weight acts. ceases to act.
C e n t r i p e t a l A c c e l e r a t i o n : Electromagnet: A temporary magnet
A c c e l e r a t i o n p r oduce d by the when electric current flows through a
centripetal force. coil wrapped around an iron rod.
Centripetal Force: The force which Energy: Ability of a body to do work.
keeps an object to move in a circular Equilibrium: A state of a body which
path. has no acceleration.
Circular Motion: Motion of a body Force: The agent that changes or tends
along a circular path. to change the state of a body.
Components of a Vector: Such Fossil Fuels: Oil, gas and coal which
vectors when added give the resultant can be burnt.
vector.
Friction: The force that tends to
Couple: When two equal and unlike prevent the bodies from sliding over
parallel forces act at different points of each other.
a body, then they constitute a couple.
195
Geothermal Energy: Energy of the hot Kinetic Energy: Energy of a body due to its
rocks deep under the surface of the motion.
Kinetic Friction: Friction during motion.
Earth.
Least Count: The minimum measurement
Gravitational Field: The region recorded by an instrument.
around an object where its force of Light Year: The unit of distance for celestial
gravity acts. bodies equal to 9.46 x10 m
15

Gravitational Force: Mutual force of Like Parallel Forces: Forces acting along
attraction between the objects. parallel lines in the same direction.
Limiting Friction: The maximum value of
Gravitational Potential Energy:
static friction.
Energy of body due to its position in
Line of Action of a Force: The straight line
the gravitational field. along which the force acts.
Heat: The form of energy, which is Linear Motion: The motion of body along a
transferred from one place to another straight line.
because of difference of temperature. Mass: That characteristics of a body, which
determines the acceleration produced by the
HorizontalComponent:The
application of a force.
component of a vector which is along Mechanics: The branch of Physics which deals
horizontal or x-direction. with the study of motion of bodies.
Hydraulic Brakes: Brakes working Magnet: It attracts magnetic materials and
according to Pascal's law. stays north-south direction when suspended
freely.
Hydraulic Press: A press that work
Magnetic Compass: A direction indicating
under Pascal's law. device using a magnetic needle.
H y d r o e l e c t r i c G e n e r a t i o n : Magnetic Field: Space around a magnetic in
Conversion of kinetic energy of flowing which force is exerted on another magnet.
water into electrical energy. Momentum: The product of mass and
Inertia: The characteristic of a body velocity of a moving body.
Neutral Equilibrium: The condition of a body
due to which it resists against any
in which its centre of gravity neither rises nor
change in its state. lowers of i ts original position after
Internal Energy: Total energy of disturbance.
molecules of an object. Orbital Speed: A critical speed of a satellite in
Joule: The unit of work in System order to keep on moving around the Earth at a
specific height.
International.
Parallel Forces: Forces acting along the
Kilowatt-hour: Work done in one hour at a
parallel lines.
rate of one Kilowatt.
Physical Quantities: Measurable
Kinematics: Study of motion of bodies characteristics of objects.
without taking into consideration of the mass
and forces.
196
Physics: That branch of Science, which which it comes to its original condition after
explains the properties of matter, energy, being disturbed.
space and time. Static Friction: The force of friction arising due
Plasma: A state of matter in which most of the to applied external force before motion of one
atoms are ionized into positive ions and body over the other.
electrons. Temperature: Degree of hotness or coldness
Power: Rate of doing work. of a body.
Precision: Determined by the instrument Tension: The force acting along a string
used equal to its least count. Thermometry: Art of measurement of
Prefix: Symbols added to a unit to write it by temperature.
power of 10. Torque: Product of force and its moment arm.
Pressure: Force exerted normally on unit area Trigonometric Ratios: The ratios of the sides
of an object.
of a right-angled triangle.
Random Motion: Motion without any
Uniform Acceleration: Equal changes in
consideration of time and direction.
velocity in equal intervals of time.
Perpendicular Components: The
components of a vector which are mutually Uniform Speed: Equal distances covered by a
perpendicular to each other. body in equal intervals of time.
Resolution of a Vector: Division of a vector Uniform Velocity: Equal changes in
into its components. displacement in equal intervals of time.
Resultant Vector: Such a vector which shows Unlike Parallel Forces: Forces acting along
the combined effect of two or more vectors. parallel lines but in opposite directions.
Rolling Friction: The friction produced during Unstable Equilibrium: The condition of a body
the motion of one body over the other with in which it does not come to its original
the help of wheels. condition after disturbance.
Scalar Quantities: Quantities which can be Vectors Quantities: Quantities which can be
specified by their magnitudes only. specified by magnitude as well as direction.
Scientific Method: Logical applications of Velocity: Rate of change of displacement with
argumentsthat explain a certain time.
phenomenon. Vertical Component: The component of a
Scientific Notation: The number written as vector which is along vertical or y-direction.
power of ten or prefix in which there is only Vibratory Motion: The to and fro motion of
one non zero number before decimal. body about a fixed point.
Significant Figures: In a measurement, the Volume Expansion: Increase in volume.
correctly known digits and the first doubtful Watt: The unit of power in System
digit. International.
Sliding Friction: The friction between two Weight: The force with which the Earth pulls a
surfaces sliding against each other. body towards its centre.
Solar Energy: Energy of the sunlight.
Wind Energy: Kinetic energy of fast-moving
Speed: Distance covered by a body in one
air/wind.
second.
Work: The product of force and the
Stable Equilibrium: The condition of a body in
displacement in the direction of force.
197
 INDEX
A Derived units 9
Acceleration 29 Displacement 34
Action 34 Distance 34
Accuracy 20 Distance-time graph 38
Addition of vectors 29 Dynamics 29
Ampere 8 E
Applications of centripetal force 98 Efficiency 122
Area under graph 43 Electromagnet 169
Artificial satellites 97 Elastic limit 129
Atmospheric pressure 136 Elastic potential energy 111
Axis of rotation 82 Elasticity 129
B Energy 109
Bar magnet 164 Energy flow system 119
Barometer 138 Equation of motion 46
Base quantities 7 Equilibrium 90
Biofuel-energy 117 F
Biomass 117 First equation of motion 46
C First law of Newton 57
Candela 8 Force 53
Car lift 140 Forms of energy 109
Centre of gravity 88 Fossil fuel energy 112
Centre of mass 88 Friction 53
Centripetal force 98 G
Circular motion 33 Geothermal energy 115
Components of a vector 85 Graphical analysis of motion 38
Conditions of equilibrium 91 Gravitational field strength 53
Conservation of energy 112 Gravitational force 53
Couple 83 Gravitational potential energy 110
D H
Density 131 Head-to-tail rule 31
Derived quantities 7 Heat 149

