science 9

Based on New Curriculum

According to the compulsory Science
curriculum prescribed by the Curriculum
Development Centre of Nepal

Times’ Crucial

SCIENCE
9Grade

Authors
Kamal Prasad Sapkota
Rajan Kumar Shrestha

TIMES Banasthali, Kathmandu, Nepal
Tel.: 01-4385227, 4355052
Int’l Publication Pvt. Ltd. E-mail: [email protected]
Website: timespublication.com.np
“Time for good reading”

Times’ Crucial

SCIENCE

Published by:
Times International Publication Pvt. Ltd.

Authors:
Kamal Prasad Sapkota
Rajan Kumar Shrestha

Edition:
First: 2070 B.S.
Revised Edition: 2074 B.S.
Reprint: 2075 B.S.

Layout and Design:
Times Desktop

ISBN 993758046-3

© Copyright: Publisher

Printed in Nepal

Preface

Human life is always in progress. Newer technologies and equipmen are developed or
discovered in every second. Lengthy and time consuming work of past are now done
within a few moments. People can travel far off distances within short time. Several
fatal diseases have been eradicated. The achievements, that we are enjoying today
are the results of advancement in science and technology. Hence, science has become
an integral part of our education system.

Times' Crucial Science is a series of text books for the school level students of grades
LKG to class Ten. The series has been prepared for the young learners emphasizing
on student-centred teaching techniques, Learning Circle Based Activities, practicable
activities, scientific approaches and innovative learning techniques. The text of each
lesson is preceded by a warm up activity that encourages students to take part actively
in the learning process. The series includes the teaching techniques and methods for
the teachers under the title Note to the Teacher. It is based on the latest syllabus
prescribed by CDC Government of Nepal. Hence, this series acts as the foundation
of science for the curious and inquisitive young minds.

Each book of this series covers the syllabus of Science . The first part contains chapters
of Science and the second part, chapters of Environment Science. All the chapters
of Science and Environment are provided with a wide variety of exercises which
encourage the students in learning and sharpening their mind. A Project Work is
asked at the end of each lesson so that student can apply their knowledge to solve the
problems of their day-to-day life. In the beginning of each lesson, thought provoking
questions are given under the heading Mind Openers. This activity will encourage
students to use their brain.

We feel delighted to extend our sincere gratitude to all Principals of the schools,
teachers and students for their contribution in revising the book and making it
simpler and more crucial. We are equally thankful to the publisher Mr. Sunil Subedi
without whom this series would not have been possible in the present form. We are
also thankful to Times Desktop for providing this smart form to the book.

Constructive suggestions and recommendations from teachers, students and well
wishers for the further improvement of the books are the most welcome.

- Authors

Contents Page No.

Chapter 1-148
Physics
1
1 Measurement 17
48
2 Force 67
3 Simple Machine 85
4 Work, Energy and Power 104
5 Light 128
6 Sound 149-257
7 Current Electricity and Magnetism 149
170
Chemistry 180
193
8 Valency and Molecular Formula 216
9 Chemical Reaction 227
10 Solubility 235
11 Some Gases 250
12 Metals 258-378
13 Carbon and Its Compounds 258
14 Water 294
15 Chemical Fertilizers Used in Agriculture 312
344
Biology 356
368
16 Classification of Living Things 379-416
17 Adaptation of Organisms 379
18 Systems 389
19 Sense Organs 397
20 Evolution 410-412
21 Nature and Environment

Geology and Astronomy
22 Natural Hazards
23 Green House
24 The Earth in the Universe

Specification Grid / Model Test Paper

Chapter

1 Measurement
Louis Essen
He is known for the precise
measurement of time and the
determination of the speed of light.
Estimated Periods: 6

ObjAetctthiveeesnd of the lesson, students will be able to:

• define fundamental and derived quantities;

• show the relationship between fundamental and derived units;

• measure some fundamental quantities and derived quantities.

Mind Openers

• What is measurement?

• What is physical quantity?

• What are fundamental and derived units?

• How do you measure mass and time? Discuss.

Introduction
In our practical life, we need to measure various quantities. We
measure volume of water and amount of rice at the time of cooking
food. Measurement of length of cloth and size of human body is done
before sewing clothes. When we go to a shop for buying things, the
shopkeeper measures the quantity of things and gives to us. Thus,
measurement is common and general human activity.
We can measure some quantities whereas some other quantities
cannot be measured. The quantities which can be measured are
called physical quantities. Length, mass, time, volume, speed,
acceleration, etc are physical quantities. But sorrow, happiness,
sadness, beauty, etc cannot be measured. Therefore, they are called
non-physical quantities.
For measuring any physical quantity, we need certain standard
or known quantity called unit. The measurement of any unknown
quantity can be done by comparing it with a known or standard
quantity. Thus, measurement is defined as the process of comparison
of an unknown quantity with a known or standard quantity.

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Importance of measurement
1. It is needed for selling, buying and exchanging of goods.
2. It is needed for performing scientific experiments.
3. It is needed for preparing medicines and treating patients.
4. It is needed for preparing food.
5. It is needed for global understanding of the quantity of a substance.

Unit

Unit is a known or standard quantity in terms of which other
physical quantities are measured. For examples, kilogram, metre,
second, etc. Metre is a unit because it is used to measure the
physical quantities like length, area, volume, velocity, etc and value
of 1 meter is known. If the value of 1 meter is unknown, we don’t
understand the value of 6 meter, 7 meter and so on. When we say
length of a bench is 6 metres, it means the length of the bench is 6
times of one metre. For complete measurement, we need numerical
value and unit. If we express the measurement in numerical value
only, it is meaningless. For example, if we say length of a bench is
6, it does not give full sense. It may be 6 feet, 6 inch, or 6 metre.

Physical quantity = Numerical value × Unit

Example: Length =5 × m = 5m

There are different units for measuring different physical quantities.
The units having following features are suitable for measurement:

1. The unit should be well defined and accepted.
2. The unit should be reproducible.
3. The unit should not change with the change in

temperature, pressure, time, etc.
4. The unit should be of suitable size.

Sometimes, some fraud devices are used for measuring physical
quantities. To monitor the measuring devices and to punish the
wrong doers, the Government of Nepal has a separate department.
The Nepal Bureau of Standards and Metrology monitors the
measuring devices in every two years in the markets and seizes
fraud devices. Culprits are caught and punishment is recommended.

The Nepal Bureau of Standards and Metrology has regional offices
in different parts of the country. One of them lies in Kathmandu
valley whereas seven others are outside the valley.

Times' Crucial Science Book - 9 2

Activity 1.1 Mark two points in a white sheet of paper. Measure the distance between

these two points using the ruler (scale) of each student of your class. Did you get the same
length in each case? Why do these scales give different measurements? Discuss in class.

Fundamental quantities

The quantities which are independent of other quantities are
called fundamental quantities. For examples, length, mass, time,
temperature, electric current, luminous intensity and amount of
substance are fundamental quantities.

Derived quantities

The quantities which are derived from fundamental quantities
are called derived quantities. For examples, velocity, area, speed,
acceleration, density, etc.

Speed is calculated as distance travelled by a body per unit time.

Speed = Distance
Time

Distance means the length and, hence, speed can be expressed as:

∴Speed = Length
Time

Thus, speed is derived from two fundamental quantities: length and
time. Therefore, it is a derived quantity. In the same way, area is
derived from two lengths, i.e. Area = (length)2. Therefore, area is a
derived quantity. There are thousands of derived quantities.

Systems of Measurement

Different traditional and local systems of units and measurements
are still in use at various places. Dharni, Ser, Chhatak, etc are used
for the measurement of mass. Feet, hand-span, fingers, yard, etc
are used for the measurement of length. Mana, pathi, muri, etc are
used for the measurement of volume. Those units can be understood
by the local people only. Moreover their values differ from person to
person and place to place. To maintain uniformity in the units and
measurement, following systems of measurement are used:
a) FPS System: The system of measurement in which length is
measured in feet, mass in pound and time in second is called FPS
system.

3 Times' Crucial Science Book - 9

b) CGS System: The system of measurement in which length is
measured in centimeter, mass in gram and time in second is called
CGS system.
c) MKS System: The system of measurement in which length is
measured in meter, mass in kilogram and time in second is called
MKS system.
d) SI System: The full form of SI is system international de units.
In 1960, an international convention of scientists from the various
countries was held in France. All the scientists agreed to use the
same units throughout the world. These units are called SI units.
Thus, SI system is the system of units which is recommended by
the international convention of scientists in 1960 and is accepted
throughout the world.
It is the extended form of MKS system. In this system, some other
quantities are also added as fundamental quantities. Following
table shows the fundamental quantities and their units.

