Green Science 9 Final PDF (2076)

Approved by Government of Nepal, Ministry of Education, Curriculum
Development Centre, Sanothimi, Bhaktapur as an additional material

Green

9

Editor
Dr. Deepak Chand

M.Sc. (TU, Kirtipur, Kathmandu)
Ph.D. (University of Idaho, USA)

Author
Bishnu Prasad Bhatt

M.Sc. (TU, Kirtipur, Kathmandu)

Lalitpur, Nepal, Tel: 977-1-5529899
e-mail: [email protected]
www.greenbooks.com.np

Publisher: Green Books 9

Copyright: Author (2074 BS)

All rights reserved. No part of this book may
be reproduced, stored in a retrieval system,
or transmitted in any form or by any means
without prior permission in writing from the
author and editor.

Edition
First : B.S. 2074 (2017 AD)
Reprint : B.S. 2075 (2018 AD)
Revised : B.S. 2076 (2019 AD)
Revised : B.S. 2077 (2020 AD)

Illustrator
Prakash Samir

Layout
The Focus Computer
[email protected]

Printed in Nepal

Preface

It gives me an immense pleasure in presenting this book-
Green Science for class 9. This book is written specially to
meet the requirements of the new syllabus introduced by the
Government of Nepal, Ministry of Education, Curriculum
Development Centre, Sano Thimi, Bhaktapur, Nepal.

My aim and effort while writing this book has been to help
students understand, enjoy and appreciate the fascinating
subject of Science and Environment by making the process of
learning enjoyable and stimulating. I have attempted to present
the subject matter covering the entire prescribed syllabus in a
simple language and interesting style with a large number of
illustrative examples for easy understanding and application
of the fundamental principles of science. Each unit of the book
has been carefully planned to make it student-friendly and
present the subject matter in an interesting, understandable and
enjoyable manner. A Structural Programme Learning Approach
(SPLA) has been followed and exhaustive exercises are given
at the end of each unit to test knowledge, understanding and
applications of concepts taught/learnt.

The text is supplemented with weighting distribution, learning
objectives, word power, teaching instructions, sample test
papers and a large number of well-labelled accurate pictures. I
sincerely hope that this book will serve its intended purpose and
be received enthusiastically by both the students and teachers
concerned.

I wish to express my sincere gratitude to Green Books Team for
publishing this book. My hearty thank goes to Focus Computer
for excellent type setting and layout.

I also wish to acknowledge my great indebtedness to many
teachers for their valuable suggestions and advice concerning
the textbook. I am confident that as result of their suggestions
this book will be more useful than any other textbooks. However,
sympathetic criticisms and constructive suggestions for further
improvement of the book, if any, will be welcomed and with
warm regards incorporated in the subsequent editions.

Author

Kathmandu, Nepal
September 2016

Contents

Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1. Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Force and Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3. Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4. Energy, Work and Power . . . . . . . . . . . . . . . . . . . . . . . 69
5. Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6. Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7. Current Electricity and Magnetism . . . . . . . . . . . . . 122

Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8. Classification of Elements . . . . . . . . . . . . . . . . . . . . . . 141
9. Chemical Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
10. Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
11. Some Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
12. Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
13. Carbon and its Compounds . . . . . . . . . . . . . . . . . . . . 224
14. Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
15. Chemical Fertilizers used in Agriculture . . . . . . . . . 245

Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
16. Classification of Plants and Animals . . . . . . . . . . . . . 253
17. Adaptation of Organisms . . . . . . . . . . . . . . . . . . . . . . 287
18. System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
19. Sense Organs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
20. Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
21. Nature and Environment . . . . . . . . . . . . . . . . . . . . . . 356

Geology and Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . 371
22. Natural Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
23. Greenhouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
24. The Earth in the Universe . . . . . . . . . . . . . . . . . . . . . . 392
Specification Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
Model Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

Physics

UNIT Measurement

1

Weighting Distribution Theory : 3 Practical: 1

Before You Begin

Measurement is the comparison of an unknown physical quantity
with a known quantity of the same kind. We can measure the mass of
a brick by using a beam balance. We can measure the length of a book
by using a ruler. We can measure the time by using a watch. We can
measure the temperature of a hot object by using a thermometer. Mass,
length, time and temperature can be measured. These quantities are
called physical quantities. The quantities which can be measured are
called physical quantities. Mass, length, time, temperature, pressure,
force, power, density, speed, acceleration, electric current and energy
are some examples of physical quantities. In physics, we study about
so many physical quantities and their measurement. A physical
quantity is always represented by a number followed by a unit.

Learning Objectives Syllabus

After completing the study of this unit, students will be able to: • Introduction to physical
quantities
i. introduce basic (fundamental) units and derived
units with examples. • Basic (fundamental) physical
quantities
ii. describe the relation between fundamental units and
derived units. • Derived physical quantities

• Units and their types

• Fundamental units and
derived units

• SI system

Glossary: A dictionary of scientific/technical terms

measurement : the comparison of an unknown physical quantity with a known standard
quantity of the same kind
unit
: the standard quantity which is used for the comparison with an unknown
fundamental physical quantity
derived
mass : basic, forming the source or base from which everything else is made
weight : the thing obtained from something else
time : the total quantity of matter present in a body
moment : the force with which a body is pulled towards the surface of the earth
: the duration between any two events
: the product of force and perpendicular distance

GREEN Science (Physics) Book-9 5

Physical quantities

We can measure various quantities like length, mass, time, area, volume, temperature,
etc. These quantities are known as physical quantities. Thus, those quantities which can
be measured are called physical quantities. Some other examples of physical quantities
are force, speed, pressure, acceleration, energy, power, electric current, etc. We cannot
measure love, feeling, kindness, anger, beauty, desire, experience, happiness, etc. So they
are not called physical quantities.

There are two types of physical quantities. They are:

1. Fundamental physical quantities

2. Derived physical quantities

1. Fundamental physical quantities Do You Know

Those physical quantities which are independent A physical quantity is represented
of other physical quantities are called by a number followed by a unit.
fundamental physical quantities. There are The number with unit is known as
seven fundamental quantities in SI system. They the magnitude/size of the physical
are length, mass, time, temperature, electric quantity. The number alone is
current, amount of substance and luminous meaningless. For example, 20 is a
intensity. Fundamental physical quantities are mathematical pure number but 20
also called basic physical quantities. metre is a physical quantity. Therefore,

2. Derived physical quantities the unit must always be written while
writing a physical quantity.

Those physical quantities which are obtained

by multiplying or dividing one fundamental physical quantity with another are called

derived physical quantities. Area, volume, speed, velocity, acceleration, density, pressure,

work, energy, power, etc. are some examples of derived physical quantities. These physical

quantities depend on one or more fundamental physical quantities.

Unit and its Types

Unit is the standard quantity which is used to compare an unknown physical quantity.
Similar physical quantities are measured in terms of unit. Metre (m), kilogram (k), second
(s), newton (N), pascal (Pa), joule (J), watt (W), etc. are some examples of units.

While expressing the amount of a physical quantity, we use a unit along with a numerical
value, e.g. 5m length, 3 N force, 10 s time, 2m/s² acceleration, etc.

Units are of two types, viz. fundamental units and derived units.

1. Fundamental units

The units of fundamental physical quantities like metre (m), kilogram (kg), second (s),
kelvin (K), etc. are called fundamental or basic units. These units are independent of each
other. So the units which are independent of each other are called fundamental or basic
units. There are seven fundamental units in SI system which are as follows:

6 GREEN Science (Physics) Book-9

Fundamental units Symbol Fundamental quantities

1. metre m Length
2. kilogram kg Mass
3. second s Time
4. kelvin K Temperature
5. ampere A Electric current
6. candela Cd Luminous intensity
7. mole mol. Amount of matter

A variety of physical devices are used for measuring different fundamental quantities.
Some of them are follows:

Length is measured by using a scale or ruler, mass is measured by using a beam balance
and time is measured by using a watch. Similarly, temperature is measured by using a
thermometer and electric current is measured by using an ammeter.

thermometer watch beam balance ammeter

Fig.

1.1 ruler

Q1. Kilogram is called a fundamental unit, why?
Ans: Kilogram is the unit of a fundamental physical quantity, i.e. mass and it is an

independent unit. So, kilogram is called a fundamental unit.

Q2. Second is called a fundamental unit, why?
Ans: Second is the unit of a fundamental physical quantity, i.e. time and it is an

independent unit. So, second is called a fundamental unit.

