Modern Concept Science and Technology 9

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

MODERN CONCEPT

SCIENCE

9

Authors

Chinta Mani Panthee

M.Sc., B.Ed., Ph.D. Scholar

Janak Raj Pant Kamal Neupane

M.Sc., B.Ed. M.Sc.

Nova Publication (Pvt) Ltd.

Satungal, Kathmandu, Nepal

Tel: 0977-1-4230545

MODERN CONCEPT

SCIENCE

9

Publisher & Distributor

Nova Publication (Pvt) Ltd.
Satungal, Kathmandu, Nepal

Tel: 0977-1-4230545

Author Chinta Mani Panthee
Kamal Neupane
Janak Raj Pant


Editor Romharsh Panthi


Edition First, 2075
Revised, 2076


Copyright Chinta Mani Panthee


Computer Layout
Sanjay Suwal, #9843159467

Printed in Nepal

Science is a systematic study of the phenomena occurring in the world. Development of Science and Teaching is a great
achievement of the 21st century. So, understanding the facts, concepts, laws and principles of science is very essential rather
than rote-learning. Teaching inside a classroom in a formative assessment-oriented way is not a goal of teaching-learning
activities. The effective teaching-learning activities help students to achieve the goals of life by gaining knowledge, skills
and values of life. Therefore, various teaching learning activities can be adopted to science according to the nature of the
branch, area, topic and sub-topics. For effective teaching learning process teachers are expected to emphasize the use of
various teaching learning tools, technique and materials. Teachers are also expected to use the local teaching learning
materials as far as possible. To achieve the goal of teaching learning-process, we can adopt various methods according to
situation, place and interest of the students.

If a teacher flies, then the students run.
If a teacher runs, then the students walk.
If a teacher walks, then the students sit.
If a teacher sits, then the students sleep.

Facilitating Learning
Facilitating learning includes the teaching learning processes which are easier, faster and sustainable. Teachers need to
facilitate true learning experience by using effective process of teaching-learning activities. The teaching-learning facilitation
process includes different methods. Some of them are given below.

i. Lecture method: Oral presentations to a large group of passive students contribute very little to real learning. In
most of the cases of group teaching, lecturing skills and experience of the teachers do not correlate students’ grades.
Despite the limitations of the lecture method, it is an alternative method in a situation with limited resources.

ii. Discussion method: The level of students’ participation in learning activities is expected more in a discussion
method. It can be:
a. Teacher- centered: Here, students answer the teacher's questions.
b. Student-centered: In this method, students address to each other, and the teacher mainly guides the
discussion towards the important points.

iii. Demonstration method: It is an effective way to illustrate concepts in the class. Mostly, the use of everyday
objects for the demonstration of scientific phenomena is more effective. Students' interest is increased if they are
asked to make predictions about the possible outcomes. In this method, the teacher’s careful attention to engage
all students is mandatory. Otherwise, it may result in a passive learning.

iv. Question-answer method: Questioning is an old strategy. The steps of this method are:
a. Prepare questions and arrange them in a logical sequence to increase the curiosity of the students.
b. Ask new questions by linking them with the learners' response.

v. Field Study: Teaching various natural phenomena in a scientific way becomes more effective when students learn
by going on a real field visit. Field visits to botanical gardens, research centers, industries, zoo, etc. are important
in the sense of real learning through experience.

vi. Experimental method: Teaching science without an experimental method is not an effective teaching-learning
activity. Experimentation is essential for scientific knowledge and understanding. The following experiments are
incorporated in the course of study of class 9 compulsory science.

a. Physics Experiments:

Exp. Experiments Exp. Experiments
No. No.

1. To measure the length of the object, mass of the 2. To demonstrate the inertia of rest and inertia of

object and time interval. motion in an object.

3. To illustrate the newton’s laws of motion. 4. To demonstrate the law of moment.

5. To show the refraction of light through the glass 6. To demonstrate the types of waves and

slab experimentally. propagation of sound waves.

7. To verify Ohm’s law in the laboratory. 8. To calculate the power of a person in a
laboratory.

9. To perform the comparative study of 10. To demonstrate magnetic field and magnetic

conductivity of different substances. lines of forces.

b. Chemistry Experiments:

Exp. Experiments Exp. Experiments
No. No.

1. To draw the chart of valency and electronic 2. To demonstrate the flow of electricity in solution
configuration of different elements. due to ionization of electrolytes.

3. To study the Unsaturated, Saturated and 4. To study the variation of solubility of the
Supersaturated solution in the laboratory. substance with temperature.

To study the process of crystallization

5. and obtain the crystals of copper sulphate 6. To prepare hydrogen gas in the laboratory

(CuSO4).

7. To prepare oxygen gas in the laboratory. 8. To prepare nitrogen gas in the laboratory.

9. To test the properties of metals. 10. To demonstrate the methods of removing
temporary hardness of water.

11. To demonstrate the methods of removing
permanent hardness of water.

c. Biology Experiments:

Exp. Experiments Exp. Experiments
No. No.

1. To observe the physical structure of algae and draw 2. To draw the diagrams of invertebrates.
its diagram.

3. To draw the diagram to show the life cycle of 4. To enlist the advantages of plants and animals to
mosquito. human beings and also enlist the adverse effects
of human activities upon the environment.

5. To make a temporary slide of animal cell and 6. To draw the various parts of human skeletal
plant cell and also draw the diagrams. system.

7. To enlist human sense organs along with their 8. To draw a well labelled diagram of human
function in a chart. digestive system and enlist function of each part
in a table.

9. To draw a well labelled diagram of respiratory 10. To enlist the dependence of human beings upon
system or excretory system and enlist functions plants.
of each part in a table.

11. To show the interrelationship between plants
and animals.

d. Geology and Astronomy Experiments:

Exp. Experiments Exp. Experiments
No. No.
To demonstrate solar eclipse and lunar eclipse
1. To demonstrate umbra and penumbra shadow 2. with the help of model then draw the diagram.
and draw the diagram.

vii. Mini project method: Knowledge and skill gained through practical work and project work are more sustainable.
It outlines what our students need to know in this era of science and technology. It is an educational approach in
teaching by an intellectual effort of students or students and teacher together.

Project Based Learning (PBL): It is an authentic learning activity that fosters students' interest and motivation. It
provides skill as well as contents to the students in 21st century. So, we request teachers to give a chapter-wise or
term-wise project work for effective science teaching-learning activities.

viii. Problem solving method: It is a student-centered strategy. It requires students to become active participants in
the learning process. In this method, students are presented with problems, which require them to find scientific
solutions.

1. A Course Syllabus Plan:

Teaching in an organized way results in real learning outcomes. Course content is a matter of great concern. A syllabus
includes the organization of topics into an outline of the course of study, examinations, and grading schemes.

i. Course of Study:

S.N. Estimated Teaching Periods S.N. Estimated Teaching Periods
Branch Biology Branch
Chapters Theory Practical Chapters Theory Practical

1. Measurement 3 1 16. Classification of plants 7 3
and animals
2. Force 5 1 17. Adaptation of 5 1
2 18 organisms 13 4
3. Simple machines 5 System 2 o
Physics 2 19. 4 0
4. Work, energy and 8 Sense organs
power 1 20 8 2
2 Evolution
5. Light 3 2 21 41 11
Nature and 4 1
6. Sound 8 10 environment 4 0
2 22. 4 1
7. Current electricity 10 0 23. Total 12 2
and magnetism 2 24.
3 Natural hazards
Total 42 1
Greenhouse
8. Classification of 9 0 Geology & The earth in the
elements 2 Astronomy universe
9. Chemical reactions 2 0 Total
11
10. Solubility 5

11. Some gasesChemistry 5

12. Metals 4

13. Carbon and its 6
compounds
14. Water 4

15. Chemical fertilizer 6
used in agriculture

Total 41

ii. Examination: The examination mechanism is equally important along with the course of study.

a. Theoretical Test: Weighting of marks assigned to the theoretical test is 75 marks. It is divided into four
branches of class 10 science. They are as follows:

S.N. Branches Weighting (in %) Weighting (in marks)
1. Physics 30.67 23
2. Chemistry 29.33 22
3. Biology 30.67 23
4. Geology and Astronomy 9.33 7
Total 100 75

b. Practical Test: Weighting of marks assigned to the practical test is 25 marks. The criteria and the
corresponding marking scheme are as follows:

S.N. Criteria Weighting (in marks)
1. Drawings/Labellings/ Explaining characteristics 5
2. Record of practical work 5
3. Model designing/ materials construction and their uses 5
4. Mini project work 6
5. Viva voce 4
Total 25

iii. Grading: In this system, alphabets A, B, C, D and E are used in place of percentage to grade the performance
of students in their examination. CDC, Nepal has introduced nine grades to show the performance of students.