SN Fundamental quantities Fundamental units Symbol

1 Length Meter m

2 Mass Kilogram kg

3 Time Second s

4 Temperature Kelvin K

5 Electric Current Ampere A

6 Luminous intensity Candela cd

7 Amount of substance Mole mol

Importance of SI units

1. It brings uniformity in measurement all over the world.

2. It eliminates the inaccuracy and solves the

problems due to local system of measurement.

3. It has solved the problems in carrying out different

scientific experiments.

Differences between MKS and SI system

MKS system SI system

1. It is the metric system of measurement. 1. It is the refined and extended form of MKS system.

2. It is based on three fundamental quantities: 2. It is based on seven fundamental quantities (including

mass, length and time. three quantities of MKS system).

3. It has a limited use. 3. It is used all over the world.

Times' Crucial Science Book - 9 4

Fundamental units
The units which are used to measure fundamental quantities are
called fundamental units. In other words, fundamental units are
the units which are independent of other units. Meter, second,
kilogram, Kelvin, Ampere, candela, etc are some fundamental units
Derived units
The units of derived quantities are called derived units. In other
words, the units which are derived from fundamental units
are called derived units. For examples, units of velocity, area,
acceleration, force, volume, density, etc are derived units because
they are derived from two or more fundamental units.

The derived units of some physical quantities are given below:

Derived Related Fundamental
SN formulae
Units Symbol units
quantities
Metre per involved
second
1. Velocity Distance ms-1 m/s
Time Meter per
square second
2. Acceleration Velocity Square metre ms-2 m
Time Cubic metre m2 s×s
m3
3. Area length × breadth Newton N m×m
m×m×m
4. Volume length × breadth× height Joule J
kg×m
5. Force mass × acceleration Watt W s×s
Kilogram per
6. Work Force × distance kg/m3 kg×m×m
7. Power cubic metre s×s
8. Density Work Pascal Pa
9. Pressure Time kg×m×m
10. Frequency Hertz s×s×s
11. Potential difference Mass
12 Moment Volume Volt kg
Newton × Meter m×m×m
Force
Area kg
Velocity s×s×m
Wave length
Hz Cycle/s
work done
charge V kg×m×m
Nm s×s×s×A
Force × distance
kgm2/s2

Why is unit of velocity a derived unit?

The units that are expressed in terms of two or more fundamental units are called
derived units. In case of velocity,

We have:

Velocity = Displacement = Length m
Time Time =s

Since the unit of velocity contains two fundamental units, i.e. metre and second,
it is a derived unit.

5 Times' Crucial Science Book - 9

Similarly, unit of density is a derived unit. It is derived from two fundamental units
kilogram (kg) and metre (m).

Density = Mass = kg
Volume m3

Thus, unit of density is kg/m3.
Similarly, the unit of acceleration is a derived unit.

Change in velocity m/s m
Acceleration = Time = s = s2

Thus, unit of acceleration is m/s2, which is derived from two
fundamental units: metre (m) and second (s) and is a derived unit.

Solved Numerical Problem 1.1

What are the fundamental units involved in Watt?

Solution:Watt is the unit of power.

We know that,

Power = Work done
Time taken
Force × Displacement

=
Time

Mass × Acceleration × Displacement
= Time

= Mass × Velocity × Displacement
Time × Time

Mass × Displacement × Displacement
= Time × Time × Time

Mass, displacement and time are fundamental quantities. Now putting their

SI units in their places,

= Kg × m × m = kgm2s-3
s×s×s

∴Thus, the fundamental units involved in watt are kgm2s-3.

Measurement of length

Length is defined as the distance between any two points. Its SI
unit is metre. It is also measured in the units such as centimeter,
kilometer, feet, mile, etc.

One standard metre is defined as the distance between two fine gold
lines marked on Platinum-Iridium alloy rod at temperature of 0°C
kept at the International Bureau of weights and measures at Sevres
near Paris. Copies of one standard meter are made and distributed

Times' Crucial Science Book - 9 6

to standardizing agencies of different countries. In Nepal standard
metre has been kept in Nepal Bureau of Standards and Metrology,
Kathmandu. Commercial standard metres are made based on the
standard metre kept by the standardizing agency. The commercial
standard metres are checked periodically by this metrology
department.

Multiples and sub multiples of metre Conversion of Units

10 millimetre (mm) = 1 centimetre (cm) 1 cm = 10−2m
10 centimetre = 1 decimetre (dm)
10 decimetre = 1 metre (m) 1mm = 10−3m
10 metre = 1 decametre (dam)
10 decametre = 1 hectometre (hm) 1mm = 10−6m
10 hectometre = 1kilometre (km)
1nm = 10−9m

1Å = 10−10m

mm= micrometer, nm=nanometre

Å= angstrom

Correct method of measuring length

Following precautions should be taken for correct measurement of
length.

a) Avoid gap between the scale and the object to be measured.
b) Put the scale in such a way that its zero reading lies at one end

of the object.
c) Fix your eyes perpendicular to the scale at the end of the object.
d) Use error free scale.

Measurement of mass
The total amount of matter contained in a body is called its mass.
The mass of an object depends upon the number of molecules and
size of the molecules contained in it. Its SI unit is kilogram (kg). It
is also measured in gram, quintal, ton, etc.

1 kilogram mass of platinum iridium alloy

7 Times' Crucial Science Book - 9

One standard kilogram is defined as the mass of Platinum-Iridium
alloy cylinder of diameter equal to its height kept at International
Bureau of Weights and Measures at Sevres in France. A copy of
one standard kilogram is kept in the standardizing agency of every
country.

Multiples and sub-multiples of gram Conversion of Units

10 milligram (mg) = 1 centigram (cg) 1mg = 10−3 g

10 centigram = 1 decigram (dg) 1g = 10−3 kg

10 decigram = 1 gram (g)

10 gram = 1 decagram (dag) 1kg = 103 g

10 decagram = 1 hectogram (hg) 1mg = 10−6kg

10 hectogram = 1 kilogram (kg)

100 kilogram = 1 quintal 1quintal = 102kg

1000 kilogram = 1 metric tonne 1metric tonne = 103kg

Measurement of time

The duration between any two events is called
time. Its SI unit is second. Time is also measured
in minute, hour, day, week, month, year, decade,
etc.

One standard second is defined as the time taken
by Cesium-133 atoms to make 9192631770 vibrations.

The time taken by the earth to make one complete rotation around
its axis is one solar day. A solar day is divided into 24 equal parts.
Each part is called an hour. One hour is divided into 60 equal parts.
Each such part is called minute. One minute is again divided into
60 equal parts; each part is called second. Thus,

1 solar day = 24 hrs

1 hour = 60 minutes

1 minute = 60 seconds

1 solar day = 24 × 60 × 60 seconds

1 solar day = 86400 seconds

∴1 second = 1/86,400 th of a solar day

Thus, 1 second may also be defined as 1/86,400 th part of a mean
solar day.

Time is measured by different types of watches or clocks.

a. Mechanical watch: This watch works on the basis of oscillation

Times' Crucial Science Book - 9 8

of a simple pendulum. The length of a pendulum changes due to
the change in temperature thereby changing the time period of
oscillation. So, it cannot measure time accurately.

b. Quartz watch: It works due to vibrations of quartz crystals. It
measures the time more accurately than mechanical watch.

c. Atomic watch: This watch works on the basis of vibrations of
Cesium-133 atom. It measures time the most accurately.

Activity 1.2 To observe the oscillation of a pendulum.

Materials required:

A thread, a metallic bob, stop watch, etc.

Procedure:

1. Take a metallic bob and tie it with one end
of a thread of about 50 cm length.

2. Tie another end of the thread to a nail fixed A B
on the wall.

3. Pull the bob upto the point A and then release it.

4. The movement of the bob from point A to B then back to A is called
oscillation.

5. Note the time required for 20 oscillations and then calculate the time
required for 1 oscillation.

Differences between pendulum clock and quartz clock

Pendulum clock Quartz clock

1. It works on the basis of oscillation 1. It works on the basis of

of a simple pendulum. oscillation of quartz crystals.

2. The time shown by a pendulum 2. The time shown by a quartz

clock fluctuates by a few seconds to clock fluctuates by a few seconds

minutes in a day. in a month.