2. Derived units

The units of derived physical quantities like square metre (m2), metre/second (m/s),
newton (N), pascal (Pa), watt (W), etc. are formed by combination of one or more physical
quantities. These units are called derived units. So, the units which are formed by

GREEN Science (Physics) Book-9 7

multiplying or dividing one or more fundamental units are called derived units. Derived
units can be expressed in terms of fundamental units. In SI system, there are so many
derived units. Some them are given below:

Physical Expression/ SI units Symbol Basic units
quantities Formula involved
1. Area metre × metre m2
2. Volume length × breadth metre × metre × m3 m×m
length × breadth ×
3. Speed/ height metre m×m×m
velocity distance/time metre/second
m/s m/s or ms–1
4. Acceleration change in velocity/ metre/second2
time m/s2 m/s2 or ms–2
5. Force mass × acceleration kilogram × metre
(second)2 kg × m/s2 kgms–2

6. Density mass/volume kilogram/(metre)3 kg/m3 kgm–3
newton×metre J or Nm kg × m × m
7. Work/Energy force ×
displacement watt or W or J/s s×s
joule/second kg × m × m
8. Power Work done Pa or N/m2 (s × s × s)
9. Pressure time pascal or
newton/metre Hz kg
force/area (m × s × s)
hertz
10. Frequency 1 s–1
11. Moment second newton × meter
Nm Nm
force ×
perpendicular

distance

Q3. The unit of acceleration is called a derived unit.
Ans: The unit of acceleration is m/s2. It depends on two basic units, viz. metre (m) and

second (s). So, the unit of acceleration is called a derived unit.
∴ Acceleration (a) = Change in velocity (m/s)

Time taken (s)
a = m/s2

Q4. The unit of density is called a derived unit.
Ans: The unit of density is kg/m3. It depends on two fundamental units, viz. kilogram

(kg) and metre (m). So, the unit of density is called a derived unit.

Q5. The unit of pressure is called a derived unit.
Ans: The unit of pressure is pascal (Pa) or N/m2. It depends on three fundamental units,

viz. kilogram (kg), metre (m) and second (s). So, the unit of pressure is called a
derived unit.

8 GREEN Science (Physics) Book-9

Activity 1

Make a list of various units that are used to measure different physical quantities.
Classify these units in terms of fundamental and derived units and fill in the given
table.

Fundamental units Derived units
1.
2.
3.
4.
5.

Differences between Fundamental (Basic) units and Derived units

Fundamental (Basic) units Derived units

1. The units which are independent of 1. The units which are formed by

one another are called fundamental or multiplying or dividing one or more

basic units. fundamental units are called derived

units.

2. They are the units of fundamental 2. They are the units of derived physical

physical quantities. quantities.

3. In SI system, there are seven 3. In SI system, there are so many derived

fundamental units. units.

SI System of Measurement

To make measurement more scientific, uniform and convenient, the French Academy of
Science in 1971 AD designed a metric system of measurement based on the decimal
system. In October 1960, the 12th General Conference of Weights and Measures adopted
an international system of units called SI units. The name SI is an abbreviation of the
“System International d’ Units” in French which means “International System of Units.”

In SI system, there are seven basic or Do You Know
fundamental units. They are metre (m),
kilogram (kg), second (s), ampere (A), The symbols of SI units are always written
kelvin (k), candela (Cd) and mole (mol.). in singular even if the value of the physical
The units of all other physical quantities quantity being represented is more than 1.
are derived from the seven fundamental We never put ‘s’ with the symbol of an SI
units. These days, SI system is being used unit. For example, 15 metres is written as 15
and followed throughout the world. It m and not as 15 ms. Similarly, 12 kilograms
makes buying, selling and exchanging of is written as 20 kg and not as 20 kgs.
goods easy, accurate and convenient.

GREEN Science (Physics) Book-9 9

SI units were made by Paris Conference. Now-a-days, these units are used by all countries
of the world maintaining uniformity in measurement system. According to SI system
of measurement, different physical quantities are well defined and their models or
prototypes are made. These prototypes are distributed to different countries of the world.

On the basis of the prototypes or models made by SI system, different physical quantities
are being measured throughout the world. So, SI system of measurement plays a
significant role to bring uniformity in measurement throughout the world.

Do You Know

One standard meter is defined as the distance between two fine parallel golden lines

engraved near the ends of a platinum-iridium rod at standard atmospheric pressure

which is kept at the International Bureau of Weights and Measures near Paris, France.

One standard kilogram is defined as the mass of a platinum-iridium cylinder having

equal diameter and height kept at 0°C at the International Bureau of weights and

Measures, near Paris, France. The mass of this cylinder is equal to the mass of 1 litre

pure water at 4°C.

Zenith is the point in the space just above the observer’s head.

One mean solar day is the time taken by the sun to return to the zenith. It can also be

defined as the time required by the earth to complete one rotation around the sun about

its axis. 1
86400
One standard second is defined as th part of a mean solar day.

One standard second can also be defined as the time interval of 9,192, 631, 770 periods

of specified energy change in the Caesium-133 atom.

Activity 2

Find out traditional units or local units and standard units which are used to measure
different physical quantities Also, write down with reason which of them (traditional
or standard unit) is more reliable.

S.N. Physical units Traditional units Standard units
1. Length
2. Mass
3. Time
4.
5.

Scientific Notation

It requires more space and consumes more time while writing very large and very small
numbers. So, very large and very small number are expressed in the power of ten, which
is called scientific notation or standard notation.

10 GREEN Science (Physics) Book-9

Rule of writing scientific names

1. While shifting the decimal to the left, the power of ten should be increased by ‘one’ in

each shift, e.g. 2654215.
= 2.654215 × 101 × 101 × 101 × 101 × 101 × 101 [The decimal point shifts to six steps left.]
= 2.654215 × 106
= 2.65 × 106
2. While shifting the decimal to the right, the power of ten should be increased by

‘minus one’ in each shift, e.g.
0.000123
= 1.23 × 10–1 × 10–1 × 10–1 × 10–1 [The decimal point shifts to four steps right.]
= 1.23 × 10–4

Solved Numerical: 1

Convert 13236.321 into scientific notation.

Solution:

13236.321 (Here, the decimal point shifts to four steps left.)
= 1.3236321 × 104

≈ 1.3 × 104

Solved Numerical: 2
i. Convert the following numbers in the scientific notation.

a. 23560000 b. 1456000000 c. 456000000

d. 0.00000456 e. 0.0000000000125

Solution:

a. 23560000 b. 1456000000 c. 456000000

= 2.356 × 107 = 1.456×109 = 4.56×108

d. 0.00000456 e. 0.0000000000125

= 4.56×10–6 = 1.25×10–11

ii. Convert the following scientific notation into general form.

a. 2.35×107 b. 1.45×109 c. 4.56×108
d. 4.56×10–6 e. 1.25×10–11

Solution:

a. 2.35×107 b. 1.45×109 c. 4.56×108

= 23500000 = 1450000000 = 456000000

GREEN Science (Physics) Book-9 11

d. 4.56×10–6 e. 1.25×10–11

= 0.00000456 = 0.0000000000125

Key Concepts

1. Those quantities which can be measured are called physical quantities.

2. Those physical quantities which are independent of other physical quantities are
called fundamental physical quantities. There are seven fundamental quantities in
SI system.

3. A physical quantity is represented by a number followed by a unit.

4. Those physical quantities which are obtained by multiplying or dividing one
fundamental physical quantity with another are called derived physical quantities.

5. Unit is the standard quantity which is used to compare an unknown physical
quantity with a known standard quantity of the same kind.

6. The units of fundamental physical quantities like metre (m), kilogram (kg), second
(s), etc. are called fundamental or basic units.

7. Kilogram is the unit of a fundamental physical quantity, i.e. mass and it is an
independent unit. So, kilogram is called a fundamental unit.

8. The units of derived physical quantities like square metre (m2), metre/second (m/s),
newton (N), pascal (Pa), watt (W), etc. are formed by combination of one or more
physical quantities. These units are called derived units.

9. Derived units can be expressed in terms of fundamental units. In SI system, there
are so many derived units.

10. The unit of density is kg/m3. It depends on two fundamental units, viz. kilogram
(kg) and metre (m). So, the unit of density is called a derived unit.

11. To make measurements more scientific, uniform and convenient, the French
Academy of Science in 1971 AD designed a metric system of measurement based
on the decimal system.

12. In SI system, there are seven basic or fundamental units. They are metre (m),
kilogram (kg), second (s), ampere (A), kelvin (k), candela (Cd) and mole (mol.).

13. The symbols of SI units are always written in singular even if the value of the physical
quantity being represented is more than 1.

Sequential General Exercise 1

1. Choose the best answer from the given alternatives.
a. Which of the following is not a physical quantity?

mass length time love
m
b. Which of the following is the SI unit of mass?

kg g mg

12 GREEN Science (Physics) Book-9

c. Which of the following is a fundamental unit?

s m/s N Pa
s
d. Which of the following is a derived unit? kg m3

N kg m

e. Which of the following is the SI unit of density?

m/s kg/m3 g/cm3

2. Answer the following questions.
a. What are physical quantities?
b. Name two types of physical quantities.
c. Define basic or fundamental physical quantities.
d. Name the seven fundamental physical quantities.
e. Define derived physical quantities with any five examples.
f. What is a unit? Give any three examples.
g. Name two types of units.
h. What are fundamental units? Name seven fundamental units of SI system.
i. What are derived units? Give any five examples.