Percentage obtained Grade Grade Description Grade Point
90 % - above 90% A+ Outstanding 4.0
80 % - less than 90 % A Excellent 3.6
70 % - less than 80% B+ Very Good 3.2
60 % - less than 70 % B Good 2.8
50 % - less than 60 % C+ Above Average 2.4
40 % - less than 50 % C Average 2.0
30 % - less than 40 % D+ Below Average 1.6
20 % - less than 30 % D Insufficient 1.2
Less than 20 % E Very Insufficient 0.8

a. Grade Point (GP) Calculation: For every grade, there is a specific grade point (GP) associated with
it. Each grade point is the upper limit point within its class. For example, if anyone gets 90 marks and
above in any individual subject then he/she gets an A+ grade in that subject with the grade point 4.0.

b. Grade Point Average (GPA) Calculation: For this, the total GP of a student is divided by the total
number of subjects he/she appeared.

2. Guidelines to make questions papers:

Area Knowledge Understanding Application Higher Total Total
based based questions based Ability questions marks
Physics based
Chemistry questions questions questions 12 23
Biology 11 22
Geology and Astronomy 54 2 1 12 23
Total 44 2 37
54 2 1 38 75
11 0
15 13 6 1

1

4

3. Guidelines to select questions:

There are a total of four areas, from where we need to select questions. While selecting questions, we consider the
following action verbs and topics.

Area Useful verbs Sample questions
Knowledge
State, name, list, write, what, definition, What is….?, How many……?, Who…?, List
Understanding
data, units, full forms, classification, the number of………..,State...?, Define.... , etc.

examples, labeling, etc. Write full form of......, Label the pars of......,Give

any two examples of....

Differentiate, Distinguish, Similarities, Differentiate between…. and …., Write

Why, How, Explain, Parts of activity, similarities......, Write down characteristics......,

Justify, compare, Short note, etc. Give reason...... etc.

Uses, Application, Apply, Generalize, Solve the given numerical problems. Complete

Application Solve, Show, Use, Illustrate, Complete, the given chemical equations, Write down the
Higher Ability
Examine: Construct, Draw, Relate, uses of, etc.

Transfer, etc.

Derive, Verify, Argue, Discuss, Explain, Derive the formula……. , Explain an

Formulate, Criticize, Evaluate, Choose, experiment……, Analyse the....Formulate

Analysis, Determine, etc. the.....

4. Use of Technology in the Contemporary Teaching Strategy
The 21st century science teachers are concerned about preparing today's children for tomorrow's world. A major challenge
for the teachers is to meet the target of the 21st century learning outcomes. Teachers can use technology in the classroom to
exploit the learning of their students. It develops the interest of students in new theories and inventions in the field of science.

i. ICT Guideline:
Audio-video classes are more effective over lecturing methods. The use of smart boards in classrooms,
teaching softwares online classes, are the practices to introduce technology in teaching. A projector screen,
computer, and sound system are required to use technology in a classroom.

ii. Use of power point slides;
Teachers can prepare Microsoft Power Point slides or directly download from different sites. Some web links
to search: www.slideshare.net , www.powershow.com, etc.

iii. Use of discs:
Playing course-related discs (DVDs) can help students in learning. Such discs are available in the market.

iv. Use of videos or documentaries:
Google search can give us links for so many videos like www.sciencechannel.com . Similarly, free download
of videos/ documentaries is possible from www.youtube.com

5. Way to proceed the unit from this book
The first page of each unit drives the whole chapter.

i. The course of study issued by CDC and its learning objectives are given in the first page to keep the teachers
and students through their paces.

ii. The terms and terminologies on the same page are from screening of the chapter. It helps to understand the
whole unit. Teachers are expected to explain the difficulties of the students.

iii. Teachers can make students follow the highlighted definitions, catchy memory plus box and bubble box on
the pages inside of a chapter for a quick look on important points to be remembered.

iv. Facts with reasons are given along with the sub-topic to understand the scientific concepts.

v. Before exercise problems, a practice of different level of questions (knowledge, understanding, application,
and higher ability) with their answer as answer writing skill is provided. After this, students are allowed to
do exercise from step 1 to step 4.

Physics Table of Contents 1-11
12-43
Chemistry 1. Measurement 44-70
2. Force 71-91
Biology 3. Simple Machines 92-112
4. Work, Energy and Power 113-136
Geology & 5. Light 137-160
Astronomy 6. Sound 161-183
7. Current, Electricity and Magnetisms 184-194
8. Classification of Elements 195-208
9. Chemical Reaction 209-228
10. Solubility 229-240
11. Some Gases 241-251
12. Metals 252-260
13. Carbon and its Compounds 260-269
14. Water 270-304
15. Chemical Fertilizers used in Agriculture 305-324
16. Classification of Plants and Animals 325-350
17. Adaptation of Organisms 351-364
18. System 365-379
19. Sense Organs 380-395
20. Evolution 396-406
21. Nature and Environment 407-415
22. Natural Hazards 416-428
23. Greenhouse
24. The Earth in the Space

UNIT Estimated teaching periods Theory Practical
3 1
1
Measurement

Syllabus issued by CDC Kelvin

 Introduction to measurement
 Types of units (fundamental units and derived units)
 SI units

LEARNING OBJECTIVES

At the end of this unit, students will be able to:
 define fundamental units and derived units and describe the relations between them.
 differentiate between the fundamental physical quantities and the derived physical quantities.
 measure the length, mass and time.

Key terms and terminologies of the unit

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

2. Measurement: Measurement is the comparison of an unknown physical quantity with a
known standard quantity of the same kind.

3. Unit: The standard known quantity which is used to measure the unknown quantity
of the same kind is called unit.

4. CGS System: The system of measurement in which length is measured in centimeter (cm),
mass is measured in gram (g) and time is measured in second (s) is called
CGS system of measurement.

5. FPS System: The system of measurement in which length is measured in foot, mass is
measured in pound and time is measured in second is called FPS system of
measurement.

6. MKS System: The system of measurement in which length is measured in metre (m), mass
is measured in kilogram (kg) and time is measured in second (s) is called
MKS system of measurement.

7. SI units: The General Conference of Weights and Measures held in Paris, France,
in 1960 introduced a new system of units known as international system of
units (SI units). It is accepted all over the world.

8. Fundamental physical quantities: Those physical quantities which are independent of each other are called
fundamental physical quantities.

9. Derived physical quantities: Those physical quantities which are derived from the fundamental physical
quantities are called derived physical quantities.

10. Fundamental units: Those units which are independent of each other are called fundamental
units. There are seven fundamental units of seven fundamental quantities.

11. Length: The distance between any two points is called length.

Modern Concept Science - 9 1

12. One metre: The distance between two parallel gold lines on a platinum-iridium rod preserved at 00C and

standard atmospheric pressure and kept in the international bureau of weight and measures at

Sevres, near Paris, France is called one metre.

13. Mass: The total amount of matter contained in a body is called its mass.

14. One kilogram: The standard one kilogram is the mass of a cylinder with height equal to its diameter which is

made from platinum-iridium alloy and kept in the International Bureau of Weight and Measures

at Sevres in Paris.

15. Time: The duration between any two events is called time.

16. One second: One second is a time which is equal to 1/86400 part of a mean solar day.

17. Derived units: Those units which are formed by the combination of two or more fundamental units are called

derived units. Exmples: m/s, m/s2, Newton (N), Pascal (Pa), etc.

Introduction Memory Tips

Measurement is an essential process for the accurate A measurement leads us from an
description of various quantities. For example, one should unknown to a known situation.
know the measurement of the quantity of matter in a body
to describe its exact mass. In our daily life, measurement of Memory Tips
distance, time and mass is necessary. These measurable
quantities are called physical quantities. Thus, the quantities Nepal Bureau of Standards and
which can be measured by using different kinds of physical Metrology (NBSM) at Balaju,
devices are called physical quantities. Mass, length, time, Kathmandu is the National
volume, force, density, temperature, work, energy, power, Standards Body of Nepal.
speed, etc. are some examples of physical quantities.

The process of measurement is basically a comparison
process. In order to measure a physical quantity, we assume
a certain magnitude of the quantity as a standard called
unit. Thus, measurement is the comparison of an unknown
physical quantity with a known standard quantity of the
same kind.

Unit Measuring length Weighing

The standard known quantity which is used to measure the unknown quantity of the same
kind is called unit. The unit is a fixed quantity. It is used to measure other quantities of the
same kind. For example, one unit of length is assumed as the distance between two parallel
gold lines on a platinum-iridium rod which is preserved at 0°C and standard atmospheric
pressure. It is kept in the international bureau of weight and measures at Sevres, near Paris,
France.

Characteristics of unit

i) Suitable size : A unit of measurement should be neither too large nor too small in
comparison to the quantity to be measured. It should be of a suitable size.

ii) Well-defined : Unit should be accurately defined.
iii) Accessibility : It should be easily available.

2 Measurement

iv) Reproducibility : Standard unit is defined at a particular place. It should be easily
reproducible at all the places.

v) Invariability : Unit should be invariable. It should not change with time, place and

physical conditions like temperature and pressure. For example, one standard kilogram

and one standard metre are kept at fixed temperature i.e. 0°C.