Zenith
When one stands at a particular place, the point in the sky directly
above the head is called zenith. If the sun is at a particular zenith,
it takes 24 hours to come back to the same zenith.
Measurement of area
The space occupied by a surface of a body is called its area. Its SI

9 Times' Crucial Science Book - 9

unit is square metre (m2).
The other units of area are square centimeter (cm2), square feet
(ft2), etc.
Areas of regular objects are calculated by different formulae.

breadth radius
height
length base

Area of a rectangle = length × breadth

A=l×b

Area of right angled triangle = 1 × base ×height
1
2

Area ofAci=rc2le×=b×(hradius)2

[ [A=r2
22
Where,  = 7

Area of a square = length × length

A= l×l

A = l2

Area of an irregular body is calculated by using a graph paper.

Activity 1.3 To find the area of a leaf

Materials required:

Graph paper, a leaf, pencil, etc.

Procedure:

1. Take a leaf and place it on a graph paper.

2. Mark the boundary of the leaf with a pencil.

3. Remove the leaf and count the number of complete squares and

then the number of incomplete squares within the boundary of the

leaf.

4. Calculate the area of the leaf by using following formula:

Area of the leaf

= (No. of complete squares + 1 × No. of incomplete squares) × Area of
2
a unit square in graph

Times' Crucial Science Book - 9 10

Measurement of volume

Total space occupied by a body is called its volume. The SI unit of
volume is cubic metre (m3). The other units of volume are cubic feet,
cubic centimeter, cubic kilometer, etc. Volume of regular objects is
calculated by different formulae.

height r 50 0
40 0
length breadth 30 0
20 0
10 0

Volume of a cuboid body = length × breadth × height

V=l×b×h

Volume of a cube = length × length × length

=l×l×l ∴ V = l3

Volume of a cylindrical body =  × (radius)2 × height

V = r2h

Volume of a sphere = 4 (radius)3 ∴ V = 4 r3
3 3

Volume of liquid is determined by using a measuring cylinder.

Similarly, volume of irregular objects is calculated by using

measuring cylinder. In this method, a principle is used, in which

Volume of irregular body = Volume of the displaced liquid.
Activity 1.4 To find the volume of an irregular object.

Materials required:

Measuring cylinder, water, a piece of stone, etc.

Procedure:

1. Take a measuring cylinder and pour
water in it upto 50cc.

2. Tie a piece of stone to a thread and immerse it into the water of the
cylinder.

3. Note the new volume of the water.

4. Calculate the volume of the stone by using formula.

Volume of stone = Volume of the water after immersing stone − initial volume of water

= V2 −V1
= 70−50 (from the figures)

= 20cc.

Thus, the volume of the irregular object, i.e. a piece of stone is 20cc

11 Times' Crucial Science Book - 9

Scientific notation
Very small and very large numbers can be expressed in power of
ten which is known as scientific notation. Following points should
be kept in mind while expressing numbers in power of ten:
i) While shifting decimals to the left, the power of 10 should be

increased by one in each shift.
Example

3750000
Here, decimal is at last, shifting decimal to left by one shift,
then

3750000 = 375000.0 × 101
Similarly, 375000 = 3.75 × 101 × 105

3750000 = 3.75 × 106
ii) While shifting decimals to right, the power of ten should be

decreased by one in each shift.
Example

0.000754
= 7.54 × 10−4
Note: The number which is kept in power of l0 should not be more
than 10 and less than 1.
Solved Numerical Problem 1.2

a. Express 98410000 in power of 10.

98410000

= 9841000.0 × 101 [Shifting decimal to the left by one shift)

= 9.841000 × 101 × 106 [Shifting decimal to the left by 6 shift)

= 9.841 × 107

∴98410000 = 9.841 × 107

b. Express 0.0000732 in power of 10.

0.0000732

= 00.000732 × 10−1 [Shifting decimal to the right by one shift)

= 7.32 × 10−1 × 10−4 [Shifting decimal to the right by four shifts)

= 7.32 × 10−5

∴ 0.0000732 = 7.32 × 10−5

Times' Crucial Science Book - 9 12

Solved Numerical Problem 1.3

Calculate the volume of a sphere whose radius is 6cm.

Given,

Radius (r) = 6cm

Volume of sphere (V) =?

We have,

V= 4 r3 = 4 × 22 = 905.14cm3
3 3 7 × 63

∴ Volume of the sphere = 905.14cm3

Learn and Write

1. SI system is extended form of MKS system. Why?
In MKS System, only three quantities, i.e. length, mass and time
are used as fundamental quantities. But in SI system, four more
quantities, i.e. temperature, current, luminous intensity and
amount of substance are also included as fundamental quantities.
It shows that, the units of length, mass and time are same in both
the systems. Thus, the SI system is the extended form of MKS
system.

2. The unit of work is derived unit. Why?
The quantity of work done is obtained by using formula:
Work = Force × displacement
= Mass × acceleration × displacement

= Mass × Velocity × displacement
Time

= Mass × Displacement × displacement

Time× Time

= kg×m×m [Writing the units of quantities]
s×s

= kgm2 / s2

Since the unit of work involves the use of three fundamental units,
i.e. kg, m and s; it is a derived unit.
3. The SI units make the measurement systematic. Why?
Before the declaration of SI units, there were various local systems
of measurement. The units used in one place could not be understood
in another place or their amounts used to be different. When SI
units were declared, they started to be used throughout the world.
Thus, the measurement system became uniform and systematic.

13 Times' Crucial Science Book - 9

4. Write any two advantages of SI system of measurement.
The SI system of measurement is the more accurate and scientific
system of measurement. It has the following advantages:
a. It includes the units of seven fundamental quantities.
Using these fundamental quantities, we can determine the
units of any derived quantity.
b. It has brought uniformity in measurement all over the
world.

5. The weight and length measuring devices in the market are
checked by the Nepal Bureau of Standards and Metrology
once in every two years. Why?
The correct measuring devices may get errors due to different
factors such as weather, wear and tear due to excessive use, etc.
Sometimes, the ill-minded and corrupt businesspersons may use
false devices for the measurement purpose. To correct errors and to
remove the false devices from the market, the measuring devices
are checked by Nepal Bureau of Standards and Metrology once in
every two years.

6. What is meant by scientific notation or standard notation?
The short representation of large figures of numbers using the
power of 10 is called scientific notation. It is also known as standard
notation.

Main points to remember

1. The process of comparison of an unknown quantity with a
known or standard quantity is called measurement.

2. Unit is the known or standard quantity in terms of which other
physical quantities are measured.

3. The quantities that can be measured are called physical
quantities.

4. The physical quantities which are independent of other
physical quantities are called fundamental quantities.

5. The quantities which are derived from fundamental quantities
are derived quantities.

6. MKS, CGS, FPS and SI systems are various systems of
measurement.

7. Length is defined as the distance between any two points.
8. The duration between any two events is called time.
9. One standard meter is defined as the distance between two gold lines

marked on Platinum-Iridium rod at temperature of 0°C kept at the
International Bureau of Weights and Measures at Sevres in France.

Times' Crucial Science Book - 9 14

10. One standard kilogram is defined as the mass of Platinum

IridiumalloycylinderofdiameterequaltoitsheightkeptatInternational

Bureau of Weights and Measures at Sevres in France.

11. One standard second is defined as 1/86,400 th part of a mean

solar day.

12. The space occupied by the surface of an object is called area.

13. Total space occupied by a body is called its volume.

Exercise

1. Choose the best alternative in each case.
a. Which of the following is a physical quantity?
i. Tension ii. Grief iii. Heat iv. Happiness
b. Which of the following is a fundamental quantity?
i. Speed ii. Area iii. Volume iv. Length
c. Which of the following is not the derived unit?
i. Mole ii. Newton iii. Pascal iv. Watt
d. When was the SI system of measurement brought into use?
i. 1995 ii. 1960 iii. 1980 iv. 2000
e. Which of the following is a fundamental unit?
i. Candela ii. Ampere iii. Mole iv. All of these

2. Answer these questions in brief.
a. Define:
i) Measurement ii) Physical quantity iii) One standard metre
iv) Zenith v) One standard second
b. Why is measurement important?
c. What is fundament unit? Give some examples.
d. What is unit? What are the features of good units?
e. What are various systems of measurement?
f. What is SI unit? Why is it better system of units?
g. Write differences between:
i. Pendulum clock and quartz clock
ii. Fundamental unit and derived unit
h. What are the fundamental units involved in the units of following
quantities:

i. Volume ii. Work iii. Power iv. Density

v. Potential difference
i. What is area? How do you measure the area of an irregular body?
j. What is volume? How do you measure volume of an irregular body?

3. Give reasons:
i. Watt is a derived unit.
ii. SI system is the extended form of MKS system.

15 Times' Crucial Science Book - 9

iii. Pendulum clock is not accurate clock for the measurement of time.