3. Give reason:
a. Mass and volume are called physical quantities.
b. Length is called a fundamental physical quantity.
c. Pressure is called a derived physical quantity.
d. Kilogram is called a basic unit.
e. Pascal is called a derived unit.
f. The unit of temperature is called fundamental unit.

4. Write down the SI units of the given physical quantities.

a. Mass f. Force

b. Length g. Pressure

c. Time h. Volume

d. Temperature i. Density

e. Electric current j. Power

GREEN Science (Physics) Book-9 13

5. Find out the fundamental units involved in the given derived units.

a. newton b. pascal
c. watt d. joule
e. cubic metre f. square metre

6. Write any two differences between fundamental units and derived units.

7. Find out the fundamental units involved in the units of

a. velocity b. acceleration
c. work d. pressure
e. power f. density
g. volume h. force

8. Write a short note on “SI system of measurement”.

9. The standard weights and metre scales of the shops in the market are checked in
every two years by the Department of Weights and Measures of Nepal, why?

10. Why was SI system of measurement developed? Explain with a suitable example.

Grid-based Exercise 2

Group ‘A’ (Knowledge Type Questions) (1 Mark Each)

1. What is measurement?

2. Define one metre length.

3. How is ‘one second’ time defined in SI system?

4. How is ‘one metre length’ defined in SI system ?

5. Define one solar day.

6. Define derived unit.

7. What is mass of a body?

8. How much time of a solar day is considered as one second?

9. Define 1 kilogram mass.

10. What do you mean by physical quantity?

14 GREEN Science (Physics) Book-9

For Group ’B’ (Understanding Type Questions) (2 Marks Each)

11. Write any two differences between fundamental unit and derived unit.

12. Write any two advantages of writing very large and very small numbers in the terms
of power of ten.

13. The unit of time is called a fundamental unit but unit of velocity is called derived unit.
Why?

14. What difficulties would arise due to lack of uniformity in measurement in different
countries? Write in brief.

15. Quartz clock is more appropriate than pendulum clock to measure time, why?

16. Why was SI system developed? Write with reason.

17. The unit of mass is called a fundamental unit and that of acceleration is called derived
unit, why?

For Group ‘C’ (Application Type Questions) (3 Marks Each)

18. What is SI system? Why is SI unit developed? Describe in brief.

19. List the fundamental units included in pascal (Pa) and watt (W).

20. Describe the method of measuring the volume of an irregular solid with a neat and
labelled figure.

21. Write down the given numbers in the power of ten.

a. 2560000 b. 0.005346 c. 1
25200

22. Write any three advantages of using SI system of measurement.

For Group ‘D’ (Higher Abilities Type Questions) (4 Marks Each)

23. Write down the formula, derived units and fundamental units involved in the units
of given physical quantities.

a. Force b. Pressure

24. Write down the formula and derived units of the given physical quantities. Also, find
out the fundamental units involved in those derived quantities.

a. Force b. Power

25. Write down the formula, derived units and fundamental units involved in the units
of given physical quantities.

a. Acceleration b. Density

26. SI system plays a significant role to bring uniformity in measurement system of the
countries all over the world. Justify this statement with examples.

27. The length of a pond is 1700cm, breadth is 14m and height is 1000cm. If the pond is

half-filled, calculate the volume of water in the pond. (Ans: 1190 m3)

GREEN Science (Physics) Book-9 15

UNIT Force and Motion

2

Weighting Distribution Theory : 5 Practical: 1

Before You Begin

Force is an external agency which changes or tries to change the
position, speed, direction of motion and shape of a body. It is a
vector quantity having magnitude and direction. The SI unit of force
is newton (N). A force can change the position, i.e. the state of rest
or uniform motion, of a moving body. Similarly, force can change
the shape and direction of motion of a body. We see many things
around us. All these things do not appear to move. The things that
do not move from one place to another are called things at rest. The
things that change their position with respect to other objects in their
surroundings are called the things in motion. A book kept on a table
is an example of a body at rest and a flying bird is an example of a
body in motion. In this unit, we will study rest and motion, speed
and velocity, acceleration and retardation, equations of motion and
numerical problems based on velocity and acceleration.

Learning Objectives Syllabus

After completing the study of this unit, students will be able to: • Introduction to force
• Rest and motion
i. introduce force and write its SI unit. • Speed and velocity
• Uniform and non-uniform
ii. describe and demonstrate rest and motion.
velocity
iii. introduce speed, velocity, uniform velocity, non- • Acceleration and retardation
uniform velocity and acceleration. • Equations of motion
• Inertia and its types
iv. derive equations of motion. • Relationship between mass

v. introduce inertia and its types with examples. and inertia
• Momentum
vi. state Newton’s laws of motion and solve simple • Newton’s laws of motion
numerical problems related to motion. • Balanced and unbalanced

vii. introduce balanced force and unbalanced force with force
examples.

Glossary: A dictionary of scientific/technical terms

motion : if the position of a body changes with respect to other objects in its
surroundings
reference
velocity : a standard by which something can be compared
acceleration : the rate of change of displacement of a moving body
displacement : the rate of increase in the velocity of a moving body
retardation : the distance travelled by a moving body in a certain direction
: the rate of decrease in velocity of a moving body

16 GREEN Science (Physics) Book-9

Rest and Motion

If we look around in the classroom we see

a variety of things. All these things do not

move, they are said to be at rest. A body is

said to be at rest, if it does not change its

position with respect to a fixed point taken

as reference point in its surroundings. A
Fig. Fig.
Fig.book lying on a table, walls of a house,

blackboard, desk, etc. are some examples 2.1
of body at rest.
Object at rest
Human beings, animals, birds, insects,

etc. move from one place to another. A man running on the road, a bus moving on a road,

a bird flying in the sky, etc. keep on changing their position continuously. These are some

examples of things in motion. A body is said to be in motion, if it changes its position with

respect to a fixed point taken as a reference point in its surroundings. The planets of the

solar system revolve around the sun. The moon revolves around the earth. Birds fly in

air and vehicles ply on the road. These are some examples of the body in motion. Objects

like houses, trees, etc. do not move from one place to another. These are the examples of

the body at rest.

2.2 Do You Know
A bird in motion
A reference point is a body at rest with
respect to which the state of another body
is compared. Reference point may be a
certain point, object or place about which
the state, i.e. rest or motion, of a body is
studied.

Rest and motion are relative terms

Let us consider that we are sitting

in a moving train. We are in motion

with respect to the trees or buildings

outside the train because our position is

changing with respect to them. However,

if we compare our position with respect

to the things inside the train, i.e. other

passengers, seats, fan of the train, walls

and roof of the train, etc.; we are at rest.
Thus, an object can be at rest in relation 2.3
to one object while it can be in motion
in relation to another object at the same Moving train

instant of time. Therefore, we can say that rest and motion are relative terms.

GREEN Science (Physics) Book-9 17

Scalar and Vector Quantities Do You Know

A physical quantity which is described The sum of scalar is always positive but
completely by its magnitude only is called a the sum of vectors may be positive, zero
scalar quantity. Thus, a scalar quantity has or negative.
only magnitude but no direction. Length,
distance, time, area, temperature, speed, mass, Scalars are added by the rules of simple
energy, power, volume, etc. are some examples algebra but vectors are added by the
of scalar quantities. rules of vector algebra.

A physical quantity which requires both Scalars are not written in a special way
magnitude and direction for its complete but vectors are written in a special way,
description is called a vector quantity. Thus, e.g. vector PQ is denoted by PQ .
a vector quantity has both magnitude and
direction. Displacement, velocity, force,
acceleration, weight, etc. are some examples
of vectors quantities.

Differences between Scalars and Vectors

Scalars Vectors

1. Scalars have magnitude but no 1. Vectors have both magnitude and

direction. direction.

2. The sum of scalars is always positive. 2. The sum vectors may be positive, zero
or negative.

3. They are added by the rules of simple 3. They are added by the rules of vector

algebra. algebra.

Distance and Displacement C

A distance is the actual length of E

4km
Fig.
the path covered by a moving body 4km
5km
irrespective of its direction. In the 5km
B
SI system, distance is measured in A D

metre (m). 2.4

In the given figure, the total distance
covered by a moving body from A to E is

Distance covered (s) = AB + BC + CD + DE

= 5km + 4km + 4km + 5km

= 18 km

18 GREEN Science (Physics) Book-9

During the calculation of distance covered, the direction in which a body is moving is not
considered. So, the distance covered by a body is a scalar quantity.

P

3km di5skpmlacement

Fig.

2.5 Q 4km R

Displacement is the shortest distance between the initial and the final position of a moving
body in a certain direction. It is a vector quantity. It can be positive, zero or negative.

Distance covered from P to R (s) = (3 + 4) km

= 7 km

Displacement (s) = 5 km

Suppose a bus moves from P to Q (3km) towards south and Q to R (4km) towards east.

Then the distance covered by the bus is PQ + QR = 3km + 4km = 7km

But the displacement of the bus PR from P to R is given by

PR = PQ2 + QR2

= 32 + 42

= 25

= 5

\ The displacement of the bus is 5 km.