198
Hooke's Law 129 Measuring cylinder 17
Hydraulic brakes 140 Measuring instruments 11
Hydraulic press 141 Mechanics 185
Hydroelectric energy 113 Methods to reduce friction 69
Hypothesis 189 Metre rule 11
I Metre 8
Impulse 69 Mole 8
Inertia 58 Molecular theory of matter 150
Internal energy 152 Moment arm of a force 82
J Momentum 69
Joule 108 Motion 32
Junction 154 Motion under gravity 44
K N
Kelvin 8 Neutral equilibrium 95
Kilogram 8 Newton's laws of motion 57
Kinetic energy 109 Normal force 54
Kinetic friction 66 Nuclear energy 115
Kinetic molecular model of matter 150 P
L Paramagnetic materials 173
Law of conservation of momentum 72 Parallax error 12
Laws of motion 57 Pascal's law 140
Least count 12 Permanent magnet 165
Like parallel forces 81 Physical balance 16
Limiting friction 75 Physical quantities 6
Line of action of a force 82 Physics 183
Linear motion 33 Plasma 151
Liquid pressure 134 Position 29
M Potential energy 110
Magnet 167 Power 120
Magnetic field 167 Prefixes 9
Magnetic compass 165 Pressure 133
Magnetic domains 176 Precision 21
Magnetic materials 163 Principle of moments 87
Manometer 139

199
 R Thermometers 153
Random motion 33 Thermometric properties 151
Rectangular components 84 Third equation of motion 47
Renewable energy resources 117 Third law 60
Representation of vectors 30 Torque 83
Resolution of vectors 84 Translatory motion 33
Rigid body 82 Trigonometric ratios 86
Rolling friction 68 Turning effect of a force 82
Rotatory motion 33 Types of motion 33
S U
Scalar quantities 29 Uniform acceleration 37
Science 181 Uniform speed 39
Scientific notation 10 Uniform velocity 36
Screw gauge 13 Unit of force 59
Second 8 Unit of work 108
Second equation of motion 46 Units of power 121
Second law 59 Units of system international 8
Significant figures 20 Unlike parallel forces 81
Sliding friction 66 Unstable equilibrium 95
Slope of a graph 40 V
Solar energy 114 Variable velocity 36
Speed 34 Variation of 'g' with altitude 62
Speed-time graph 41 Vector quantities 29
Spring balance 16 Velocity 34
Stable equilibrium 94 Vernier Callipers 12
Static friction 67 Vibratory motion 33
Stopwatch 17 W
System of units 8 Watt 121
T Weight 62
Technology 188 Wind energy 116
Temperature scales 154 Work 106
Temporary magnet 166 Z
Tension in the string 57 Zero error 12
Theory 188

200
201