4. Numerical problems
a. Convert the following.
i) 2.4 millimetres into metre ii) 4 hours into seconds
iii) 200 grams into kilogram iv) 124 milligram into gram
v) 300 cm2 into m2 vi) 4 km2 into m2
b. A book has dimensions of 24cm × 15cm × 4cm and weight 1.5 kg. It
consists of 500 sheets of papers. Find
i. the volume of the book ii. thickness of each sheet
iii. the area of each sheet
c. Find the volume of a cylinder whose length is 150 cm and diameter
is 60 cm.
d. Express the following numbers in power of 10. Simpliy if necessary.
i. 753000000 ii. 0.000835 iii. 3.75 × 10−2× 4.2 × 106

Answers 4.a) i. 0.0024 mii. 1.44 × 104 s iii. 0.2 kg iv. 0.124 g

v. 0.03 m2 vi. 4 × 106m2 b) i. 1440 cm3 ii. 8 × 10–3 cm iii. 360 cm2

c) 4.24 × 105 cm3 d) i. 7.53 × 108 ii. 8.35 × 10–4 iii. 1.575 × 105

Project Work

Observe the different devices that are being used to measure different physicalquantities
in your home and locality. Then write your findings in the given table.

Glossary

Numerical: Related to number
Culprits: Wrongdoers
Mana: A local unit to measure the volume of grains
Pathi: Eight manas is equal to one Pathi
Commercial: Related to commerce and trade, available in the market

Times' Crucial Science Book - 9 16

Chapter

2 Force
Sir Isaac Newton
He discovered Newtonian mechanics, Universal
gravitation,Calculus, Newton's laws of motion,
Optics, Binomial series, Newton's method, etc.
Estimated Periods: 12

ObjAetctthiveeesnd of the lesson, students will be able to:

• tell effects of force;

• define inertia and explain its types;

• define acceleration and calculate the acceleration of a moving object;

• explain equations of motion and solve simple problems related to the motion;

• explain Newton’s laws of motion and tell their uses.

Mind Openers

• A ball easily moves but not a bus when we push them. Why?

• Why do passengers of a bus fall backward when the bus moves suddenly?

• What is acceleration? How can you calculate acceleration of an object? Discuss.

Introduction

Suppose, a book is lying on a table. It remains in the same position
until someone displaces it by pushing or pulling. When anyone pulls
or pushes, force is applied.

Now, consider a ball is rolling on a ground. The ball finally stops
after covering some distance. But, the ball covers more distance
if more force is applied to the ball in the same direction of motion.
The ball covers more distance when the roughness of the ground
decreases. The reason that the ball stops after covering some
distance is the opposing force called friction created between the
ball and the rough surface.

Consider a big stone is at rest. Apply force to it by pushing and
pulling. Here, your force may not be sufficient to move it. Similarly,
a moving body does not stop when the applied force is insufficient.
It is clear from the above discussion that force is used to change the
position or state of a body. But, it is not always sure that force can

17 Times' Crucial Science Book - 9

change the state. Thus, force is defined as the pull or push which
changes or tends to change the state of rest or motion of an object. The
SI unit of force is Newton. It is measured in Dyne in CGS system.
Relationship between newton and dyne
1 newton = 1kg × 1m/s2 (∴ F= m × a)

= 1000g × 100cm/s2
=100000gcm/s2
=105gcm/s2
=105dynes
∴1N=105dynes

Effects of force

a. Force can change the state of rest or motion of a body.
b. It can change the speed of a moving body.
c. It can change direction of a moving body.
d. It can change the shape of a body.

Vectors and scalars

Physical quantities are classified into two categories. They are:

i. Vectors ii. Scalars

Vector quantities

The quantities which have both magnitude and direction are called
vector quantities. Displacement, force, velocity, acceleration, etc
are vector quantities. A vector quantity is generally represented
by a line with arrowhead. The length of the line represents the
magnitude and the arrowhead represents the direction.

For an example,

A body covers displacement of 10m from point A to B towards east.

It is represented by a straight line AB with an arrowhead towards

east, i.e. it is represented as AB . 10m
AB

If the displacement of 20m is covered from point C to D due east,

it is represented by a straight line CD with an arrowhead towards

east, i.e. it is represented as CD .

20m
CD

Vectors cannot be added by simple algebraic methods. Their
additions are done by the laws of vectors such as triangle law,
parallelogram law, etc.

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Example:
1. Consider two forces 1 N and 3 N are applied on a body in
the same direction. The resultant force of those two forces is
given by the addition of these two forces. Mathematically,
Resultant force = (1N + 3N = 4N)
1N
4N

3N .

2. Consider 1N force is applied to an object towards one
direction and 3 N force is applied to the same object in
opposite direction as shown in the figure. The resultant force
is calculated by subtracting one force from another force.

Resultant force = 3N —1N = 2N.

1N 3N 2N

3. Consider 2N force is applied to an object towards one
direction and another 2N force is applied to the same object
in opposite direction. The resultant force will be zero because
two forces cancel each other.

Resultant force = 2N —2N = 0

2N 2N

Scalar quantities

The quantities which have only magnitude but no direction are
called scalar quantities. Mass, time, volume, area, temperature, etc
are scalar quantities. They are added by simple algebraic rules. For
an example, 5 kg of sugar when added to 6 kg sugar, the resultant
mass will be 11 kg. Similarly, 5 pens when added to 20 pens, the
total pens will be 25 pens and so on.

Differences between vectors and scalars

Vector quantities Scalar quantities

1. The quantity which has both 1. The quantity which has only

magnitude and direction is magnitude but no direction is

called vector quantity. called scalar quantity.

19 Times' Crucial Science Book - 9

2. It is represented by a straight 2. It is represented by a straight

line with an arrowhead. line without an arrowhead.

3. The sum of two vectors may 3. The sum of two scalars is
be positive, negative or zero. always positive.

4. Vector quantities cannot be 4. The scalar quantities can

added or subtracted by simple be added by simple algebraic

algebraic methods. methods.

Distance and displacement

When a person has to move 3
from point A to point B. He/ 2
She can go along the paths

1, 2, 3 or 4 as shown in the A 1 B
figure.

When the person travels 4

through paths 1, 2, 3 and 4, suppose that he has to travel 20m, 30m,

40m and 50 meters respectively.

Here, the actual length of path 1, 2, 3 and 4 is 20m, 30m, 40m and
50m respectively. Therefore, the distance of path 1, 2, 3 and 4 is
20m, 30m, 40m and 50m respectively. Here, between the same
points A and B, the actual lengths of different paths are different.

The actual length of a path travelled C

by a body is called distance. The SI

unit of distance is meter (m). Distance 5m
is a scalar quantity. 3m

But, the shortest distance between

the points A and B is the length of B

the path 1. It is displacement. The A 4m
shortest distance between initial and

final positions of an object is called

displacement. It can also be defined as the shortest distance between

any two points in a particular direction. The SI unit of displacement

is meter (m). Displacement is a vector quantity.

Suppose a person moves from point A to B then to C. Let, the
distance between A and B is 4m and distance between B and C
is 3m. Thus, the total distance he travels is 7m. But the shortest
distance between A and C is the length of AC. It is 5m. Thus, the
actual distance travelled by the person is 7m but the displacement

Times' Crucial Science Book - 9 20

is only 5m.
Differences between distance and displacement

Distance Displacement

1. It is the actual length of a 1. It is the shortest distance

path travelled by an object. between any two points in a

particular direction.

2. It is a scalar quantity. 2. It is a vector quantity.

3. It can be added or subtracted 3. It is added or subtracted by
by simple mathematical rule. using vector laws.

4. Its value is always positive. 4. Its value may be positive,
negative or zero.

Speed

Suppose a body moves from one place to another either in a straight
or curved path and covers 20 meter distance in 2 seconds. In such
case, we can say that it covers 10m distance in 1 second and its
speed is 10m/s.

Speed is defined as the distance travelled by an object in unit time.

Distance covered (d) ∴V = d
Speed = Time taken (t) t

Since the distance is measured in meter and time in second, speed is
measured in meter per second (m/s). It is also measured in kilometer
per hour (km/hr). Speed is a scalar quantity.

Velocity

When a body moves from one point to another in a straight path in
a particular direction, its speed is called velocity.

Therefore, velocity can be defined as the speed of a body in a
particular direction.

Since distance in a particular direction is called displacement,

velocity can be defined as displacement of an object in unit time.

Displacement ∴V = s
Velocity = Time taken t

Since the SI unit of displacement is meter and that of time is second, the
SI unit of velocity is meter per second (m/s). Velocity is a vector quantity.

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Solved Numerical Problem 2.1

A motor cyclist travels a distance of 4.2 kilometers in 4 minutes. Calculate his speed.