Speed and Velocity

The speed of a moving body is defined as the distance covered by it per unit time, i.e.

Speed = Distance covered
Time taken

The SI unit of speed is metre per second (m/s) and CGS unit is centimetre per second
(cm/s). Speed is a scalar quantity. The speed of fast moving bodies like car, bus, motorcycle,
aeroplane, etc. is expressed in kilometre/hour (km/h). The speed of a moving body may
be uniform or non-uniform.

GREEN Science (Physics) Book-9 19

The velocity of a moving body is defined as the distance covered by the body per unit
time in a fixed direction. It is also called the rate of change of displacement.

Velocity (v) = Displacement (s)
Time taken (t)

The SI unit of velocity is metre per second (m/s) and CGS unit is centimetre per second
(cm/s). Velocity is a vector quantity.

Differences between Speed and Velocity

Speed Velocity

1. The rate of change of distance of a 1. The rate of change of displacement of a

moving body is called speed. moving body is called velocity.

2. Its magnitude is always positive. 2. Its magnitude can be negative, zero or
positive.

3. It is a scalar quantity. 3. It is a vector quantity.

Fig.

2.6 Leopard Running woman
Jet plane

Do You Know

Solved Numerical: 1 The average speed of jet aeroplane is
1100 km/h.
A truck travels 100 km in 80 minutes towards
the south. Calculate the velocity of the truck. The average speed of leopard is 112
Solution: km/h.
Given,
Displacement (s) = 100 km The average speed of falcon bird is 349
km/h.

The average speed of man is 5km/h.

= 100 × 1000 m [ 1km = 1000 m]

= 100000 m

Time taken (t) = 80 minutes

= 80 × 60 seconds [ 1 min. = 60 s]

= 4800 s

Velocity (v) = ?

20 GREEN Science (Physics) Book-9

We know,

Velocity (v) = Displacement (s)
Time taken (t)

= 100000
48000

= 20.83 m/s

\ The velocity of the truck is 20 m/s.

Uniform velocity and Non-uniform velocity

A body is said to be moving with uniform velocity if it covers equal distance in equal
intervals of time in a fixed direction.

The velocity of a car in the given figure 2.4 is called uniform or constant because the car
covers equal distance in every one second toward the east.

West East

Fig. Fig.2.7 0s 10m 1s 10m 2s 10m 3s 10m 4s 10m 5s

A body is said to be moving with non-uniform or variable velocity if it covers unequal
distance in equal intervals of time in a certain direction. In the given figure 2.5, the velocity
of the car is called non-uniform or variable velocity as it covers unequal distance in every
one second.

West East

2.8 1s 20m 2s 10m 3s 16m 4s 8m 5s

Solved Numerical: 2

A car covers 100 m in 5 seconds and 225 m in 11 seconds. Calculate the average velocity
of the car.

Solution:

Given,

Total distance covered (s) = 100 m + 225 m

= 325 m

Total time taken (t) = 5 s + 10 s

= 15 s

Average velocity (v) = ?

GREEN Science (Physics) Book-9 21

We know, = Total distance covered (s)
Average velocity (v) Total time taken (t)

= 325
15

= 21.66 m/s

\ The average velocity (v) of the car is 21.66 m/s.

Average velocity

Average velocity of a moving body is defined as the arithmetic mean of the initial and the
final velocity over a given period of time.

If ‘u’ is the initial velocity and ‘v’ is the final velocity of a body moving in a certain
direction, then

Average velocity (Aav) = u + v
2

Concept of Acceleration

Let us consider a body moving in a straight line with a non-uniform velocity. Let a school
bus starts from rest at “Stop A”. When it starts moving, its velocity increases and after a
certain time it gains a constant velocity. As the “Stop B” approaches, its velocity gradually
decreases and finally becomes zero at the “Stop B”. These changes in the velocity of a
moving body are described in terms of acceleration.

Velocity P Constant velocity Q
AcVceleloecirtatyiionncreasing Retardation
Velocity decreasing
Fig.

2.9 Stop A time (t) Stop B

The rate of change of velocity of a body with respect to time is called its acceleration, i.e.

Acceleration = Change in velocity
Time interval
We know,

Change in velocity = Final velocity (v) – Initial velocity (u)

Thus, Acceleration (a) = Final velocity (v) – Initial velocity (u)
Time interval (t)

\ a = v – u
t

22 GREEN Science (Physics) Book-9

SI unit of acceleration

We know,
Acceleration = Change in velocity

Time interval
In SI system, the unit of velocity is ‘m/s’ and that of time is ‘s’.
\ The SI unit of acceleration is m/s or m/s2 or ms–2.

s
So, in SI system, the unit of acceleration is metre per second square (m/s2 or ms–2).

Positive acceleration and Negative acceleration

If the final velocity of a moving body is Do You Know
greater than the initial velocity, i.e. v > u,
then, When a ball is thrown vertically
downwards, its velocity increases with
Acceleration (a) = v – u = Positive quantity time. So the acceleration of a ball thrown
t vertically downwards is always positive.
In other words, when the velocity of a

body increases with time, its acceleration

is positive. In common practice, positive

acceleration is simply called acceleration.

If the final velocity of a moving body is less than the initial velocity, i.e. v < u then,

Acceleration (a) = v–u = Negative quantity
t
In other words, when the velocity of a
Do You Know
body decreases with time, its acceleration is

negative. Negative acceleration is also called When a ball is thrown vertically upwards,
retardation.
its velocity decreases with time. So, the

If a body has an acceleration of – 5 m/s2, acceleration of a ball thrown vertically
then the retardation of the body is + 5 m/s2. upwards is negative (a case of retardation).

The SI unit of retardation is m/s2 or ms–2. In

fact, retardation is the acceleration with a negative sign.

Solved Numerical: 3

A motorcycle starts to move from rest and gains a velocity of 90 km/h after 15 seconds.
Calculate the acceleration of the motorcycle.

Solution:

Given,

Initial velocity (u) = 0 [ The motorcycle starts to move from rest]

Final velocity (v) = 90 km/h

= 90 × 1000 = 25 m/s
60 × 60

GREEN Science (Physics) Book-9 23

Time taken (t) = 15 s

Acceleration (a) = ?
We know,

a = v – u
t

= 25 – 0
15

= 1.66 m/s2

\ Acceleration of the car = 1.66 m/s2.

Velocity-time Graph

The graph drawn by plotting the velocity of a moving body along the Y-axis and
corresponding time along the X-axis is called velocity -time graph. It is the geometrical
relationship between the velocity of a moving body and time taken. The velocity-time
graph for a straight-line motion can be of following three types.

i. Zero acceleration
When the velocity of a moving body remains constant, a straight line parallel to time-axis
is obtained. In this condition, the acceleration of the moving body is zero.

Y

16 constant velocity (zero
acceleration)

14

12

10

velocity (v) 8
(m/s)
straight line parallel to
6 time axis

4

Fig. 2

0 X

2 4 6 8 10 12 14 16 18

2.10 time (t) (s)

Zero acceleration

ii. Uniform acceleration

When the velocity of a moving body changes equally in equal interval of time, a
straight line making an angle with the time-axis is obtained. In this condition, the
acceleration is uniform.

24 GREEN Science (Physics) Book-9

Y

16

14

12

10

velocity (v) 8
(m/s)
6
Uniform
acceleration4

Fig. Fig. 2

0 X

2 4 6 8 10 12 14 16 18

2.11 time (t) (s)

Uniform acceleration

iii. Non-uniform acceleration
When the velocity of a moving body changes unequally in equal interval of time, a

curve moving upwards is obtained. In this condition, the acceleration of the moving
body is non-uniform.

Y

16

14

12

10

velocity (v) 8
(m/s)
6

4

2

0 X

2 4 6 8 10 12 14 16 18

2.12 time (t) (s)

Non-uniform acceleration

GREEN Science (Physics) Book-9 25

Solved Numerical: 4
Study the given velocity-time graph of a car and answer the following questions.

Y

70

60

velocity (m/s) 50

40 B C

30

20 A

Fig. 10

D

0 X

10 20 30 40 50 60 70 80

2.13 time (s)

a. What is the velocity of car at B, C and D?
Ans. The velocity of cat at B and C is 40 m/s and that at D is 0 m/s.

b. What is the acceleration of the car while moving from A to B?

Ans. Initial velocity (u) = 20 m/s

Final velocity (v) = 40 m/s

Time taken (t) = 20 s

Acceleration (a) = ?

We know,
a = v – u

t

= 40 – 20
20

= 1 m/s2

c. What is the retardation of the car?

Ans. Initial velocity (u) = 40 m/s.

Final velocity (v) = 0

Time taken (t) = (60 – 40) s

= 20 s

Acceleration (–a) = ?

26 GREEN Science (Physics) Book-9

We know,
a = v – u

t

= 0 – 40
20

= –2 m/s2

–a = 2 m/s2

d. What is the acceleration of the car while moving from B to C? Why?

Ans. The acceleration of the car while moving from B to C is zero. Because the velocity of
the car remains constant while moving from B to C.