Selection of units Memory Tips

International acceptance is the first essential criteria to select Physical Quantity = Numerical
a unit. For this purpose an international body of scientists value × Unit
named "General Conference on Weights and Measures" For example, in 5 kg, the numerical
was set-up. It has the authority to decide the units by value is 5 and unit is kg.
international agreement. This body holds its meetings and
selects the units.

Systems of units Memory Tips

i) CGS System : The system of measurement in which CGS system is also known as French
length is measured in centimeter (cm), mass is system of units.
measured in gram (g) and time is measured in second
(s) is called CGS system of measurement. Memory Tips

ii) FPS System : The system of measurement in which FPS system is also known as the
length is measured in foot (ft), mass is measured in British system of units.
pound (lb) and time is measured in second (s) is called
FPS system of measurement.

iii) MKS System : The system of measurement in which length is measured in metre (m),
mass is measured in kilogram (kg) and time is measured in second (s) is called MKS
system of measurement. It is also known as metric system of measurement.

FACT WITH REASON

Why is MKS system also called metric system of measurement?

MKS system is also called metric system of measurement because it is decimal-based system. It can be
expressed in the multiples of ten.

iv) International system of units (SI units) : The Memory Tips
General Conference of Weights and Measures held
in Paris, France in 1960 introduced a new system of The system of measurement
units known as 'Le Systeme Internationale d' Unites' which is derived from the 12th
i.e. 'international system of units' (SI units). It is the General Conference of Weights and
extended version of MKS system. Measures held in Paris, France in
1960 and accepted all over the world
Advantages of SI units is called SI system of measurement.

i) International acceptance : SI units bring uniformity in measurement throughout the
world. So, it is accepted throughout the world.

Modern Concept Science - 9 3

ii) SI units is the coherent system of units : In SI units, derived units can be obtained

from fundamental units. Memory Tips

iii) SI units is the rational system of
units : There is only one unit for a S.N. System of units Unit of length Unit of mass Unit of time
physical quantity in SI units. For 1. FPS foot (ft) pound (lb) second (s)

example, joule (J) is the SI unit for all 2. CGS centimetre (cm) gram (g) second (s)

types of energies like heat, light, 3. MKS metre (m) kilogram (kg) second (s)
electrical, etc.

FACT WITH REASON

Why is SI units of units necessary?
When we use different units of measurement in different countries, it makes difficulties in international
trade and business. It also creates difficulties in understanding the result of researches. So, SI units is

necessary in measurement.

SI units is called an extended version of MKS system, why?
In SI units, the unit for mass, length and time are same as that of MKS system. Along with these three
fundamental units, there are four new fundamental units introduced in SI units. So, SI units is also called

an extended version of MKS system.

Mass of a body is 7 kilogram. What does it mean?
Mass of a body is 7 kilogram. It means that the mass of the body is 7 times the mass of the standard

kilogram which is kept in the office of international bureau of Weights and Measures in France.

Length of a water pipe is 4 metre. What does it mean?
The length of a water pipe is 4 metre. It means that the length of the pipe is 4 times longer than the standard
metre which is kept in the office of international bureau of Weights and Measures in France.

Classification of Physical Quantities and Units

In physics, there are a number of physical quantities to be measured. It is difficult to define a
new unit for each of them as well as to remember a large number of new units. Most of the
physical quantities are inter-related. For example, velocity is expressed as displacement upon
time. So the unit of velocity is expressed in terms of unit of displacement and time. But all the
physical quantities are not independent. Some are independent and others are dependent
(derived). On the basis of this fact, the physical quantities are classified as:

A) Fundamental physical quantities Memory Tips
B) Derived physical quantities
A) Fundamental physical quantities 1 pound = 0.454 kg

Those physical quantities which are independent of each other are called fundamental
physical quantities. Length, mass, time, temperature, electric current, amount of substance and
luminous intensity are the seven fundamental physical quantities. Other physical quantities
can be obtained from them.

4 Measurement

B) Derived physical quantities

Those physical quantities which are derived from the fundamental physical quantities are
called derived physical quantities. For example: area, volume, velocity, force, speed, work,
power, pressure, etc.

i) Area is expressed as the product of length and breadth i.e. Area = length × breadth

ii) Volume is expressed as the product of length, breadth and height i.e.

Volume = length × breadth × height

iii) Density is expressed as mass upon volume i.e. Density = mass , etc.
volume
FACT WITH REASON

Velocity is a derived physical quantity. Why?

Here, Velocity = displacement = length
time taken time taken

Velocity is formed by the combination of two fundamental quantities, i.e. length and time. So, it is a derived

physical quantity.

In order to decide units, neither it is convenient nor necessary to select units independently
for all physical quantities. Some units of physical quantities are selected randomly, while the
units for other physical quantities are derived from those selected units. Therefore, the units
of the physical quantities are divided into two types. They are:

a) Fundamental units b) Derived units.
a) Fundamental units

Those units which are independent of each other are called fundamental units. For examples,
metre (m), kilogram (kg), second (s), kelvin (K), etc.There are seven fundamental physical
quantities. To measure these seven fundamental physical quantities, there are seven
fundamental units. They are metre (m), kilogram (kg), second (s), kelvin (K), ampere (A),
candela (Cd) and mole (mol.).

In SI System, the seven fundamental physical quantities and their units are as follow:

S.N Fundamental Quantity SI units SI Symbol
1. Mass kilogram kg
2. Length metre m
3. Time second s
4. Temperature kelvin K
5. Electric current ampere A
6. Amount of substance mole mol.
7. Luminous intensity candela cd

SI units also includes two supplementary units. These are as follows:

S. N. Fundamental Quantities Units (SI) Symbol
1. Angle Radian rad
2. Solid angle Steradian sr

Modern Concept Science - 9 5

i) Measurement of length Memory Tips

The distance between any two points is called length.

Its SI unit is metre (m). It is also measured in centimetre One standard metre is the length
(cm), kilometre (km), etc. The distance between two
parallel gold lines on a platinum-iridium rod preserved of the path travelled by light in
at 0°C and standard atmospheric pressure and kept
in the international bureau of weight and measures at vacuum during a time interval of

1 of a second.
299792458

Sevres, near Paris, France is called one metre.

Scale Measuring tape

Multiples and sub-multiples of metre Some smaller units of length

10 millimetre (mm) = 1 centimetre 1 Centimetre (cm) = 10–2 m

10 centimetre (cm) = 1 decimetre 1 Millimetre (mm) = 10–3 m

10 decimetre (dm) = 1 metre (m) 1 Micron (µ) = 10–6 m

10 metre (m) = 1 decametre (dam) 1 Nanometre (nm) = 10–9 m

10 decametre (dam) = 1 hectometre (hm) 1 Angstrom (Å) = 10–10 m

10 hectometre (hm) = 1 kilometre (km) Memory Tips
Power of 10 Prefix Symbol Power of 10 Prefix Symbol

10–1 deci d 101 deca da 1. The mile is an English unit of length.
10–2 centi c
10–3 milli m 102 hecto h 1 mile = 1,609.344 m = 1.609344 km.
10–6 micro µ
10–9 nano n 103 kilo k 2. Astronomical unit (AU): It is
10–12 pico p equal to mean (average) distance
10–15 femto f 106 mega M
10–18 atto a between the earth and the sun.

109 giga G 1 AU = 1.496 × 1011m

1012 tera T 3. Light year (ly): The distance
travelled by light in one year in
1015 peta P vacuum is called light year.

1018 exa E 1 ly = 9.46 × 1015 m

ii) Measurement of mass

The total amount of matter contained in a body is called its Standard 1 kg mass
mass. Its SI unit is kilogram (kg). It is also measured in gram
(g), milligram (mg), etc. The mass of a body is measured by
using a beam balance or a pan balance. The standard kilogram
is the mass of a cylinder with height equal to its diameter
which is made from platinum-iridium alloy and kept in the

6 Measurement

International Bureau of Weight and Measures at Sevres in Paris. This cylinder is about
39 mm high. The mass of this cylinder is equal to the mass of one litre pure water at 4°C.
The accurate copies of one kilogram are prepared by comparing them with standard
kilogram.

Beam balance Digital balance Pan balance

Relation between multiples and submultiples of the kilogram

Submultiples of kilogram Multiples of kilogram
Decigram (dg) = 10-1 g 1 quintal = 100 kg
Centigram (cg) = 10-2 g 1 metric ton =1000 kg
Milligram (mg) = 10-3 g
Microgram (µg) = 10-6 g

iii) Measurement of Time

The duration between any two events is called time. The SI unit of time is second (s). It is also
measured in minute, hour, day, week, month, year, decade, century, millennium, etc. Clock

1 th

is used to measure time. One second is a time which is equal to as 86400 part of a mean solar
day. One second is also defined as the time taken by 9,192,631,770 cycles of radiations that
come from electrons moving between two energy levels of the Caesium -133 atom.