Solution:

Distance (d) = 4.2 km = 4200 m

Time (t) = 4 minute = 4 × 60s = 240s

Speed (v) =?

We have,

Speed= Distance travelled (d) = 4200 = 17.5 m/s
Time taken(t) 240

∴Therefore, the speed of the motor cyclist is 17.5 m/s.

Differences between speed and velocity

Speed Velocity

1. It is the distance travelled by 1. It is the displacement of an

an object in unit time. object per unit time.

2. It is a scalar quantity. 2. It is a vector quantity.

3. Speed of a moving body is 3. Velocity of a moving body may

always positive. be positive, negative or zero.

4. It can be added or subtracted 4. It is added or subtracted by
by simple mathematical rule. vector rules

Uniform and variable motion

When a body covers equal distance in equal interval of time, its

motion is called uniform motion.

0 sec 1 sec 1 sec 1 sec 1 sec

a 5m b 5m c 5m d 5m e

In the above figure, a car is covering 5m distance in the first one
second. It further covers 5m distance in the next one second and so
on. Its motion is uniform motion because it travels equal distance in
equal interval of time. Motion of hands of watch, motion of planets,
motion of moon, etc are examples of uniform motion.

When a body covers unequal distance in equal interval of time, its

Times' Crucial Science Book - 9 22

motion is called variable motion. The variable motion is also known
as non-uniform motion.

0 sec 1 sec 1 sec 1 sec

a 5m b 10m c 4m d

In the above figure, the car travelled 5m in the first one second,
10m in the next one second and 4m in the third one second. Thus,
it covers different distances in equal interval of time. Therefore,
its motion is called variable motion. Motion of animals, motion of
vehicles, motion of water in river, motion of human beings, etc are
examples of variable motion

Acceleration

When a body moves in variable motion, its velocity keeps on
changing. The rate by which the velocity of a body changes is called
its acceleration. Thus, the rate of change of velocity of a moving body
is called acceleration.

Suppose, a body is moving from a point. Its velocity is 5m/s in the

beginning. Suppose, its velocity slowly increases and becomes 20m/s

after 5 seconds.

u=5m/s v=20m/s

0 sec 5 sec

t=5sec

Here, the velocity of the car increased from 5m/s to 20m/s in 5s.
The increase in the velocity of the car in 5s is 15m/s. Therefore,
its velocity is increased by 3m/s in every one second. Thus, its
acceleration is 3m/s2.
Suppose, a body is moving with initial velocity ’u’ and its velocity
increases to ’v’ in time ’t’, then the acceleration ’a’ is calculated by
the formula,

Acceleration = Final Velocity - Initial Velocity ∴a = v - u
Time taken t

Unit of acceleration

In SI unit, the change in velocity is measured in meter per second
and time in second. Therefore, the SI unit of acceleration will be
meter per second per second or m/s2.

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Change in Velocit
Acceleration =

Time taken

m/s m m
= s = s × s = s2

If the velocity of a moving body decreases, its acceleration will
be negative. It is called retardation. Thus, the rate of decrease of
velocity of a body is called retardation. It is also a vector quantity
and its unit is m/s2.

Solved Numerical Problem 2.2

A bus is moving with a velocity of 15m/s. It increases its velocity to 30m/s after 5
second. Find its acceleration.

Solution

Given,

Initial Velocity (u) = 15m/s

Final Velocity (v)= 30m/s

Time (t)= 5sec

Acceleration (a) =?

v-u or, a = 30 - 15 or,a = 15 = 3m/s2
We have, a = t 5 5

∴Therefore, the acceleration of the bus is 3m/s2.

Average velocity

When a body moves in non-uniform motion, its velocity changes
continuously. In such a situation, we use average velocity. Average
velocity of a body is the total displacement travelled by the body
divided by total time.

Average velocity(v–) = Total displacement
Total time taken

Its SI unit is m/s and CGS unit is cm/s.

If a body gains a total displacement of 50 m in 10 seconds, its
average velocity is calculated as,

Average velocity(v–) = Total displacement = 50 = 5m/s
Total time taken 10

Times' Crucial Science Book - 9 24

If the velocity of a body changes with a constant rate, its average
velocity is calculated by using a formula,

Initial velocity + Final velocity (v–) = u + v
Average velocity(v–) = 2

2

Initial velocity is the velocity of a body at the beginning of the time
and is denoted by u. Final velocity is the velocity of a body at the
end of time and is denoted by v.

If a body increases its velocity from 20m/s to 30m/s with a constant

rate, its average velocity is calculated by:

Average velocity(v–) = Initial velocity + Final velocity = 20 + 30 = 25 m/s
2 2

Equations of motion

If a body moves with a constant acceleration, its initial velocity
u, final velocity v, distance travelled s, time taken t and uniform
acceleration a are related, the relation can be shown by equations.
These equations are called equations of motion. They are:

1. v = u + at

2. s = u+v× t

2

u v 3. v2 = u2 + 2as
s 1
t
4. s = ut + 2 at2

To prove: v = u + at

We know that, acceleration is the rate of change of velocity.

Acceleration = Final Velocity - Initial Velocity

v-u Time taken

a= t

or, at = v —u
∴v = u + at

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To prove: s = u+v ×t

We have, 2

Initial velocity + Final velocity
Average velocity =

2

Again, u+v
= ....................(i)

2

Total displacement = s
Average velocity = ...................(ii)
Total time taken t

From equations (i) and (ii), we have

s u+v
t= 2

∴s = u+v ×t

2

To prove: v2 = u2 + 2as

We have, Final Velocity - Initial Velocity
Acceleration =
Time taken
Again,
v-u or, t = v-u ................(i)
a= t
a

Total displacement = Average velocity × Time

Initial velocity + Final velocity
s = 2 × Time

u+v
s = × t............................(ii)

2
Substituting the value of ‘t’ from equation (i) in equation (ii), we
have:

Times' Crucial Science Book - 9 26

u+v v-u v2 - u2
s= 2 × a or, s =

2a

or, 2as = v2 − u2

∴v2 = u2 + 2as

1
To prove: s = ut + 2 at2
We have,

Acceleration = Final Velocity - Initial Velocity
Time

v-u
a= t

or, at = v - u

∴ v = u + at.....................(i)

Again,

Total distance = Average velocity × Time

Initial velocity + Final velocity

s = × Time

2

u+v
s = × t............................(ii)

2

Substituting the value of ‘v’ from equation (i) in equation (ii), we

have:

u+(u+at) 2u+at = 2ut + at2
2 2
s= ×t = ×t

2 2

1
∴ s = ut + at2

2
Special conditions

1. When a body starts from rest, u = 0.
2. When a moving body comes to rest, v = 0.
3. When a body moves under the influence of gravity, a = g.
4. When a body is thrown vertically upwards, v = 0.
5. When a body is allowed to fall vertically downwards, u = 0.

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Solved Numerical Problem 2.3

If a body gains 500m displacement in 10s. Find its average velocity.

Solution:

Given,

Total displacement (d) = 500m

Total time (t) = 10s

Average velocity =?

We have, 500
Average velocity= Total displacement = 10 = 50 m/s
Time taken

∴Average velocity of the body is 50m/s.

Solved Numerical Problem 2.4

A body changes its velocity from 54km/hr to 72km/hr in 2s. Find its

acceleration and distance travelled.

Solution: Given,

54km 54 × 1000m
Initial velocity (u) = 54km/hr = = = 15m/s
1hr 3600s

Final velocity (v) = 72km/hr = 72km 72 × 1000m = 20m/s
=
1hr 3600s

Acceleration (a)= ?
Distance (s) = ?
We have, v = u + at
or, 20 = 15 + a × 2
or, 2a = 5

∴a = 2.5m/s2
Again,

u+v
s= ×t

2

15+20

= × 2 = 35m

2

∴The acceleration is 2.5m/s2 and distance travelled is 35m.

Times' Crucial Science Book - 9 28

Solved Numerical Problem 2.5

A bus increases its velocity from 30m/s to 45m/s and covers 300m
distance. Find.
(i) time required and (ii) acceleration.
Solution:

Given,
Initial velocity (u) = 30m/s
Final velocity (v) = 45m/s
Distance travelled (s)= 300m
Time (t) = ?
Acceleration (a)= ?
We have,

S= u+v×t or, 300= 30+45 ×t or, t= 600 ∴ t = 8s
2 2 75
Again,

v = u + at

45 = 30 + a × 8 or, a = 15 ∴a=1.875 m/s2
a= 45−30 8
8

∴ Time taken (t)= 8s and acceleration(a) =1.875 m/s2.