Equations of Motion

When a body travels in a straight line with a uniform acceleration, the relationship among
the initial velocity (u), final velocity (v), distance covered (s), acceleration (a) and the time
taken (t) are called the equations of motion. There are three equations of motion which
are as follows:

i. v = u + at ii. s = ut + 1 at2 iii. v2 = u2 + 2as
2

i. Derivation of equation v = u + at

Let us consider a body having initial velocity ‘u’ is moving with a uniform acceleration
‘a’. If after time ‘t’, its velocity is ‘v’, then from the definition of acceleration ‘a’, we get,

Acceleration (a) = Final velocity (v) – Initial velocity (u)
Time taken (t)
or, a = v – u
t
at = v – u

or, v = u + at ............................. (1)

This equation helps us to find the velocity gained by a moving body in time ‘t’.

ii. Derivation of equation s = ut + 1 at2
Let us consider a body having initial v2elocity ‘u’ is moving with a uniform acceleration
‘a’. If after time ‘t’, its velocity is ‘v’. For a body moving in a straight line under uniform
acceleration, the distance covered (s) in time (t) is given by,

Distance covered (s) = Average velocity × time taken

or, s = u + v × t q Average velocity = u + v r
2 2

or, s = u + (u + at) × t [ v = u + at]
2

GREEN Science (Physics) Book-9 27

or, s = 2u + at × t
2

or, s = 2ut + at2
22

or, s = ut + 1 at2 ............................. (2)
2

iii. Derivation of equation v2 = u2 + 2as Do You Know

Let us consider a body having initial velocity If a body starts from rest, its initial
‘u’ is moving with a uniform acceleration ‘a’. velocity (u) is zero.
If after time ‘t’, its velocity is ‘v’. For a body
moving in a straight line under uniform If a body comes to rest, its final velocity
acceleration, the distance covered (s) in time (v) is zero.
(t) is given by,
If a body moves with a uniform velocity,
Distance covered (s) = Average velocity × time its acceleration (a) is zero.

taken

or, s = u + v ×t
2

or, s = v + u × v – u q a = v – u , t = v – u r
2a ta

or, s = v2 – u2
2a

or, 2as = v2 – u2

or, v2 = u2 + 2as Fig.
....................... (3)

Solved Numerical: 5
2.14
A car starts to move from rest and Inertia of rest
gains an acceleration of 2 m/s2.

Calculate the final velocity of the car after 10 seconds. Also, calculate the distance covered

by the car within that time.

Solution:

Given,

Initial velocity (u) = 0 [ The car starts from rest.]

Acceleration (a) = 3 m/s2

Time (t) = 10 s

Final velocity (v) = ?

Distance covered (s) = ?

28 GREEN Science (Physics) Book-9

We know,
v = u + at
= 0 + 3 × 10
= 30 m/s
\ The final velocity of the car is 30 m/s.
Again,

s = ut + 1 at2
2
= 0 × 10 + 1 × 3× 102

= 1 2
2 × 3 × 100

= 150 m

\ The distance covered by the car = 150 m.

Solved Numerical: 6

A car starts from rest and covers a distance of 100 m after 10 seconds. If the acceleration is
2 m/s2, calculate the final velocity of the car.
Given,
Initial velocity (u) = 0 [ The car starts from rest.]
Distance covered (s) = 100 m
Time taken (t) = 10 s
Acceleration (a) = 2 m/s2
Final velocity (v) = ?
We know,
v2 = u2 + 2as
or, v2 = 0 + 2 × 2 × 100
or, v2 = 400
or, v = 400
\ v = 20 m/s

\ The final velocity of the car (v) = 20 m/s.

Inertia

We observe in our daily life that an object lying anywhere keeps on lying there only unless
someone moves it from there. For example, a table, a chair, a book etc. cannot change their
position on their own. Similarly, a body in uniform motion cannot stop on its own. This
property of a body is called inertia. So, inertia can be defined as the inability of a body
to change its position by itself. It is the inherent property of a body by virtue of which it
resists any change in its state of rest or of uniform motion in a straight line on its own.

Inertia is of two types, viz. ii. Inertia of motion
i. Inertia of rest and

GREEN Science (Physics) Book-9 29

i. Inertia of rest

Inertia of rest can be defined as the property of a body due to which it resists a change in
its state of rest. A body at rest remains at rest and cannot start moving on its own due to
the inertia of rest.

We observe/experience a number of phenomena based on inertia of rest. Some of them
are described below:

a. The passengers in a bus tend to fall backward when the bus starts to move
suddenly.

Explanation

When passengers are standing or sitting in a bus at

rest, both the bus and passengers are at rest. When

the bus starts to move suddenly, the lower part of

the passengers’ body starts moving forward with

the bus. But the upper part of the body tends to Fig.
Fig.
remain at rest due to inertia of rest. As a result,

passengers fall backwards. 2.15

b. On shaking to the branch of a tree, the fruits fall down.

Explanation

Initially both the tree and fruits hanging on its branch

are in the state of rest. When the branch is shaken, it is

set into motion while the fruits remain in the state of

rest due to inertia of rest. Thus, the fruits get detached
from the branch and fall down due to effect of gravity. 2.16

Apple falling from

c. A bullet fired against a glass window-pane makes a a tree

hole in it but the glasspane is not cracked.

Explanation Fig.

Initially, the entire glass window pane is in Bullet fired against a glass
the state of rest. When a bullet strikes a glass window panel
pane, the part of the glass pane which comes
in contact with the bullet immediately shares
the large velocity of the bullet and flies away 2.17
making a hole. The remaining part of the
glass remains at rest due to inertia of rest and
is not cracked.

30 GREEN Science (Physics) Book-9

d. Dust particles can be removed from a hanging carpet by shaking it or beating
it with a stick.

Explanation Fig.
Fig.
Initially both the carpet and dust particles therein are at
rest. When the carpet is shaken or beaten with a stick,
the carpet is set into motion while the dust particles
remain at rest. As a result, dust particles fall down due
to effect of gravity.

2.18
Dust falling down

e. If a piece of paper placed under a pile of books is suddenly pulled, it does not
disturb the pile of books.

Explanation

Initially both the piece of paper and pile of

books are in the state of rest. When the piece

of paper placed under the pile of books is

suddenly pulled, it is set into motion, while

the pile of books remains in the state of rest

due to inertia of rest. As a result, the pile of 2.19
books does not fall.
Pile of books

ii. Inertia of Motion

Inertia of motion can be defined as the property of a body due to which it resists a change
in its state of uniform motion. A body in uniform motion can neither get accelerated nor
get retarded on its own. It also cannot come to rest on its own.

We observe/experience a number of phenomena based on inertia of motion. Some of them
are given below:

a. Passengers in a moving bus tend to fall forward when the bus stops suddenly.

Explanation Fig.

Initially both the bus and passengers are in the
state of uniform motion. When the bus stops
suddenly, the lower part of the passengers’ body
comes to rest along with the bus. But the upper
part of the passengers’ body tends the remain in
the state of motion due to inertia of motion. As a
result, passengers lean forward.

2.20

GREEN Science (Physics) Book-9 31

b. A person jumping out of a speeding bus may fall forward.

Explanation 2.2Fig. Fig. Fig.

Initially both the person and moving bus are in
the state of motion. When the passenger jumps out
of a speeding bus, the lower part of the persons
body comes to rest on touching the ground but the
upper part of his body tends to remain in the state
of motion due to inertia of motion. As a result, the
person jumping out of the speeding bus may fall
forward and get seriously injured.

c. A cyclist does not come to rest immediately after he stops paddling.

Explanation

A cyclist riding along a road does not come to rest

immediately after he stops paddling. The bicycle

continues to move forward due to the inertia of

motion. But the bicycle comes to rest due to friction

after some time. 2.22

d. An athlete runs a certain distance before taking Cycling
a long jump.

Explanation Long jump

When an athlete runs continuously, he acquires
the inertia of motion. The velocity acquired by
running is added to the velocity of the athlete at
the time of jump. Hence, the athlete can jump over
a longer distance due to the increased inertia of 2.23
motion.

Activity 1 Fig.

Take a glass tumbler and place a thick post card on the mouth of the glass. Then place a
coin on the middle of the post
card.

Now, flick the card hard with
fingers. What do you observe?
On flicking, the post card moves
away but the coin drops into the
glass tumbler due to inertia of
rest. 2.24

32 GREEN Science (Physics) Book-9

Do You Know

A running soldier cannot stop immediately while getting command to stop due to inertia
of motion.

The blades of a fan keep on moving for a while even after the switch has turned “off” due
to inertia of motion.

Relation between Mass and Inertia

We feel easier to move a small stone than a large one. Thus, a large stone shows a greater
resistance to change in its state of rest or uniform motion than a small one. It shows that
a heavier body has more inertia than a lighter body. Therefore, we can say that more the
mass, more is the inertia and lesser the mass, lesser is the inertia of a body. In fact, the
inertia of a body is measured by the mass of the body. Heavier the body, greater is the
force required to change its state and greater is the inertia. The reverse is also true.