Mechanical watch Quartz watch Automatic watch

Derived units

There are many units which are expressed in terms of fundamental units. They are called
derived units. For example, m2, m3, m/s, N, Pa. Thus, those units which are formed by the
combination of two or more fundamental units are called derived units.

Modern Concept Science - 9 7

FACT WITH REASON

The SI unit of velocity is a derived unit. Why?

From the definition of velocity,

Velocity = displacement
time taken
Unit of velocity = unit of distance = m = m s –1
unit of time s
Here, the unit of velocity (m s-1) can be expressed in terms of metre (m) and second (s). So, it is a derived

unit.

Unit of force is a derived unit. Why?
From the definition of force,
Force = Mass × Acceleration
or, unit of force = unit of mass × unit of acceleration = kg × m = kg m s –2

s2
Here, the unit of force (N) can be expressed in terms of kilogram (kg), metre (m) and second (s). So, it is a

derived unit.

Unit of power is a derived unit. Why?

Power = work done = force × displacement = mass × acceleration × displacement
time time time
kg × m s–2 × m kg m2
Unit of power = s = s3 = kg m2 s –3

Thus, the SI unit of power is derived from three fundamental units, namely kilogram (kg), metre (m) and

second (s). So, it is a derived unit.

Some derived physical quantities with their units

SN. Physical Formulae SI units Symbols Fundamental
quantities length × breadth square meter units involved

1. Area m2 m×m

2. Volume length × breadth × height cubic meter m3 m×m×m

3. Density mass / volume kilogram per cubic meter kg/ m3 kg/(m×m×m)

4. Velocity displacement / time meter per second m/s m/s

5. Acceleration change in velocity / time meter per square second m/s2 m/(s×s)

6. Force mass × acceleration newton kgm/s2 , N kg m/(s×s)

7. Work/Energy force × displacement joule J kg×m×m/(s×s)

8. Power work / time joule per second or watt J/s or W kg×m×m/(s×s×s)

9. Pressure force/area newton per square metre or Nm-2or Pa kg/(m×s×s)
pascal

10. Momentum mass × velocity kilogram metre per second kg m/s kg×(m/s)

11. Frequency 1/time per second or Hz s-1 or Hz ¹/s

8 Measurement

Differences between Fundamental units and derived units

S.N. Fundamental units S.N. Derived units

1. Those units which are independent 1. Those units which are formed by the

of each other are called fundamental combination of two or more fundamental

units. 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 units, there are seven fundamental 3. In SI units, there are many derived units.

units. They are m, kg, s, K, A, cd and Examples : m2, m3, m/s, N, W, J, etc.

mol.

ANSWER WRITING SKILL

1. Define length and write its SI unit.

Ans: The distance between any two points is called length. The SI unit of length is metre (m).

2. What is the term used for “interval between any two events”? What is its SI unit?

Ans: Time is the term used for interval between any two events. The SI unit of time is second.

3. Where and when SI units was invented?

Ans: The SI units was invented in 1960 AD at Severs near Paris, France.

4. What does it mean by 5 m length?

Ans: 5 m length means the distance between any two points is five times of the standard one metre length
which is kept in the office of international bureau of weight and measures in France.

5. Mass is called a fundamental physical quantity, why?

Ans: Mass is called a fundamental physical quantity because it does not depend upon other physical
quantities to be expressed.

6. Velocity is called a derived physical quantity. Why?

Ans: We know that, velocity = displacement
time taken

Here, velocity is expressed with the help of two fundamental quantities i.e., displacement and time.

Therefore, velocity is a derived physical quantity.

7. Standard weights and scales in the market should be checked in every two years by the government
authorities. Why?

Ans: Standard weights and scales must be checked by the government authorities in every two years so that
business persons may not use fraud weights and measuring tools in the measurement. It also preserves
consumer’s right. After using for a long time, the measuring tools might have been eroded, and they
need to be replaced.

8. Differentiate between MKS system and the SI units.

S.N. MKS system S.N. SI units

1. MKS system is a metric system of 1. SI units is a revised and redefined extended

measurement. version of the MKS system.

2. It involves three fundamental quantities, i.e. 2. It involves seven fundamental quantities.
length, mass and time.

Modern Concept Science - 9 9

9. Distinguish between local units and standard units.

S.N. Local units S.N. Standard units

1. Local units are used in the limited area by a 1. Standard units are used by the people

fewer numbers of people. throughout the world.

2. Local units invite difficulties in international 2. Standard units make international trade

trade and business. and business easy and convenient.

10. Show that joule is a derived unit.

Ans: Joule is the SI unit of work.

So, work = force × distance = mass × acceleration × distance = kg × m/s2 × m

Here, we can see that joule is made up of three fundamental units. They are kilogram, metre and second.
Therefore, joule is a derived unit.

11. SI units of units is based on the MKS system of units. How?

Ans: In the MKS system, only three fundamental quantities, i.e. length, mass and time are considered. Whereas
in the SI units, all seven fundamental quantities, i.e. length, mass, time, temperature, luminous intensity,
current and amount of substances are considered. It shows that, SI units is the extended version of the
MKS system of units. So, SI units is based on the MKS system of units.

STEPS EXERCISE

STEP 1

1. Define:

a) Physical quantities b) Measurement
c) Unit d) CGS System
e) FPS System f) MKS System
g) SI units h) Fundamental physical quantities
i) Derived physical quantities j) Fundamental units
k) Length l) One metre

m) Mass n) One kilogram

o) Time p) One second

2. Write the SI units along with their symbols of the following physical quantities:
a) Luminous intensity b) Length c) Quantity of matter
d) Electric current e) Temperature f) Time

3. Write two multiples and two sub-multiples of the followings.

a) Length b) Mass c) Time

STEP 2

4. Show the fundamental units involved in following derived units.

a) Newton (N) b) Joule (J) c) Watt (W) d) Pascal (Pa)

10 Measurement

5. Length of a rope is 5 metre. What does it mean?

6. Differentiate Between:
a) Fundamental physical quantities and derived physical quantities
b) Fundamental units and derived units
c) MKS system of units and SI units

7. Give Reason:
a) SI units is an improved version of MKS system.
b) Why is SI units necessary?
c) Length is a fundamental quantity.
d) Mass of a body is 10 kg. What does it mean?
e) Volume is a derived quantity.
f) Kelvin (K) is a fundamental unit.
g) The measuring devices used in the market are monitored time and again by the
department of weight and measures in our country.

8. A cylindrical mass is preserved inside the glass chamber. Answer the following
questions with the help of the given figure.
a) How much is its mass?
b) How much is the diameter of the cylindrical mass?
c) From which matter is the cylindrical mass made up of?

STEP 3

9. Write down the characteristics of the SI units.
10. Write the advantages of SI units.

STEP 4

11. Discuss the role of globalization in the development of SI units.
12. Explain the role of standard units to bring uniformity in measurement.

PROJECT WORK

1. Visit a local market and observe the instruments used to measure mass, length, and
volume and note them on your exercise book.

2. Make a small survey in a limited area to know about the local units of measurement.
Visit different families in your locality. Ask the old family members about the system of
measurement used in their time and collect information in a table as:

Physical Instrument Local Unit Standard unit Relation between the
Quantity Used two units

Modern Concept Science - 9 11

UNIT Estimated teaching periods Theory Practical
5 1
2
Force

Syllabus issued by CDC Sir Isaac Newton

 Introduction to force
 Rest and motion
 Speed and velocity
 Uniform and non-uniform velocity
 Acceleration
 Equations of motion
 Inertia and its types
 Momentum
 Newton's laws of motion
 Balanced and unbalanced force

LEARNING OBJECTIVES

At the end of this unit, students will be able to:
 describe and demonstrate inertia, motion and force of a moving body and the body at rest.
 explain Newton's laws of motion and state their application.
 differentiate between balanced force and unbalanced force
 calculate the acceleration of a body in motion.
 derive equations of motion and solve the numerical problems related to these equations.

Key terms and terminologies of the unit

1. Force: Force is the push or pull which changes or tries to change the position (i.e. the state

of rest or uniform motion) of a body.

2. Balanced forces: The equal forces acting in the opposite direction, which do not change the state of rest

or uniform motion of an object are known as balanced forces.

3. Unbalanced forces: The unequal and opposite forces acting on a body, which change state of rest or

uniform motion of the body are called unbalanced forces.

4. Rest: A body is said to be at rest if it does not change its position with respect to a fixed point

called reference point in its surrounding.

5. 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 surrounding.

6. Reference point: A reference point is a point or object on the basis of which we study rest and motion.

7. Scalar quantities: Those physical quantities which have only magnitude are called scalars or scalar
quantities.

8. Vector quantities: Those physical quantities which have both magnitude as well as direction are called
vectors or vector quantities.

12 Force

9. Distance: The actual length of the path travelled (or covered) by a moving body,

irrespective of its direction is called the distance travelled by the body.

10. Displacement: The shortest distance between the initial point and the final point of a

moving body in a particular direction is called its displacement.

11. Speed: The distance travelled by a body per unit time is called speed.

12. Velocity: The distance travelled by a body per unit time in a particular direction is

called its velocity.