Solved Numerical Problem 2.6

If a bus that started from rest attains an acceleration of 0.4m/s2 while
travelling a distance of 2 kilometers, what will be the final velocity of the
bus? Also calculate the time taken by bus to tavel this distance.
Solution:
Given:

Initial velocity (u) = 0
Acceleration (a) =0.4,/s2
Distance travelled (s) =2 km=2×1000m=2000m

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Final velocity (v) =?

using the formula:

v2=u2+2as

=02+2×0.4×2000

=1600

∴v= 1600 =40m/s

Hence, the final velocity of the bus is 40m/s.

Again,

Final velocity (v) = 40m/s

Initial Velocity (u) = 0

Time taken (t) =?

Now we have:

v=u+at 40- 0
v-u = =100s

t= 0.4
a

∴ The time required by the bus is 100 seconds..

Graphical representation of motion

Graphical representation of motion is the simple way of representing
the nature of motion of an object.

Distance-time graph

It is a graph which shows the relation between distance and time.
The time is plotted in x-axis and distance is plotted in y-axis. The
curve obtained in this graph is called distance-time curve. The nature
of the curve in different conditions is as follows:

a. When a body is at rest velocity

Y Time X

When a body is at rest, it does not change
its position with respect to time. Thus,
the distance remains unchanged. Then,
the distance-time curve will be parallel to
x-axis.

Times' Crucial Science Book - 9 30

b. When a body is in uniform speed Y

When a body is moving with a uniform speed, Distance
distance covered is directly proportional
to the time taken by the body. Then, the Time X
distance-time graph is the straight line
passing through the origin.

c. When a body is moving in non-uniform speed

When a body is moving in non-uniform Y
speed, the body covers unequal distance in
equal interval of time. Then, the distance Distance
time curve is a curve shaped.
Time X

Velocity-time graph

It is a graph which shows the relation between velocity and time.
Time is plotted in x-axis and velocity is plotted in y-axis. The curve
obtained in this graph is called velocity-time graph. The nature of
the curve in different conditions are as follows:

a. When a body moves with uniform velocity

When a body moves with uniform velocity, Y
the velocity remains unchanged even though
time changes. Thus, the velocity-time curve Distance
will be parallel to the x-axis. The y-intercept
is equal to the magnitude of uniform velocity. Time X

b. When a body is moving with uniform acceleration

When a body is moving with uniform Y
acceleration, the velocity of the body
increases with increase in time. So, the velocity
velocity-time graph is straight line passing
through the origin. Time X

c. When a body is moving with uniform retardation

Y

When a body is moving with uniform

retardation, the velocity of the body decreases Velocity

with increase in time. The velocity-time graph

is a straight line inclined downwards in right. Time X

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d. When a body is moving with variable acceleration

Y

When a body is moving with variable

acceleration, the velocity increases or decreases Velocity

by unequal amount in equal interval of time.

So, velocity-time graph is curve shaped. Time X

Inertia and mass

A book lying on a table does not change its position itself. Similarly,
a body moving in a particular direction does not stop itself. Here,
force is to be applied to change their state of rest or motion. This
property of a body is called inertia.

Inertia is the property of a body due to which it remains or tends to
remain in its previous state of rest or uniform motion in a straight
line.

Inertia of a body depends upon the mass of the body. An object
having more mass has more inertia and vice versa.

Activity 2.1 To study the relationship between mass and inertia.

Materials required:

Two cans, sand, thread or rope, etc.

Procedure:

1. Take two cans of equal size and fill one of them with sand.

2. Suspend both the cans as shown in the figure.

3. Apply force to each of them to bring into motion. Which one is easier to
bring into motion?

Observation:
More force is required for the can filled with sand to bring into motion.
Conclusion:
Inertia increases with increase in mass.

Times' Crucial Science Book - 9 32

Types of inertia
Inertia is of three types: They are:
i. Inertia of rest ii. Inertia of motion iii. Inertia of direction
Inertia of rest
It is the property of a body by virtue of which it remains or tries to
remain in the state of rest until external force is applied.

Activity 2.2 To study the inertia of rest.

Materials required:
Card board, a glass, a coin, etc.
Procedure:
1. Take a glass and place a card board over the glass as shown in the figure.
2. Put a coin on the cardboard just over the mouth of the glass.

3. Give a sudden push to the cardboard with a finger. What happens?
Observation:
The cardboard comes into motion and falls to the ground but the coin falls into
the glass.
Explanation:
The coin tries to remain in the rest state due to inertia of rest but the card board
comes into motion due to the application of force. Thus, the coin falls into the
glass

Examples of inertia of rest
1. Passengers of a bus fall backward when a bus suddenly starts

to move: In the beginning, both the bus and the passengers are
at rest. When the bus suddenly moves, the lower parts of body
of the passengers also come in motion along with the bus, but
the upper parts of the passengers’ body try to remain at rest
due to inertia of rest. Therefore, the passengers fall backward
when a bus suddenly starts moving.

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2. When a carpet is beaten by a stick, the dust flies away or falls
down: In the beginning both carpet and dust particles are at
rest. When the carpet is beaten by a stick, the carpet comes
into motion but the dust tries to remain at rest due to inertia
of rest. Thus, the dust gets separated and flies away or falls
down when the carpet is beaten by a stick.

3. Mango fruits fall from a tree when the tree is shaken: When
a mango tree is shaken, the branches of the tree come into
motion due to the effect of force applied. But, the mango fruits
try to remain at rest due to inertia of rest. Thus, the mango
fruits get separated from the mango tree and fall down.

Inertia of motion

It is the property of a body by virtue of which a moving body tries to
remain in the state of motion in the same direction until the external
force is applied.

Examples of inertia of motion

1. Passengers of a bus jerk forward when a moving bus suddenly
stops: When a bus is moving, both the bus and the passengers
are in motion state. When the bus suddenly stops, the lower
body parts of the body of passengers come into rest along
with the bus. But, the upper parts of the body try to remain
in motion due to inertia of motion. Thus, the passengers jerk
forward when the moving bus suddenly stops.

2. An athlete runs some distance before taking a long jump: When
an athlete runs some distance before taking a long jump, the
velocity gained by him at the time of running is added to the
velocity taken by him at the time of jump. Thus, the athlete
becomes able to take longer jump.

3. When a passenger jumps out from a moving bus, he falls to
the direction of the bus: When a bus is moving, the passengers
and the bus both are in motion. When a passenger jumps from
the bus, his legs come in contact with the ground and come to
rest but his upper parts try to remain in motion in the same
direction due to inertia of motion. Thus, the passenger falls on
the ground in the direction of the bus. To prevent from falling,
the passenger has to run some distance in the direction of the
bus.

Times' Crucial Science Book - 9 34

4. When wheels of a vehicle rotate at high speed, the mud sticking to
them flies away tangentially: This is due to inertia of direction.

Momentum

If you attempt to stop a moving body, you need to apply some force.
Similarly, you have to apply force to move a stationary object.

More force is required to stop a moving body which has more mass.
In the same way, more force is required to stop a body moving with
high velocity. These observations are due to the quantity of motion
present in a body. The quantity of motion in a body depends on the
mass (m) and velocity (v) of the moving body.

The product of mass and velocity of a moving body is called its
momentum.

Mathematically,

Momentum= Mass × Velocity

∴P = m × v

Momentum is a vector quantity. Since, the SI unit of mass is kg and
that of velocity is m/s, the SI unit of momentum is kgm/s.

A stationary object has zero momentum. It is because the velocity
of a stationary object is zero.

As stated above, momentum of a body depends on its mass and
velocity. In other words, the momentum of a body is directly
proportional to the product of mass and velocity. Hence, the
momentum of a body with more mass and velocity is more than
that having less mass and velocity. It is the reason why a person
receives more injury if struck by a cricket ball than that with a
shuttle cock.

Newton’s laws of motion

Sir Isaac Newton (1642-1727 AD), a British scientist made detailed
study on the motion of bodies and gave three laws. They are known
as Newton’s laws of motion.

Newton’s first law of motion

It states that everybody continues in its state of rest or uniform motion
in a straight line unless it is acted upon by some external forces.

35 Times' Crucial Science Book - 9

Explanation

According this law, a body at rest remains in
the same state and a body in motion continues
moving in the same direction until external force
is applied. This inability of a body to change its
state of rest or motion by itself is called inertia.
Thus, the first law of motion has the same concept
as that of inertia. Therefore, the first law of motion is called law of
inertia.
From the first law of motion, it is clear that a body changes its state
of rest or motion in a particular direction due to application of force.
Thus, the first law of motion gives the definition of force. According
to it, force is an external agency that changes or tends to change
state of rest or motion of a body in a particular direction.