Activity 2

Take a bottle of 1 litre capacity and fill it completely with water.

Take another bottle of 2.25 litre capacity and fill it completely with water.

Tie both bottles with rope of equal length and hang them as shown in the figure.

waterFig.water
1l 2.25 l

2.25

Now, push both of the bottles upto a certain distance. Which bottle requires more force
to push?

The bottle of 2.25 l capacity requires more force than the bottle of 1 l capacity to be pushed.

Now, pull both bottles upto equal distance and release. Let them oscillate and
observe,which bottle oscillates for a longer time?

The larger bottle oscillates for a larger time than the small bottle. The larger bottle has
more mass than the small bottle. So, the larger bottle requires more force while pushing
and also oscillates for a long time due to more inertia.

From this activity, it can be concluded that the body having more mass has more inertia
and vice-versa.

GREEN Science (Physics) Book-9 33

Momentum

The product of mass and velocity of a body is called momentum. In short,

Momentum (P) = mass (m) × velocity (v)

∴ P = m × v

The SI unit of mass is kilogram (kg) and that of velocity is metre per second (m/s). So the
SI unit of momentum is kilogram metre per second (kgms–1).

The quantity of motion in a body depends on the mass and velocity of the body.
Momentum is a vector quantity. In fact, momentum is considered to be a measure of
quantity of motion of a body.

Solved Numerical: 7

Calculate the momentum produced when a body of mass 25 kg moves with a uniform
velocity of 25m/s.
Solution
Mass (m) = 25 kg
Velocity (v) = 25 m/s
Momentum (P) = ?
We know
Momentum (P) = mass (m) × velocity (v)
= 25 × 25
= 625 kg.m/s
∴ Momentum (P) = 625 kg. m/s.

Newton’s Laws of Motion

Newton has propounded three laws to describe the
motion of different bodies. These laws are known
as Newton’s laws of motion. The Newton’s laws of
motion give a precise definition of force and establish
a relationship between the force applied on a body and
the state of motion acquired by it.

Newton’s First Law of Motion Fig.

Some objects around us remain at rest and others 2.26
remain in motion. Newton’s first law describes the
behaviour of such bodies which are in a state of rest or Sir Issac Newton
uniform motion in a straight line.

34 GREEN Science (Physics) Book-9

According to Newton’s first law of motion, a body at rest will remain at rest and a body
in motion will continue in motion in a straight line with a uniform speed unless it is
compelled by an external force. This law recognizes that every body has some inertia. So,
Newton’s first law of motion is also called law of inertia. Newton’s first law of motion can
be made clear by the given example.

Suppose a book is lying on a table. It is at rest. This book will not move by itself, that
is, it cannot change its position of rest by itself. It can change its state of rest only when
compelled by the force of our hands, that is, when we lift or push the book from the table.
Similarly, a moving vehicle keeps on moving in a straight line unless it is stopped by
applying force on brakes.

Newton’s Second Law of Motion

Newton’s second law of motion gives the magnitude of the force which produces
acceleration in a body. It has been found experimentally that the magnitude of the
force acting on a body is directly proportional to the mass of the body and acceleration
produced in the body.

According to Newton’s second law of motion, the force acting on a body is directly
proportional to the product of the mass of the body and the acceleration produced in the
body by the action of force and it acts in the direction of the acceleration.

Suppose a force ‘F’ acts on a body of mass ‘m’ and produces an acceleration ‘a’ in the body.
Then, according to Newton’s second law of motion,

Force (F) ∝ mass (m) × acceleration (a)

or F ∝ m × a

or F = k ma

Where ‘k’ is a constant. The value of ‘k’ in SI unit is 1, so the above equation becomes.

F = m × a

∴ Force (F) = mass (m) × acceleration (a)

Thus, Newton’s second law of motion gives us a method of measuring the force in terms
of mass and acceleration. In other words, the force acting on a body can be calculated by
using the formula F = m × a.

We can also write the equation

F = m × a as

a= F
m

It is obvious from the above relation: The acceleration produced in a body is directly

proportional to the force acting on it and inversely proportional to the mass of the body.

This is another way of stating Newton’s second law of motion.

GREEN Science (Physics) Book-9 35

Do You Know

Since the acceleration produced is inversely proportional to the mass of a body, therefore,
if the mass of a body is doubled, its acceleration will be halved. And if the mass is halved
then acceleration will get doubled provided the force remains the same. Moreover, since the
acceleration produced is inversely proportional to the mass of the body, it means that it will
be easier to move light bodies than heavy bodies.

Prove that F = ma

Suppose a body of mass ‘m’ is moving by application of a force ‘F’ which produces an
acceleration ‘a’. According to Newton’s second law of motion.

The acceleration (a) produced on a body is directly proportional to the force applied (F),
i.e.

a ∝ F .................... (i)

The acceleration (a) produced on a body is inversely proportional to the mass (m) of the
body, i.e.

a= 1 .................... (ii)
m

Combining equation (i) and (ii), we get

a= F .................... (iii)
m

or F ∝ ma

or F = k ma .................... (iv)

Where, ‘k’ is a constant.

If m = 1 kg, a = 1 m/s2 and F = 1N.

Then k = 1.

or F = 1 ma

∴ F = ma
Proved.
From the above relation, we get the definition of one newton (1N) force.
One newton (1N) force is that force which when acting on a body of 1 kg mass produces
an acceleration of 1 m/s2.
F = m × a.
Putting m = 1 kg and a = 1 m/s2, F becomes 1 N.
So, 1N = 1 kg × 1 m/s2.

36 GREEN Science (Physics) Book-9

Do You Know

We can get an idea of 1N force by holding a weight of 100 grams on our outstretched palm.
The force exerted by 100 grams weight on our palm is approximately equal to 1 N.

Newton’s second law of motion gives us a relationship between the force applied to a
body and the acceleration produced in the body. It should be noted that just a minus sign
for acceleration shows that the acceleration is acting in a direction opposite to the motion
of the body. Similarly, if a minus sign comes with the force, it will indicate that the force
is acting in a direction opposite to that in which the body is moving.

Solved Numerical: 8

Calculate the force required to impart to a car a velocity of 15 m/s in 5 seconds. The mass
of the car is 800 kg.

Solution:

Initial velocity (u) = 0 ( Car starts from rest.)

Final velocity (v) = 15 m/s

Time taken (t) = 5 s
Acceleration (a) = ?

We know

a= v-u
t
15-0
a= 5

= 3 m/s2

Now,
Mass of the car (m) = 800 kg
Acceleration (a) = 3 m/s2
Force (F) = ?
We know,
F=m×a
= 800 × 3 N
= 2400 N
∴ The force required (F) = 2400 N

GREEN Science (Physics) Book-9 37

Solved Numerical: 9

Calculate the acceleration produced by a force of 24N exerted on an object of mass 6 kg.

Solution:

Force (F) = 24 N

Mass (m) = 6 kg

Acceleration (a) = ?

We know,

F=m×a

or, a= F
m

a= 24
6

= 4 m/s2

∴ Acceleration produced (a) = 4 m/s2

Newton’s Third Law of Motion

Newton’s third law of motion describes the relationship between the force of interaction
between two bodies. According to Newton’s third law of motion, “To every action, there
is an equal and opposite reaction; action and reaction forces act on different bodies.” In
other words, whenever two bodies interact with each other, the force exerted by the first
body on the second (called action) is equal and opposite to that exerted by the second
body on the first body (called reaction).

Reaction (force exerted by ground on the
block in upward direction)

Metal
block

ground

Fig. W = mg

2.27 Action (weight of the block
acting downward)

Action and reaction act on different
bodies

Do You Know

Both action and reaction are forces.
Action and reaction act simultaneously but on different bodies. So they cannot cancel

each other.
Action and reaction forces occur in pairs only.

38 GREEN Science (Physics) Book-9

Activity 3

Take two similar spring balances X and Y. Attach the ring of spring balance Y to the
hook fixed in a wall and then attach the hook of spring balance X to the hook of spring
balance Y.

Fig. Wall action reaction Hand
10 N 10 N
2.28
spring balance spring balance
Y X

Now pull the spring balance X gently and read the both spring balances. It is found that
both the spring balances show the same reading.

Repeat this activity by applying force of different magnitude and read the spring balances.

Write down the conclusion of this activity.

We observe/ experience a number of phenomena that describe Newton’s third law of
motion. Some of them are described below:

a. When a person swims, he pushes the water in the Fig. Fig.

backward direction with his hands (action). As the

reaction, the water pushes the person in the forward 2.29

direction with an equal force (reaction).

b. When a bullet is fired from a gun, the bullet goes out Swimming
due to force applied on it through the trigger (action). Bullet fire
According to Newton’s third law of motion, the gun
recoils backwards due to the reaction acting on it in
the opposite direction (reaction). This gives a backward 2.30
jerk to the shoulders of the gun man.

c. In rockets and jet engines, the fuel is burnt to produce

a large quantity of hot gases. These hot gases come out

of the nozzle with a great force (action). According to Fig.