13. Uniform velocity: A body is said to have uniform velocity if it moves in a particular direction

and covers equal distance in an equal interval of time.

14. Non-uniform velocity: A body is said to have non-uniform velocity when it travels in a particular

direction and covers unequal distances in equal interval of time.

15. Acceleration: The rate of change in velocity of a moving body is called its acceleration.

16. Positive acceleration: The rate of increase in velocity is called positive acceleration.

17. Negative acceleration: The rate of decrease in velocity is called negative acceleration(retardation).

18. Distance-time graph: The graphical relationship between the distance travelled by a body and

the time taken is called the distance-time graph.

19. Velocity-time graph: The graphical relationship between the velocity of a moving body and the

time taken is called the velocity-time graph.

20. Equation of motion: The relationship between the initial velocity (u), final velocity (v), distance

travelled (s), acceleration (a) and time taken (t) is called the equation of

motion.

21. Inertia: The property of a body by virtue of which it resists any change in its state

of rest or uniform motion is called inertia.

22. Inertia of motion: The property of a body by virtue of which it resists any change in its state

of uniform motion is called inertia of motion.

23. Inertia of rest: The property of a body by virtue of which it resists any change in its state

of rest is called inertia of rest.

24. Inertia of direction: The inability of a body to change its state of uniform motion along a

straight line is called inertia of direction.

25. Momentum: The momentum of a body can be defined as the product of its mass and

velocity.

26. Newton's first law of motion: Newton's first law of motion states that "Everybody continues to be in

a state of rest or of uniform motion in a straight line unless an external

force is applied on it".

27. Newton's second law of motion: Newton's second law of motion states that "Acceleration produced on

a body is directly proportional to the force applied on it and inversely

proportional to its mass.”

28. One newton force: The force which produces 1 m/s2 acceleration on a body of mass 1 kg is

called 1 newton force.

29. Newton's third law of motion: Newton's third law of motion states that "For every action there is an

equal and opposite reaction".

Modern Concept Science - 9 13

Introduction

We perform various activities in our daily life. For example, pushing, pulling, lifting, walking,
pressing, opening, closing, kicking, beating and so on. All these activities are possible only
when we apply force. Thus, force is the push or pull which changes or tries to change the
position,(i.e. the state of rest or uniform motion) of a body." In this unit, we will discuss linear
motion of a body in terms of velocity, acceleration, etc. We will also discuss the equations of
motions and newton's laws of motion.
Units of Force
The SI unit of force is newton (N) and the CGS unit of force is dyne.
Relationship between newton and dyne
1 newton = 1 kg × 1m/s2

or, 1 netwon = 1000 g × 100 cm/s2

∴ 1 newton = 105 dynes

FACT WITH REASON

Why is force a vector quantity?
Force has both magnitude and direction. So, it is a vector quantity.

Effects of Force

Force can cause the following effects on a body.

i) Force can change the shape and size of the body.

ii) Force can change the state of rest and motion of the body.

iii) Force can change the speed of the body.

iv) Force can change the direction of the moving body.

Balanced and unbalanced forces Memory Tips
Balanced Forces
If a number of balanced forces act
The equal forces acting in the opposite direction, which do on a body at rest, the body continues
not change the state of rest or uniform motion of an object, to remain in its position of rest.
are known as balanced forces. In case of balanced forces, the Similarly, if a number of balanced
resultant of all the forces acting on a body is zero. Under forces act on a body in uniform
the action of the balanced forces, a body does not change its motion, the body continues to be in
position of rest or of the uniform motion. In such cases, the its state of uniform motion.
object is said to be in an equilibrium state. It appears in the
state of rest. For example:

a) If both the contestants in arm wrestling are equally strong and apply equal forces in
opposite direction then their arms stay in the same place. Figure (a) 

b) In a tug of war, if two teams have equal strength, the rope does not change its position.
The rope stays in the same place. Figure (b)

c) If a heavy box does not move when we push it, then the box is acted upon by a number
of balanced forces as,

14 Force

i) weight of the box is cancelled by the upward force (i.e. reaction) of the ground.
ii) the frictional force balances the pushing force. Figure (c)

a. Arm wrestling b. Tug of war c. Pushing a box

Unbalanced Forces Memory Tips
The unequal and opposite forces acting on a body, which

change the state of rest or the uniform motion of the body Unbalanced forces acting on a rest

are called unbalanced forces. In case of unbalanced forces, body can change the state of rest of

the resultant of all the forces acting on a body is not zero. the body. Similarly unbalanced forces

Unbalanced forces acting on a body can change the state of acting on a moving body can change

rest or the uniform motion of the body. It means that, the state of motion of the body.
unbalanced forces can move a stationary body or they can

stop a moving body. The body moves in the direction of the resultant unbalanced force. For

example,

a) In a tug of war, if two teams do not have equal 400 N 300 N

strength, or force, the rope changes its position.

It will move in the direction of greater force.

b) If a box moves when we push it, then the box
is acted upon by a number of unbalanced force. The pushing force is
grater than the frictional force. The unbalanced force moves the box
in the direction of greater force (i.e. pushing force)

Rest and Motion

Most of the things in our surrounding do not change their position with respect of the time
and surrounding. For example, tree, electric pole, house, school, mountain, etc. These things
are in the state of rest. Thus, a body is said to be at rest if it does not change its position with
respect to a fixed point called reference point in its surrounding. For example, a book on a
table does not change its position with respect to the table. So, the book is said to be in a state
of rest. Similarly, the bench, chairs, etc. of a classroom are also in the state of rest.

Animals, birds, human beings and other objects in our surrounding move from one place to
another. They are called bodies in motion. Thus, 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 surrounding. A reference
point is a point or object on the basis of which we study rest and motion.

FACT WITH REASON

Rest and motion are relative terms, why?

When we are on the seat of a moving bus, we are in motion with respect to the trees or buildings along the
side of the road. However, if we compare our position with respect to other passengers, we are at rest. Thus,
an object can be at rest with respect to one reference point while it can be in motion with respect to another
reference point at the same time. So, rest and motion are relative terms.

Modern Concept Science - 9 15

Scalar and vector quantities

In physics, we study a large number of physical quantities such as velocity, mass, weight,
force, work, energy, power, etc. All these physical quantities can be classified into two groups.
They are:

i) Scalar quantities (scalars)
ii) Vector quantities (vectors)
Scalar Quantities

Those physical quantities which have only magnitude are called scalars or scalar quantities.
Examples of scalar quantities are distance, speed, mass, time, pressure, work, energy, area,
volume, etc. A scalar quantity has only magnitude and no direction. They are represented
simply by letters like mass 'm', time 't', etc. Addition and subtraction of the scalars is done by
general algebraic rule. For example, sum of 50 kg and 60 kg is 110 kg.

Vector Quantities

Those physical quantities which have both magnitude as well as direction are called vectors or
vector quantities. Examples of vectors are displacement, velocity, acceleration, force, weight,
etc. A vector quantity requires both magnitude and direction for its complete description.
They are represented by letters with arrow head on them like force ' F ' acceleration 'a ', etc.
Addition and subtraction of vectors is done by the rules of vector algebra.

FACT WITH REASON

Mass, length, time, etc. are scalars but displacement, acceleration, etc. are vectors. Why?
Mass, length, time, etc. have only magnitude. They do not need direction to express. So, they are called scalars.
But displacement, acceleration, etc. have both magnitude and direction. So, they are called vectors.

Differences between vectors and scalars

S.N. Vectors S.N. Scalars

1. Those physical quantities which have 1. Those physical quantities which have

both magnitude as well as direction only magnitude are called scalars.

are called vectors.

2. Vectors are added by the rules of 2. Scalars are added by the rules of simple

vector algebra. algebra.

3. Vectors are represented by a letter 3. Scalars are represented simply by letters

with an arrow head like, force ' F ' like mass 'm', time 't', etc.
acceleration 'a ', etc.

4. The sum of vectors may be positive 4. The sum of scalars is always positive.

or zero or negative. Examples: force, Examples: distance, mass, speed, etc.

displacement, velocity, etc.

16 Force

Distance and Displacement

Distance

The actual length of the path travelled (or covered) by a moving body, irrespective of its

direction is called the distance travelled by the body. It is a scalar quantity. The SI unit of
B
distance is metre (m).

For example, when a bus moves 2 km from a point A to point B, 4 km 4 km
from a point B to point C and then 3 km from a point C to point D,
2 km
Then, the total length of the path covered by the bus = AB + BC + CD
A C 3 km D
Distance travelled by a body

= 2 km + 4 km + 3 km = 9 km

Displacement N C

The shortest distance between the initial point and the final point of a D5iskpmlacement 3 km
moving body in a particular direction is called its displacement. It is a 4 km
vector quantity. Its SI unit is metre (m). B

For example, when a bus moves 4 km from a point A to point B towards
east and 3 km from the point B to the point C due north,
then, the distance moved by the bus = AB + BC = 4 km + 3 km = 7 km A

But, the displacement of the bus, AC = √ AB2 + BC2

or, AC = √ 42 + 32 = √ 16 + 9 = √ 25 = 5 km

FACT WITH REASON

Displacement can be zero but distance is not zero, why?