Examples of first law of motion

a. When a mango tree is shaken, mango fruits fall down.
b. Passengers of a bus fall backward when the bus suddenly

moves.
c. The blades of a fan continue to move for sometime even though

it is switched off. When the fan is switched off, the blades of the
fan try to remain in the previous state of motion due to inertia
of motion. Thus, the blades of the fan rotate for sometime even
after the fan is switched off.
d. A man jumping from a moving bus may fall down.When a
man jumps from a moving bus, his feet come in contact with
the ground and come to the rest state. But, his upper parts try
to remain in the previous state of motion in the direction of the
moving bus. Thus, the man falls in the direction of the bus.

Newton’s second law of motion

It states that acceleration produced in a body is directly proportional
to the force applied and inversely proportional to its mass.

Explanation

When a force is applied to a body continuously, acceleration is
produced. When more force is applied, the acceleration produced is
also more. It means acceleration is directly proportional to the force
applied, i.e. a a F.

Similarly, when two bodies, one lighter and another heavier are
acted by equal amount of force, the lighter body moves faster. It

Times' Crucial Science Book - 9 36

means the acceleration produced on the lighter body is more than
ai.cec.ealearam1tiofnor’ath’ eisgpivroednufcoerdceo. n
that on heavier body, a body having
Let us suppose that,

mass ’m’ due to the application of force ’F’. According to Newton’s

second law of motion,

a a F………….(i)

a a 1 ……….(ii)
m
Combining equations (i) and (ii), we have:

a a F × 1 or, a a F or, F a m × a
m m

or, F = km × a……(iii) (Where k is a proportionality constant)

1 Newton force is defined as that force which when applied to a body
of mass 1 kg, produces an acceleration of 1m/s2. It means,
If F = 1N and m = 1 kg, then a = 1m/s2. Putting their values in
equation (iii),

1=k×1×1 ∴k=1

Substituting the value of k in equation (iii), we have:

F=1×m×a ∴F = ma

Thus, the amount of force is equal to the product of mass and
acceleration. If the value of acceleration and mass are known,
the amount of force can be calculated using this equation. Thus,
Newton’s second law of motion gives the measurement of force.

Solved Numerical Problem 2.7

What amount of force is required to move a body of mass 5 kg with an
acceleration of 4m/s2?
Solution:

Mass (m) = 5 kg
Acceleration (a) = 4m/s2
Force (F) = ?
We have,
F = m × a = 5 × 4 = 20 N
∴ The amount of force required is 20 N.

37 Times' Crucial Science Book - 9

Solved Numerical Problem 2.8

What amount of force is required to displace a body of mass 5 kg through
a distance of 20m in 4s?

Solution:

Mass (m) = 5 kg

Distance (s) = 20 m

Time (t) = 4 s

Initial velocity (u) = 0 m/s

Acceleration (a) = ?

Force (F) = ?

We have,

s = ut + 1 at2 or, 20 = 0 × 4 + 1 × a × 42
2 2
1 20
or, 20 = 2 × a × 16 or, 20 = 8a or, a = 8 = 2.5 m/s2

Again,

F = ma = 5 × 2.5 = 12.5 N

∴Amount of force required = 12.5 N.

Solved Numerical Problem 2.9

Application of Newton’s second law of motion
AcsArecicccoarknriedctoksfbebatmylpala.slpaspy5ley0ri0n0mgkobgvreamskoehsv.iisnCgahlwacnuitdlhastaeb:sapcekewdaorfd7s2 wkmhi/lehrcasttocphsinagftetrhe6
In the ab.egthinendiinsgta, ntcheetrvaevleolclietdy boyf tthheecabrall is u . When the cricket
player bca. tthcheeasmtohuenbtaolfl,fotrhcee fainpapllivedelocity becomes zero.

ISnoltuhteioeqnu: ation,

Mass (m) = 5000ukg− v
[ [F=ma 7=2kmmv−m7u2 o1r0,0F0=m1t=(m20vm−m/su)
F =m × or , F t= ×
oInr,itial Velocity (u)t=72km/hr =
The quFainnatlitvyelo(cmitvy−(mv)u=) 0ims /sconstant.1hTrhus, f3o6r0ce0s is inversely
1
proportTioimnael(to)=t6hse time, i.e. F a t .

It meaDnsistwahnecne tmraovreelletdim(se)=i?s taken to stop the ball, less force is
spulaffyieciremAnmtovtooeusnbhrtiionsfghfoatrhncedesb(Fba)al=lctk?owtahredsreasntd. Fsaorveins chriesahsainngdsthfreomtiminej,utrhye.

Times' Crucial Science Book - 9 38

We have: u+v 20+0
Again: s= ×t = × 6 = 60m
22

v=u+at or, 0=20+a×6 or, 6a=−20

−20 −10
or, a = 6 or, a = 3 m/s2

According to Newton's second law of motion

( )−10

F=ma = 500 × 3 = −1666.67N

Here, negative force means force is applied against the motion of the
body.

∴The amount of force applied is 1666.67N

Newton’s third law of motion

It states that ”to every action, there is equal and opposite reaction”.

Explanation

When a force is applied to a body, the body also produces another
force. When a body A exerts force on a body B , the body B also
exerts equal and opposite force on the body A . Thus, a single force
is impossible to exist. Force always exists in pair. The pair of the
forces involved are called action and reaction. The force action is the
cause and the force reaction is the effect.

Activity 2.3 To show that the action and reaction are equal.

Materials required: AB

Two spring balances
Procedure:

1. Take two spring balances.

2. Put hook of one balance to the hook of another balance as
shown in figure.

3. Hold one of the balances firmly on a support and pull the
another balance. What readings do you see in both balances?

Observation:

Reading in both balances will be same.

39 Times' Crucial Science Book - 9

Explanation:

When the spring balance A applies force to the spring balance B , it
is action. The spring balance ’B’ also applies equal and opposite force
to the balance B as reaction. Since action and reaction are equal, the
reading in both balances become equal.

Activity 2.4 To show that action and reaction act in opposite direction.

Materials required:

A balloon, cello tape, paper, a Balloon pushes on air Air pushes on balloon
long thread, etc.

Procedure:
1. Make a paper spool by rolling a paper.
2. Take a long thread and pass one end of the thread through the spool.
3. Tie two ends of the thread on opposite walls of the room to

make the thread stretched as shown in figure
4. Inflate a balloon and tie its mouth.
5. Fix the balloon in the spool with the help of pieces of tape.
6. Release the air from the balloon by opening its mouth. What

happens?

Observation:

The balloon moves backward when the air comes out.

Explanation:

Coming out of air from the balloon is action. As a reaction, the
balloon moves backward.

Examples of third law of motion

a. When a man swims, he pushes the water in the backward
direction as an action. The water pushes the man in the
forward direction as a reaction. Thus, swimming is possible.

b. When a person walks, he pushes the ground backward. Here
the force applied by the person to the ground backward is
action. As a reaction, the ground applies force to the feet in the
forward direction. Thus, he can walk.

c. In rockets, the burnt gases come out vertically downwards
with a great force as action. As a reaction, the gases give equal
and opposite force to the rockets. Thus, the rocket flies up.

d. A bullet is fired from a gun as an action. The bullet gives equal
and opposite force to the gun as reaction. Thus, the gun recoils

Times' Crucial Science Book - 9 40

backwards when bullet is fired from it.
e. While rowing a boat, a person pushes water backward as

action. As a reaction, the water gives equal and opposite force
to the boat. Thus, the boat moves forward.

Solved Numerical Problem 2.10

Study the given velocity-time graph and answer the following questions.

i. Name the motions

represented by OA, AB 8 A B
Velocity (m/s)
and BC.

ii. Find the acceleration in

each segment. 0 2 Time (s) 6 C
iii. How long is the motion 8

uniform?

Solution:

i. OA represents motion having uniform acceleration, AB

represents uniform velocity and BC represents the motion

having uniform retardation.

ii. In OA segment, the acceleration is uniform.

Here,

Initial velocity (u) = 0 m/s

Final velocity (v) = 8 m/s

Time (t) =2s

Acceleration (a) =?

We have,

v = u + at Or, 8 = 0 + a × 2 ∴ a = 4 m/s2

In AB segment, the velocity is uniform. Thus, the acceleration is 0m/s2.

In segment BC, the motion has uniform retardation,

Here,

Initial velocity (u) = 8 m/s

Final velocity (v) = 0 m/s

Time taken (t) = 8 − 6 = 2s.

Acceleration (a) =?