Newton’s third law of motion, the equal and opposite

reaction pushes the rocket and jet aeroplanes forward

with a great speed (reaction). 2.31

Playing basketball

d. When we strike a basketball against a hard floor, the ball exerts a force (action) on
the floor. According to Newton’s third law of motion, the floor exerts an equal and
opposite force (reaction) on the ball. As a result the basketball rebounds.

GREEN Science (Physics) Book-9 39

e. While rowing a boat, the boatsman pushes the water

backwards with the oars (action). According to

Newton’s third law of motion, the water exerts an
Fig.
Fig. Fig.equal and opposite push on the boat which moves

forward (reaction). 2.32

Balanced Forces Boating

When a number of forces acting on a body do not change the state of rest or uniform motion
of a body, these forces are called balanced forces. Balanced forces are equal in size and
opposite in direction. Balanced forces can be observed in arm wrestling and tug of war.

2.33 Tug of war
Arm wrestling

Unbalanced Forces

When a number of forces acting on a body change its state of rest or uniform motion,
these forces are called unbalanced forces. These forces always cause a change in position
(rest or motion) of a body. Unbalanced forces are not equal and opposite. Unbalanced
forces can be observed while pushing, throwing and kicking various objects.

2.34 Pulling a cart Kicking a football
Pushing car

Project work

Take a kinetic trolley, cylinders of different weights and a spring balance.
Select a smooth surface and verify Newton’s second law of motion by showing the

relation between acceleration produced into trolley with applied force and mass.
Prepare a short report and submit to your science teacher.

40 GREEN Science (Physics) Book-9

Key Concepts

1. A body is said to be at rest, if it does not change its position with respect to a fixed
point taken as a reference point in its surroundings.

2. A body is said to be in motion, if it changes its position with respect to a fixed point
taken as a reference point in its surroundings.

3. A physical quantity which is described completely by its magnitude only is called a
scalar quantity.

4. Length, distance, time, area, temperature, speed, mass, energy, power, volume, etc. are
some examples of scalar quantities.

5. A physical quantity which requires both magnitude and direction for its complete
description is called a vector quantity.

6. Displacement, velocity, force, acceleration, weight, etc. are some examples of
vectors quantities.

7. The speed of a moving body is defined as the distance covered by it per unit time.

8. The velocity of a moving body is defined as the distance covered by a body per unit
time in a fixed direction.

9. A body is said to be moving with uniform velocity if it covers equal distance in
equal intervals of time in a fixed direction.

10. A body is said to be moving with non-uniform or variable velocity if it covers
unequal distance in equal intervals of time in a certain direction.

11. Average velocity of a moving body is defined as the arithmetic mean of the initial
and the final velocity over a given period of time.

12. The rate of change of velocity of a body with respect to time is called its acceleration.

13. The graph drawn by plotting the velocity of a moving body along the Y-axis and
corresponding time along the X-axis is called velocity -time graph.

14. Inertia can be defined as the inability of a body to change its position by itself. It is
the inherent property of a body by virtue of which it resists any change in its state
of rest or of uniform motion in a straight line on its own.

15. Inertia of rest can be defined as the property of a body due to which it resists a
change in its state of rest.

16. According to Newton’s first law of motion, a body at rest will remain at rest and
a body in motion will continue in motion in a straight line with a uniform speed
unless it is compelled by an external force.

17. Newton’s second law of motion gives the magnitude of the force which produces
acceleration in a body.

18. According to Newton’s second law of motion, the force acting on a body is directly
proportional to the product of the mass of the body and the acceleration produced
in the body by the action of force and it acts in the direction of the acceleration.

19. The acceleration produced in a body is directly proportional to the force acting on
it and inversely proportional to the mass of the body. This is another way of stating
Newton’s second law of motion.

GREEN Science (Physics) Book-9 41

20. Newton’s second law of motion gives us a relationship between the force applied to
a body and the acceleration produced in the body.

21. Newton’s third law of motion describes the relationship between the force of
interaction between two bodies. According to Newton’s third law of motion, “To
every action, there is an equal and opposite reaction; action and reaction forces act
on different bodies.”

22. When a number of forces acting on a body do not change the state of rest or uniform
motion of a body, these forces are called balanced forces. When a number of forces
acting on a body change its state of rest or uniform motion, these forces are called
unbalanced forces. These forces always cause a change in position (rest or motion)
of a body.

Sequential General Exercise 1

1. Choose the best answer from the given alternatives.
a. The SI unit of force is ................................

N n kg g

b. ................................ is a scalar quantity.

time velocity acceleration force

c. The rate of change in velocity of a moving body is called ......................

speed momentum acceleration force

d. ................................ is the product of mass and velocity of a body.

force speed velocity momentum

e. Launching of a rocket is based on Newton’s ................... law of motion.

first second third fourth

2. Answer the following questions.
a. Define force with its SI unit.
b. Define rest and motion with any two examples of each.
c. Define scalar and vector quantities with any three examples of each.
d. What is speed? Write its SI unit.
e. Define velocity, uniform velocity and non-uniform velocity.
f. What is acceleration? Write its SI unit.
g. What is meant by retardation? Write its SI unit.
h. What are equations of motion? Write any two equations of motion.

42 GREEN Science (Physics) Book-9

i. What is velocity-time graph?
j. Draw velocity-time graph that represents
i. uniform acceleration
ii. zero acceleration
iii. non-uniform acceleration
k. Define inertia and write its types.
l. Define inertia of rest with any two examples.
m. Define inertia of motion with any two examples.
n. Write down the relationship between mass and inertia.
o. What is momentum? Write its formula and SI unit.
p. State Newton’s first law of motion.
q. State Newton’s second law of motion.
r. State Newton’s third law of motion.
s. What are balanced forces?
t. What are unbalanced forces?

3. Differentiate between:
a. Scalar quantity and Vector quantity
b. Speed and Velocity
c. Acceleration and Retardation
d. Balanced forces and Unbalanced forces

4. Give reason:

a. Rest and motion are called relative terms.
b. Speed is called a scalar quantity but velocity is called a vector quantity.
c. The passengers in a bus tend to fall backward when the bus starts to move

suddenly.
d. On shaking to the branch of a tree, the fruits fall down.
e. Dust particles can be removed by beating a carpet.
f. A person jumping out of a speeding bus falls forward.
g. While rowing a boat, the boatman pushes the water backwards.
h. A balloon moves backward when air rushes out of it.

5. Prove that:

a. v = u + at

b. s = ut + 1 at2
2

c. v2 = u2 + 2as

d. F = ma

GREEN Science (Physics) Book-9 43

6. Numerical Problems

a. A bus covers a distance of 3.6km in 3 minutes. Calculate the velocity of the bus.
[Ans: 20 m/s]

b. A motorcycle is moving with the velocity of 72 km/h. If the velocity reaches 40

m/s after 0.5 minutes, calculate the acceleration. [Ans: 0.66 m/s2]

c. A car starts to move from rest and attains an acceleration of 0.8 m/s2 in 10 seconds.
Calculate the final velocity and distance covered by the car. [Ans: 8m/s, 40 m]

d. A bus is moving with the velocity of 90 km/h. If the bus is stopped in 8 seconds

by applying the brakes. Calculate retardation. [Ans: 3.12m/s2]

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

i. What is the acceleration of Y
the car in initial 2 seconds.
70

[Ans: 20 m/s2] 60

ii. What is the acceleration of velocity (m/s) 50
the car when it travels from
B to C? Why? [Ans: 0 m/s2] 40 B C

iii. What is the velocity of car at 30
point C and D.
[Ans: 40 m/s, 0 m/s] 20

iv. What is the retardation of 10
the car when it travels from
C to D. [Ans: 20 m/s2] D

0A 1 2 3 4 5 6 X

7 80

time (s)

f. A body of mass 20 kg is moving with a velocity of 90 km/h. Calculate the

momentum. [Ans: 500 kg m/s]

g. The mass of a car is 1200 kg. If the car is moving with the velocity of 30 m/s, how
much force should be applied to stop the car in 20 seconds? [Ans: 1800 N]

h. A bus of 900 kg is moving with the velocity 60km/h. If it is stopped at a distance
of 50m by applying brakes, calculate the force required to stop the bus.
[Ans: 2500 N]

i. A truck is moving with the velocity of 45 km/h. The driver applied the brakes

and stopped the truck within 6 seconds. Calculate the retardation and distance

covered by the truck to come to the rest. [Ans: 2.08 m/s², 112.44 m]

44 GREEN Science (Physics) Book-9

Grid-based Exercise 2

Group ‘A’ (Knowledge Type Questions) (1 Mark Each)

1. What is force? Write down its SI unit.

2. Define vector quantity with any two examples.

3. Define 1N force.

4. Which factor does the inertia of a body depend? Write.

5. What is the relation between the mass and inertia of a body?

6. What is retardation? In which condition is it possible?

7. What is displacement?

8. What is acceleration? Write down its unit in SI system.

9. “Every action has equal but opposite reaction.” Which law of Newton is stated by this
statement?