If a body is revolving in a circular path, after one complete revolution, it reaches
to its original position. The distance travelled by the moving body is equal to the
circumference of the circular path. i.e. = 2πr , where r is the radius of the circular path.
But, the displacement is zero. So displacement can be zero but distance is not zero.

Differences between distance and displacement

S.N. Distance S.N. Displacement

1. The actual length of the path travelled 1. The shortest distance between the initial

(or covered) by a moving body, point and the final point of a moving

irrespective of its direction is called body in a particular direction is called its

the distance travelled by the body. displacement.

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

3. It is always positive. 3. It can be positive, zero or negative.

Speed and Velocity
Speed

Speed describes the rapidity of a body in motion at a particular moment. Whenever we try to
find out which of the two or more vehicles are moving faster, then we compare the distance

Modern Concept Science - 9 17

moved by them in a unit time. It is called speed. Thus, the distance travelled by a body per

unit time is called speed.

Speed = Distance travelled (s)
Time taken (t)

It is a scalar quantity. In SI units, the unit of speed is metre per second. It is written as m/s. In

CGS system, the unit of speed is centimetre per second. It is written as cm/s. The speed of the

fast moving bodies like cars, bus, etc. is expressed in kilometre per hour and is written as km/h.

FACT WITH REASON

Speed is a scalar quantity, why?
Speed has only magnitude but no direction. So, speed is a scalar quantity.

Velocity

Velocity is the physical quantity which has both direction of motion and the distance travelled

by it in given time. Thus, the distance travelled by a body per unit time in a particular direction

is called its velocity. If a body covers a distance of 's' in time 't' in a specific direction, then its

velocity 'v' is given by,

Velocity (v) = Distance travelled in a particular direction (s) = Displacement (s) = s
Time taken (t) Time (t) t

It is a vector quantity. The SI unit of velocity and speed is the same. In SI system, the unit of
velocity and speed is m/s.

FACT WITH REASON

Velocity is a vector quantity, why?
Velocity has both magnitude and direction. So, velocity is a vector quantity.

Differences between speed and velocity

S.N. Speed S.N. Velocity

The distance travelled by a body per The distance travelled by a body per

1. unit time is called speed. 1. unit time in a particular direction is

called its velocity.

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

3. It cannot be zero. 3. It can be zero.

Solved Numerical 2.1

A bus travels a distance of 30 km in 20 minutes towards the north. Calculate the velocity of
the bus.
Solution: Given,

Displacement (s) = 30 km = 30 × 1000 m [∵ 1 km = 1000 m]
= 30000 m

18 Force

Time taken (t) = 20 min. = 20 × 60 [∵ 1 min. = 60 seconds]

= 1200 s

Velocity (v) = ?

We know,

Velocity (v) = Displacement (s) = 30000 = 25 m/s
Time (t) 1200

∴ The velocity of the bus is 25 m/s.

Uniform velocity, non-uniform velocity and average velocity

Uniform velocity

A body is said to have uniform velocity if it moves in a particular direction and covers equal
distance in an equal interval of time. For example, a car moving along a straight road towards
east, covers a distance of 5 m. in every second. Here, the uniform velocity of the car is 5 m/s
in the east direction.

5m 5m 5m 5m 4s
0s 1s 2s 3s

Non-uniform velocity (Variable Velocity)

A body is said to have non-uniform velocity when it travels in a particular direction and

covers unequal distances in equal interval of time. For example, a body starts from a point

A and reaches to the points B, C, D and E, towards the east covering unequal distances in

equal interval of time as shown in the given figure. In this case, the body is moving with non-

uniform velocity.

AB CD E

3m 4m 2m 4m East
0s 2s 3s 4s
1s

FACT WITH REASON

Is it possible to have uniform speed but variable velocity?
Yes, when a car is moving in a circular track and covers the equal distances in equal interval of time then the
direction of the car changes continuously. In this case, the car has variable velocity but uniform speed.

Average velocity

If the velocity of a body in a particular direction changes continuously at a uniform rate, then

the arithmetic mean of the initial velocity and final velocity over a given period of time is

called average velocity.

AB CD E

3m 4m 2m 4m East
0s 2s 3s 4s
1s

Modern Concept Science - 9 19

Average velocity (Vav) = Initial velocity (u) + final velocity (v)
2

or, Average velocity (v) = Total displacement
Total time taken
In the given figure above,

Total displacement (s) = 3 m +4 m + 2 m + 4 m = 13 m

Total time (t) = 4 seconds

∴ The Average velocity = total displacement = 13 = 3.25 m/s in the east direction.
time taken 4
Acceleration

All the moving objects may not have a uniform velocity. For example, a bus starts from the

rest and after a certain time interval it attains a constant velocity. If a person comes on the road

in front of the bus then the driver applies brakes and the velocity gradually decreases. Finally,

the velocity of the bus becomes zero when it stops. Thus, the velocity of the body sometimes

increases and sometime decreases with respect to time. This change in velocity with respect

to time is called acceleration. The rate of change in velocity of a moving body is called its

acceleration.

Acceleration (a) = Final velocity (v) – initial velocity (u)
Time taken (t)

a = v – u
t

The SI unit of acceleration is metre per second square. It is written as m/s2. It is a vector quantity.

Meaning of Acceleration

An acceleration of 2 m/s2 means that the velocity increases by 2 m/s in every second.

FACT WITH REASON

The acceleration of a moving body with a uniform velocity is zero, why?

When a body is moving with a uniform velocity, the change in velocity (i.e. v – u) becomes zero. So, the
acceleration of a body moving with a uniform velocity is zero.

Solved Numerical 2.2

A car is moving with the velocity of 36 km/h speeds up to 72 km/h in 5 seconds. Calculate
its acceleration.

Solution: Given,

Initial velocity (u) = 36 km/h = 36 × 1000 = 10 m/s
60 × 60

Final velocity (v) = 76 km/h = 76 × 1000 = 20 m/s
60 × 60

Time taken (t) = 5 seconds

Now, acceleration is given by (a) = v – u = 20 – 10 = 10 = 2 m/s2
t 5 5

So, the acceleration of the car in 5 seconds is 2 m/s2.

20 Force

Positive acceleration

If the final velocity (v) of a moving body is greater than the initial velocity (u), i.e. v > u then,
it is called positive acceleration or acceleration.

Acceleration (a) = final velocity (v) – initial velocity (u) = positive quantity = positive quantity
time taken (t) time

The increase in velocity of a moving body causes positive acceleration. Thus, the rate of
increase in velocity is called positive acceleration. For example, a body falling toward the
earth has a positive acceleration.

FACT WITH REASON

Acceleration of a freely falling object on the surface of the moon is 1.67 m/s2. What does it mean?

Acceleration of a freely falling object on the surface of the moon is 1.67 m/s2. It means that the velocity of the
freely falling object on the surface of the moon increases by 1.67 m/s in every second.

Negative acceleration (Retardation)

If the final velocity (v) of a moving body is less than the initial velocity (u), i.e. v < u then, it is
called negative acceleration or retardation.

Acceleration (a) = final velocity (v) – initial velocity (u) = negative quantity = negative quantity
time taken (t) time

The decrease in velocity of a moving body causes negative acceleration. The rate of decrease
in velocity is called negative acceleration. Negative acceleration is also called retardation. For
example, a ball thrown upward from the earth's surface has a negative acceleration up to the
maximum height. A football rolling on a plane football ground also has a negative acceleration.

FACT WITH REASON

Acceleration of a ball thrown vertically upward from the earth's surface is - 9.8 m/s2 . What does it mean?

Acceleration of a ball thrown vertically upward from the earth's surface is - 9.8 m/s2. It means that its
velocity decreases by 9.8 m/s in every second.

Uniform acceleration
When a body travels in a straight line and its velocity changes by equal amounts in equal
interval of time, then it is said to have uniform acceleration. For example, a body falling freely
on the surface of the earth has uniform acceleration.

Non-uniform acceleration
When the velocity of a body changes by unequal amounts in the equal intervals of time, it is
said to have non-uniform acceleration. For example, when brakes are applied frequently on a
bus, it has non-uniform acceleration.

Graphical representation of the linear motion

The motion of a body can be described by using line graphs. In the line graphs, we can show
the dependence of distance, velocity, etc. upon time.

Modern Concept Science - 9 21

Distance-time graph

The graphical relationship between the distance travelled by a body and the time taken is
called the distance-time graph. In the distance-time graph, the distance travelled is plotted
along Y-axis and time taken is plotted along X-axis. The slope of the distance-time graph gives
the speed of a body.