We have,

v = u + at Or, 0 = 8 + a × 2 ∴ a = − 4 m/s2

Thus, acceleration in segment OA is 4m/s2, in segment AB is 0m/s2 and

in segment BC is −4m/s2.

iii. The segment AB, represents uniform motion. The time period of the
uniform motion is 6 − 2 = 4s.

41 Times' Crucial Science Book - 9

Balanced and unbalanced forces

Forces occur in pair. The forces can be either balanced or unbalanced.
If the resultant magnitude of all the forces acting up on a body
is zero, the forces are called balanced forces. The balanced forces
cannot bring a body into motion. The balanced forces are equal
in magnitude but opposite in direction. Sometimes, the resultant
magnitude of more than two forces can be zero. For example, in tug
of war, players pull the rope in two different directions. If the total
forces of both the sides are equal, the rope does not move. This is an
example of balanced forces.

If the resultant magnitude of all the forces acting up on a bady is
not zero, the forces are called unbalanced forces. The unbalanced
forces bring an object into motion. Kicking a football on the ground,
pushing a small box on the table, pushing a piece of stone forward,
etc are the examples of unbalanced forces. While pushing a small
box on the table, the force of friction tries to oppose the motion
of box. However, the force applied by you overcomes the frictional
force and the box moves on the table. Here, the force applied by you
and the frictional force are two different forces that act in opposite
directions. As their resultant magnitnde is more than zero, the box
moves forward.
Learn and Write

1. It is easier to catch a tennis ball than a cricket ball. Why?

According to Newton’s second law of motion,

F = ma

v-u

Suppose, t is same for both the tennis and cricket ball. It
means the tennis and cricket ball have equal velocity u while
catching and they are brought to rest (v = 0) in equal time (t).
Then, the force applied is directly proportional to the mass. i.e.
F  m. Thus, the cricket ball needs more force than the tennis
ball to bring to the rest due to more mass of the cricket ball.

2. An object can be accelerated without change in its speed.
How?

Times' Crucial Science Book - 9 42

When an object is moving in a circular path with a constant
speed, its di-rection keeps on changing and hence velocity too.
Due to change in velocity, the body has acceleration. Thus, a
body with constant speed possesses acceleration.
3. A boat is pushed backward when a man jumps out from
the boat. Why?
When a man jumps out from a boat as an action, the force
is applied by the man to the boat as reaction. As a result of
reaction, the boat moves backwards.
4. Action and reaction are equal and opposite but they do not
cancel each other. Why?
Action and reaction are equal and opposite but they do not act
on a same object. Action acts on one object whereas reaction acts
on another object. Due to this, they do not cancel each other.
5. What is the relationship between mass and inertia of a body?
The mass of a body is the measure of its inertia. The greater
the mass of a body, the greater is its inertia. It means that
inertia of a body is directly proportional to its mass.
6. The acceleration of a car is 1 m/s2. What does it mean?
Acceleration means the rate change of velocity of a moving
body. If the acceleration of a car is 1 m/s2, it means that the
velocity of the car is increasing by 1 m/s in every second.
7. How does Newton’s first law of motion define force?
According to the Newton’s first law of motion, a body at rest
remains at rest and a body in motion continues to be in uniform
motion in a straight line unless an external force acts upon it.
The body at rest does not move if the force is not sufficient
for moving it. It means that force is an external agency which
changes or tries to change the state of rest or uniform motion
of a body in a straight line.

8. A gun recoils when a bullet is fired from it. Why?

When a bullet is fired from a gun, the gun exerts some force on
the bullet. This force is the action which makes the bullet move
forward. According to Newton’s third law of motion, the bullet
also exerts an equal and opposite force on the gun as reaction.
Due to this reaction force, the gun recoils.

Main points to remember

1. Force is an external agency which changes or tends to change
state of rest or of motion of a body in a particular direction.

43 Times' Crucial Science Book - 9

2. Inertia is the property of a body due to which it remains or tends
to remain in its previous state of rest or motion in a straight line.

3. Inertia of rest is a property of a body by virtue of which it remains
or tries to remain in the state of rest until the external force is
applied.

4. Inertia of motion is a property of a body by virtue of which it
remains or tries to remain in the state of motion in the same
direction until the external force is applied.

5. Those quantities which have both magnitude and direction are
called vector quantities.

6. Those quantities which have only magnitude but no direction are
called scalar quantities.

7. The actual length of a path travelled by a body is called distance.
8. The shortest distance between initial and final positions of an

object is displacement.
9. The distance travelled by an object in unit time is called speed.
10. The displacement travelled by an object in unit time is called

velocity.
11. The first law of motion states that everybody continues in its state

of rest or uniform motion in a straight line unless it is acted by
some external forces.
12. The second law of motion states that acceleration produced on a
body is directly proportional to the force applied and inversely
proportional to its mass.
13. The third law of motion states that “to every action, there is equal

and opposite reaction”.

Exercise

1. Choose the best alternative in each case.

a. Which of the following is a vector quantity?

i. Force ii. Velocity iii. Acceleration iv. All of these

b. What is the SI unit of retardation?

i. m/s ii. –m/s2 iii. m/s2 iv. Km/hr

c. If a body starts moving from rest, its initial velocity is

i. u ii. v iii. zero iv. m/s

d. If the velocity time graph of a moving body is a straight line
parallel to the time axis, the velocity of the body is

i. Uniform ii. Increasing iii. Decreasing iv. Zero

Times' Crucial Science Book - 9 44

e. Which of the following is closely related to mass?

i. Motion ii. Velocity iii. Force iv. Inertia

2. Answer these questions in brief.
a. What is force? What are its effects?
b. What is inertia? What are the factors upon which the
inertia depends?
c. What is inertia of rest? Give some examples of inertia of rest.
d. What is inertia of motion? Give some examples of inertia
of motion.
e. What are vector quantities? Give some examples.
f. What are scalar quantities? Give some examples.

3. Distinguish between:
i. Vectors and scalars
ii. Distance and displacement
iii. Speed and velocity
iv. Uniform motion and non-uniform motion

4. What are equations of motion? Derive the following relations:

1 v2 = u2 + 2as
i. s = ut + 2 at2 ii.

5. State the following laws:

i. Newton’s first law of motion

ii. Newton’s third law of motion

6. State Newton’s second law of motion. Prove: F = ma.

7. Give reasons:

i. A swimmer pushes water backwards.
ii. An athlete runs before taking a long jump.
iii. We beat blanket with a stick to remove dust particles.
iv. The boat slightly moves backward when we jump from it.
v. A cricket player lowers his hands while catching the ball.
vi. Passengers of a bus jerk forward when the moving bus

suddenly stops.
vii. When we jump on a concrete surface, the feet get injured.
viii. A gun recoils when a bullet is fired from it.

45 Times' Crucial Science Book - 9

8. Numerical problems

a. If a body starts from rest and attains a velocity of 20m/s in
8 seconds. Find the acceleration produced in the body.

b. A car running with a velocity of 45 km/hr stops after 3
seconds when brakes are applied. Find the retardation of the
car and distance travelled by the car.

c. A body moving with an initial velocity of 20 m/s has an
acceleration of 4m/s2. Find the velocity of the body after 4s
and distance travelled in that time.

d. A car of mass 500 kg increases its velocity from 40 m/s to 60
m/s in 10 seconds. Find the acceleration, distance travelled
and amount of force applied.

e. A bus starts from rest and attains a velocity of 45 m/s after
10 seconds. Find the acceleration and the distance travelled
in 5 seconds and in 10 seconds.

f. A vehicle was moving with a speed of 72 km/hr. On seeing
a baby 40m ahead on the road, the driver jammed on the
brakes and it came to rest in 5 seconds. Whether accident
occurred or not?

g. A bus is running with a velocity of 72 km/hr. On seeing a baby
on the road 65 m a head, the driver jammed the brakes and
the bus stopped with uniform retardation of 5m/s2. Calculate
the distance travelled by the bus and the time to stop.

h. A car of mass 500 kg travelling with a speed of 54 km/hr is
brought to rest over a distance of 40 m. Find the retardation
and force applied on brakes.

i. The driver of a vehicle moving with velocity of 54 km/hr
sees a child and brings the vehicle to rest in 5 seconds. Find
the retarding force on the vehicle. (Given: The mass of the
vehicle is 500 kg and the mass of the driver is 70 kg)

j. A body of mass 60 kg is displaced through 90 m in 4 seconds

when force is applied to it. Calculate acceleration and the

force applied. C D
12 AB

k. From the following distance time
8
graph, Velocity (m)

i. Mention the motions 0 4 10 12 16
represented by OA, AB, BC and Time
CD

Times' Crucial Science Book - 9 46