10. State Newton’s first law of motion.

11. State Newton’s second law of motion.

12. What is momentum? On which factors does it depend? Write.

13. What is unbalanced force ? Write with one example.

For Group ’B’ (Understanding Type Questions) (2 Marks Each)

14. The blades of a fan continue to move for a while even after the switch is turned off.
Why?

15. A coin, kept on a postcard on the glass, drops in the glass when the postcard is flipped
suddenly. Why ? Give reason.

16. Why do passengers fall forward when a moving bus is stopped suddenly? Give
reason.

17. Athletes run a long distance before taking a long jump. Give reason.

18. Write any two differences between velocity and acceleration.

19. A person gets less hurt when he jumps on a muddy floor than that on a hard cemented
floor. Give reason.

20. A boat moves backward when we come out of the boat. What is action and reaction
in this statement?

For Group ‘C’ (Application Type Questions) (3 Marks Each)

21. A vehicle is moving with the velocity of 25m/s. If the vehicle is stopped within 5
seconds by applying brakes, calculate the retardation. If the mass of the vehicle is
1000kg, how much force is to be applied to stop it?

GREEN Science (Physics) Book-9 45

22. Prove that: v = u + at

23. What is the relationship among initial velocity, distance covered, acceleration
produced and final velocity of a moving body? Give an example that describes
Newton’s first law of motion.

24. A motorcycle moves with the velocity of 10 m/s and covers a distance of 4 km before
coming to rest. Calculate the retardation and time taken by the motorcycle to cover
the distance.

25. Prove that: F = ma.

For Group ‘D’ (Higher Abilities Type Questions) (4 Marks Each)

26. A truck is moving with the velocity of 72 km/h. When the driver applies brakes, the
truck is stopped in 2 seconds. Calculate the distance covered and retardation of the
truck. If the mass of the truck is 5000 kg, calculate the force applied by the brakes to
stop the truck.

27. Thevelocity-timegraphofavehicleisgivenbelow. Y
Answer the following questions on the basis of
this graph. 30

i. What is the velocity of the vehicle at the points velocity 25
b, c and d?
20
ii. How long did the vehicle move with
uniform velocity? 15 b c

iii. What is the retardation of vehicle after c? 10

5a 30 40 50 60 d
0 20 X

70

second

28. Explain Newton’s third law of motion with an example.

29. Write one difference between action and reaction. A bus is moving with the velocity of
60 km/h. By seeing a baby 11m ahead the driver applied the brakes and the retardation
produced is 13.88m/s2. Calculate the distance covered by the bus and time taken to
stop the bus.

46 GREEN Science (Physics) Book-9

UNIT Machine

3

Weighting Distribution Theory : 5 Practical: 2

Before You Begin

We feel very difficult to lift a large stone. But it can be lifted easily
by using a crow-bar. Similarly, we feel difficult to lift water from the
well. This work can be done easily by using a pulley. We use different
types of devices to make our work easy, fast and convenient. These
devices are called machines. The structure and working mechanism
of machines may be simple or complex. Crow-bar, pulley, scissors,
pliers, knife, windlass, screw, axe, etc. are some examples of simple
machines. Similarly, bicycle, motorcycle, sewing machine, printing
press, aeroplane, etc. are the examples of complex machines. A simple
machine is a device having simple structure which is used to make our
work easier, faster and to apply force in a convenient direction. In this
unit, we will study different types of simple machines, mechanical
advantage, velocity ratio, efficiency and moment in detail. Similarly,
we will solve simple numerical problems related to simple machines.

Learning Objectives Syllabus

After completing the study of this unit, students will be able to: • Introduction to simple
machine
i. introduce simple machines with examples.
• Mechanical advantage (MA)
ii. ii. describe different types of simple machines • Velocity ratio (VR)
(lever, pulley, inclined plane, wheel and axle). • Efficiency (h)
• Lever
iii. iii. define MA, VR and efficiency related to different • Pulley, Inclined plane
simple machines. • Wheel and axle
• Moment
iv. iv. solve the numerical problems related to simple • Law of moment
machines.

v. v. describe the moment in lever with a labelled
figure.

• Simple numerical problems

Glossary: A dictionary of scientific/technical terms

load : the force applied by a machine on a body
effort : the force applied to the machine to do work
mechanical advantage : the ratio of load to the effort
velocity ratio : the ratio of load to the effort
efficiency : the percentage ratio of output work to input work
moment : turning effect produced by force

GREEN Science (Physics) Book-9 47

Simple Machine

Scissors, crow-bar, beam balance, knife, axe, screw driver, forceps, etc. are the devices that
we use in our daily life. These devices have simple structure and they make our work easy
and fast. These devices are called simple machines. A simple machine is a mechanical
device which is simple in structure and makes our work easier and faster. Scissors, knife,
door knob, beam balance, fire tongs, screw, axe, wheel-barrow and crow bar are some
examples of simple machines that we use in our daily life. These machines help us to work
more efficiently, travel faster and perform certain task more accurately. Simple machines
can be operated manually. We do not need cell, diesel and petrol to operate them.

Fig.

3.1 Scissors Knife Screw driver
Wheel barrow

Simple machines are very useful to us. The major advantages of simple machines are as
follows:

1. Simple machines help to multiply the effort applied.

2. They help to apply force in convenient direction by changing the direction of force
applied.

3. They help to increase the speed of work.

4. They help to do the work safely and easily.

Terminology Related to Simple Machines

1. Effort

Effort is the force applied to a machine to do work. Its SI unit is newton (N). Without
effort, simple machines cannot be operated.

2. Load

Load is the force applied by the machine on the body on which work is done. Its SI unit is
newton (N). Load is the effect of effort applied on a machine.

3. Mechanical advantage

By using a simple machine, a heavy load can be lifted by applying less effort. It makes
our work easier. Mathematically, it is called mechanical advantage. The ratio of the load
to the effort applied is called mechanical advantage. It is denoted by MA. It is affected
by friction and weight of a machine.

Mechanical advantage (MA) = Load (L)
Effort (E)

48 GREEN Science (Physics) Book-9

Mechanical advantage (MA) has no unit as it is the ratio of two forces. The MA of a simple
machine is 2 means that an effort applied on the machine can lift two times heavier load.

4. Velocity ratio

The ratio of the distance travelled by effort to the distance travelled by load is called
velocity ratio. It is denoted by VR. It has no unit as it is the ratio of two distances.
Velocity Ratio (VR) = Distance travelled by effort = Effort arm

Distance travelled by load Load arm

\ VR = Effort arm
Load arm

The velocity ratio of a simple machine is 3 means that the load moves three times less the
effort. The VR of a machine is more than MA because VR is not affected by friction.

Differences between Mechanical advantage (MA) and Velocity ratio (VR)

Mechanical advantage (MA) Velocity ratio (VR)

1. It is the ratio of load to the effort 1. It is the ratio of effort distance to the

applied. load distance.

2. It is affected by friction. 2. It is not affected by friction.

5. Efficiency

The efficiency of a machine is defined as the percentage ratio of output work to input
work. It is expressed in percentage and denoted by letter eta (h).

Efficiency (h) = Output work × 100%
Input work

The work done by a machine is called output work. It is the product of load and distance
travelled by load. Similarly, the work done on a machine is called input work. It is the
product of effort and the distance travelled by effort.

In short, Output work = Load × distance travelled by load

Input work = Effort × distance travelled by effort

Relation among MA, VR and h of a machine

We know,
Efficiency (h) = Output work × 100%

Input work

= Load × load distance × 100%
Effort × effort distance

GREEN Science (Physics) Book-9 49

Load

= Effort × 100%

Effort distance

Load distance

= MA × 100%
VR

\ h = MA × 100%
VR

Efficiency of a machine can also be defined as the percentage ratio of mechanical advantage
(MA) and velocity ratio (VR) of a machine. It has no unit as it is the ratio of two similar
physical quantities, i.e. work done. The efficiency of a practical machine is always less
than 100%.

Perfect machine or Ideal machine

The machine in which the output work Do You Know
is equal to the input work is called perfect
machine or ideal machine. It is the machine The efficiency of a machine is 90% means
without friction. The efficiency of an ideal that 90% of the input work is converted
machine is 100%. However, in practice, no into useful output work and 10% of the
machine is 100% efficient. The output work input work is wasted to overcome the
is always less than input work because: friction and to move the parts of the
machine.
i. a part of input work is wasted in
overcoming friction and

ii. a part of input work is wasted in moving the parts of the machine.

Therefore, the efficiency of a practical machine is always less than 100%.

Differences between Practical machine and Perfect (Ideal) machine

Practical machine Perfect (Ideal) machine

1. Its efficiency is always less than 100%. 1. Its efficiency is 100%.

2. In this machine, output work is less 2. In this machine, output work is equal

than input work. to input work.

3. In this machine, MA is less than VR. 3. In this machine, MA is equal to VR.

50 GREEN Science (Physics) Book-9