Information from three different types of distance-time graphs

a) Body at rest : If the distance-time graph of a body is a straight line parallel to the X -
axis, then the body is at rest.(Figure- a)

b) Uniform speed : If the distance-time graph of a body is a straight line making an angle
with the X-axis, then its speed is uniform. The straight line may or may not pass through
the origin. (Figure-b)

c) Non-uniform speed : If the distance-time graph of a body is a curved line, then its
speed is non-uniform.(Figure- c)

YY Y
20 20
15 15 20
10 10 15
55 10
Distance (m) 5
Distance (m)
Distance (m)X X
01 2 3 4 5 X 01 2 3 4 5 01 2 3 4 5
Time (s) Time (s) Time (s)

a) Body at rest b) Uniform speed c) Non-uniform speed

FACT WITH REASON

Distance-time graph of a body is a straight line sloping upward. What does it mean?

If the distance-time graph of a body is a straight line making an angle with the X-axis, then it indicates
uniform speed. This is because there occurs change in distance with time.

Velocity- time graph

The graphical relationship between the velocity of a moving body and the time taken is called
the velocity-time graph. In velocity-time graph, the velocity of the moving body is plotted
along the Y-axis and the time taken is plotted along the X-axis. The slope of the velocity-time
graph of a moving body gives its acceleration. We get all information about the motion of an
object from the velocity-time graph.

Information from four different types velocity-time graphs

a) Uniform velocity : If the velocity-time graph of a body is a straight line parallel to the
time axis, then the body is moving with a uniform velocity. It is a condition of zero
acceleration. (Figure-a)

b) Uniform acceleration : If the velocity-time graph of a body is a straight line sloping
upward, it is a uniform acceleration. (Figure-b)

c) Uniform retardation : If the velocity-time graph of a body is a straight line sloping
downward then, it shows a uniform retardation. (Figure-c)

22 Force

d) Non-uniform acceleration : If the velocity-time graph of a body in motion is a curved
line, then it has non-uniform acceleration. (Figure-d)

YYY Y

25Velocity (m/s) X 25 X 25 X 25 X
20 Velocity (m/s)2020 20
15 Velocity (m/s)1515 15
10 Velocity (m/s)101010
5 5 5 5
234 5 234 5 234 5 234 5
01 Time (s) 01 Time (s) 01 Time (s) 01 Time (s)

a) Uniform b) Uniform accel- c) Uniform d) Non-uniform
velocity eration retardation acceleration

FACT WITH REASON

Velocity-time graph of a body is a straight line sloping upward. What does it mean?
If the velocity-time graph of a body is a straight line sloping upward, it indicates uniform acceleration. This
is because there is change in velocity with time.

Solved Numerical 2.3

Study the given velocity-time graph of a body and Velocity (m/s) 6 AB
answer the following questions. 4
2 D E C
i) Which type of motion is represented by the 4 10 16
segments OA, AB and BC? O
Time (s)
ii) Calculate the acceleration of the body.

iii) Calculate the retardation of the body.
Solution:

i) OA is a straight line graph between velocity and time. It is sloping upward from
O to A. Therefore, the graph OA represents uniform acceleration.

AB is a straight line graph between velocity and time, which is parallel to the time
axis. So, AB represents uniform velocity. So, there is no acceleration from A to B.

BC is a straight line graph sloping downward from B to C. Therefore, BC repres-
ents uniform retardation.

ii) Acceleration of the body from O to A is given by

Acceleration = Slope of OA = AD = change in velocity = 6 = 1.5 m/s2
OD time taken 4

iii) Retardation of the body from B to C is given by

Retardation = Slope of BC = BE = change in velocity = 16 6 10 = 6 = 1m/s2
CE time taken – 6

Equations of motion

When a uniformly accelerated body travels in a straight line, the relationship between the
initial velocity (u), final velocity (v), distance travelled (s), acceleration (a) and time taken (t) is
called the equation of motion. There are three equations of motion. They are:

Modern Concept Science - 9 23

i) v = u + at

ii) s = ut + 1 at2
2

iii) v2 = u2 + 2as

Derivation of the first equation of motion: v = u + at
(Relationship between initial velocity 'u', final velocity 'v', acceleration 'a' and time 't')

Let us consider a body has initial velocity 'u'. Suppose, it is subjected to a uniform acceleration
'a' so that the final velocity becomes 'v' after time ’t’. Now, from the definition of acceleration,
we have,

Acceleration (a) = Final velocity (v) – initial velocity (u)
Time taken (t)

or, a = v – u
t
or, at = v – u

∴ v = u + at

This equation shows the velocity acquired by a body in time 't'.

Solved Numerical 2.4

The retardation of a car due to brakes is 2.5 m/s2 and the car stopped in 10 seconds by

applying brakes. Calculate the initial velocity of the car. Memory Tips

Solution: Here, To solve the numerical problems

Retardation = 2.5 m/s2, i.e. acceleration (a) = – 2.5 m/s2 based on equation of motion, we

Final velocity (v) = 0 [Since the car comes to rest] should remember:
Time taken (t) = 10 seconds i) If a body starts from rest, its
Using the equation of motion,
v = u + at initial velocity, u = 0
ii) If a body comes to rest, its final

velocity, v = 0

or, 0 = u + (–2.5) × 10 iii) If a body moves with uniform

or, 0 = u – 25 velocity, its acceleration, a = 0.

or, u = 25 m/s

∴ The initial velocity of the car is 25 m/s.

Derivation of second equation of motion: s = ut + 21at2

(Relationship between initial velocity 'u', acceleration 'a', distance travelled ‘s’ and time 't')

Suppose a body has an initial velocity 'u' and uniform acceleration 'a' for time ’t’. Let the
distance travelled by the body in this time be 's'. The distance travelled by the body is the
product of average velocity and time taken.

Distance travelled (s) = Average velocity × Time

or, s = u + v × t .............(i)
2
Substituting the value of "v" from the first equation of motion, i.e., v = u + at

24 Force

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

∴ s = ut + 1 at2
2
It gives the distance travelled by a body in time ’t’.

Solved Numerical 2.5

A body starts from rest. It attains an acceleration of 5 m/s2 in 5 seconds. Calculate the
distance travelled by the body.

Solution:

Initial velocity (u) = 0 [Since the body starts from rest]

Acceleration (a) = 5 m/s2

Time taken (t) = 5 seconds

Using the second equation of motion,

s = ut + 1 at2
2

or, s = 0 × 5 + 1 × 5 × 52 = 62.5 m
2
So, the distance travelled by the body in 5 seconds is 62.5 m.

Derivation of the third equation of motion: v2 = u2 + 2as

(Relationship between initial velocity 'u', final velocity 'v', acceleration 'a' and distance
travelled 's')

Suppose a body has an initial velocity 'u', final velocity 'v' and uniform acceleration 'a' for time
’t’. Let the distance travelled by the body in this time be 's'. The distance travelled by the body
is the product of average velocity and time taken.

Distance travelled (s) = Average velocity × Time

s = u + v × t .........(i)
2
From definition of acceleration,

a = v – u
t

or, t = v – u
a

Substituting the value of ’t’ in the equation (i), we have

s = u + v × v – u
2 a

or, s = v2 – u2
2a

∴ v2 = u2 + 2as
It gives the velocity acquired by a moving body to cover the distance 's'.

Modern Concept Science - 9 25

Solved Numerical 2.6

A car was moving with the velocity 27 m/s. Brakes were applied to the car to produce a
uniform retardation of 0.9 m/s2. Calculate the distance covered by the car before coming to
rest.

Solution: Here,

Initial velocity (u) = 27 m/s

Final velocity (v) = 0 [Since the car comes to rest]

Acceleration (a) = - 0.9 m/s2

Using the third equation of motion,

v2 = u2 + 2as

s = 02 – (27)2 = – 729 = 405 m
2 × (– 0.9) – 1.8

So, the distance covered by the car before coming to rest is 405 m.

Solved Numerical 2.7

A bus was moving with a speed of 76 km/h. On seeing a child 20 m ahead on the road,
the driver of the bus applies brakes and the bus stops at a distance of 15 m. Calculate the
retardation and how long time does it take to come to rest?

Solution:

Distance travelled (s) = 15 m

Initial velocity (u) = 76 km/hr = 76 × 1000 m = 20 m/s
60 × 60 s

Final velocity (v) = 0

From the third equation of motion,

v2 = u2 + 2as

or, a = v2 – u2 = 0 – 202 = – 400 = – 13.33 m/s2
2s 2 × 15 30

The retardation of the bus is 13.33 m/s2

Again,

v = u + at

or, t= v – u = 0 – 20 = 1.5 second
a – 13.33

The time taken to bring the bus at rest is 1.5 seconds.

26 Force

Equations of motion of a body dropped from a certain height

When a body is freely falling towards the earth surface, acceleration is equal to the acceleration
due to gravity, i.e. a= g. In such case, the equations of motion are modified as:

For linear motion For vertical motion u=0

v = u + at v = u + gt

s = ut + 1 at2 h = ut + 1 gt2 hg
2 2

v2 = u2 + 2as v2 = u2 + 2gh

Note: For a body thrown vertically upward, acceleration a = – g.

Inertia

A book lying on the table remains at rest unless an external force is applied on it. Similarly,

a moving bicycle remains in motion unless an external force or frictional force is applied on

it. It shows that, a force is required to change the state of Memory Tips
rest and uniform motion of an object. Thus, the property of

a body by virtue of which it resists any change in its state of The property of a body by virtue

rest or uniform motion of a body is called inertia. Inertia is of which it resists the change in its

also defined as the tendency of a body to remain in its state state from rest to motion and vice-
of rest or of uniform motion along a straight line.
versa is called inertia.

Relation between mass and inertia

It is our common experience that pushing a bicycle is easier than pushing a motorcycle.
Similarly, on applying brakes, single loaded bicycle can stop easily compared to the double
loaded one. It means the heavier object shows greater resistance to change its state of rest or
uniform motion than a lighter one. Here, a heavier body has more mass and more inertia than
a lighter body. So, inertia of a body is directly proportional to its mass.

Inertia α mass of a body Swinging

From the above relation, it is clear that an object with small mass
has less inertia and the object with a greater mass has more inertia.
Greater the inertia of a body, greater will be the force required
to bring a change in its state of rest or of uniform motion. For
example, you push a man and a small child on swing one after
another. It is more difficult to move the adult. Once you set them
in motion, you would experience difficulty to bring the man into
rest. This is because the man has the greater mass, greater inertia
and greater resistance to change in his state than the child.

FACT WITH REASON

The heavier the body, the greater is the force required to change its state, why?
Inertia is directly proportional to the mass. A heavier object at rest has more inertia of rest. So, the heavier
the body, the greater is the force required to change its state of rest and state of motion.

It is harder to stop a big vehicle like a bus than a smaller vehicle like a motorcycle. Why?
Inertia of a body is directly proportional to its mass. There is more inertia with the bigger object. A big vehicle
has more mass and more inertia of motion than the smaller vehicle. So, it is difficult to stop a big vehicle.

Modern Concept Science - 9 27

ACTIVITY 1

1. Hang two identical buckets as shown in the given figure.

2. Fill one bucket with sand and leave another empty.

3. Equally pull them and leave in such a way that they oscillate.

4. Observe which bucket comes to the rest first. Does the empty bucket come to the AB
rest first?

Explanation: The bucket 'B', filled with sand has more mass and has more inertia. So, it keeps oscillating

for longer time. But the empty bucket 'A' has less mass and less inertia. So, it comes to the rest first.

Types of Inertia

On the basis of state of rest and motion of a body, the inertia is classified into two types. They
are:

a) Inertia of motion

b) Inertia of rest

a) Inertia of motion

A moving car remains in uniform motion along a straight line unless an external force is
applied on it. This tendency of a car is called inertia of motion. Similarly, the bicycle continues
to move in forward direction for some time even after we stop pedaling. Thus, the property of
a body by virtue of which it resists any change in its state of uniform motion is called inertia
of motion.

ACTIVITY 2

1. Take a piece of stone of about 1 to 1.5 kg mass and tie it with a soft cotton thread.
2. While tying, suspend a small piece of this cotton thread below the stone.
3. Jerk the lower end of the thread suddenly and observe.
We observe that, the thread breaks below from the stone due to the inertia of rest
of the stone. Here, the upper part of the thread does not break because the stone
resists the jerk due to inertia of rest.

FACT WITH REASON

Athletes often run for some distance before taking a long jump. Why?
Athletes set their body in motion by running. When they take off, the inertia of motion try to keep their body
in motion. It helps them to cover maximum distance in the long jump.

It is advised to tie luggage kept on the roof of a bus with a rope. Why?
When the bus is moving, luggage tends to remain in the state of motion due to inertia of motion. When
brakes are applied on the bus, the bus comes in the rest, but the luggage remains in motion due to inertia of
motion. So, they move forward and may fall.

When power supplied is switched off, the blades of a fan keep rotating for some time. Why?
A fan in motion has inertia of motion. When the power supplied is switched off, the inertia of motion tries
to keep it in motion.

28 Force

When a moving car or bus stops suddenly, the passengers are jerked forward. Why?
Due to inertia of motion, the body of passengers tries to remain in the state of motion even though the car or
bus has come to rest. So, the seat belts are provided in cars to prevent the injury which may cause when the
passengers are thrown forward violently.

The passenger getting out of a moving train or bus falls in the forward direction. Why?
When a bus is in motion, the body of passengers is also in motion. If a passenger jumps out of the moving
bus, the feet of the passenger come to rest immediately but the upper part of the body tends to remain in
motion due to inertia of motion. So, the person falls in the forward direction.

The bicycle continues to move forward direction for some time even after we stop pedaling. Why?
The bicycle continues to move forward direction for some time even after we stop pedaling because in a
moving bicycle there is inertia of motion. Due to this inertia of motion of the bicycle, it continues in motion
for some time.

b) Inertia of rest
The property of a body by virtue of which it resists any change in its state of rest is called
inertia of rest. According to the law of inertia of rest, a body continues to be in a state of rest
unless an external force acts on it. For example, a blackboard remains in the classroom unless
an external force is applied on it to carry to the next room.

ACTIVITY 3

1. Take an empty and dry glass tumbler.
2. Place a smooth post card over the mouth of the glass

tumbler. Also, place a coin at the center of the post card.
3. Now, strike the card to flip it horizontally. Do you observe

that the card flies away and the coin falls into the glass?
Explanation: Initially, the card and the coin are both at rest. On flipping, the cardboard is suddenly set
into motion, but the coin remains at rest due to the inertia of rest. Hence, the coin drops into the glass.

FACT WITH REASON

When the postcard with a coin at its middle is placed on the mouth of a glass tumbler and flipped, the coin
falls into glass tumbler. Why?
Due to the inertia of rest of the coin, while flipping, the postcard comes in motion but the coin remains at the
state of rest due to its inertia of rest. So, the coin falls into the glass tumbler.

When a car or a bus starts suddenly, the passengers fall backward. Why?
When a car or a bus is at rest, the passengers inside it are also at rest. If the bus or car comes in motion
suddenly, the body of passengers tends to stay at rest even after the vehicle has started moving. So, the
passengers fall backward.
Dust particles come out of the carpet when it is beaten with a stick. Why?
When a carpet is beaten with a stick, dust particles on it tend to remain at rest and resist the motion. So, due
to inertia of rest, the dusts come out of the carpet.

Modern Concept Science - 9 29

When the branch of a tree is jerked, fruits fall down. Why?
Before jerking, the branch of a tree and the fruits are at rest. When the tree or its branch is jerked, they come
in motion, but the fruits try to remain at rest due to the inertia of rest. Due to this condition, the fruits get
separated from the branch and fall down.
A bullet fired against a glass windowpane makes a hole in it, but the glass pane is not cracked. Why?
When the entire glass windowpane is at rest, it has inertia of rest. If a bullet is fired against the glass window
pane, only the part of contact of bullet with glass pane comes in motion and the rest part remains at rest. This

makes a hole on the glass windowpane without causing any crack in other parts of it.

A pile of the carom coins does not fall down when we hit at its bottom with a striker. Why?
A pile of carom coins at rest has inertia of rest. When we hit with a striker at the bottom of the pile of the
carom coins on a board, the bottom coin moves out quickly but the pile of the coins maintains its state of
rest. It makes the pile to shift down vertically on the board.

Differences between inertia of motion and inertia of rest

Inertia of motion Inertia of rest

1. The property of a body by virtue of which 1. The property of a body by virtue of

it resists any change in its state of uniform which it resists any change in its state of

motion is called inertia of motion. rest is called inertia of rest.

2. Due to inertia of motion, the passengers 2. Due to inertia of rest, the passengers

inside a moving bus are jerked forward inside a bus at rest are jerked backward

when the bus stops suddenly. when the bus moves suddenly.

FACT WITH REASON

When a bus turns sharply at turnings on the road, the passengers fall aside, why?

Due to inertia of direction, a body continues its state of uniform motion along a straight line. When a bus
turns sharply, the body of passengers inside the bus tries to remain in motion along a straight line and they
fall aside.

Examples of Inertia Direction Memory Tips

i) When a car takes a sharp turn suddenly to the right, The property of a body by virtue

the person sitting in the car will be pushed towards of which it resists any change in
the state of uniform motion along
the left.
a straight line is called inertia of
ii) When a car takes a sharp turn suddenly to the left, the direction.

person sitting in the car will be pushed towards the

right.

Factors affecting inertia Memory Tips

Mass is the main factor that affects inertia. Some other If a body is at rest, its velocity is zero
factors which affect inertia are force of gravity and friction. and hence its momentum is also
zero.

30 Force

a) Momentum

A cricket ball is heavier than a tennis ball. If we try to stop a tennis ball and a cricket ball
which are thrown at the same speed, it is found that more force is required to stop the cricket
ball (which has more mass) and less force is required to stop the tennis ball (which has less
mass). Momentum of a body in motion is the product of mass and its velocity. If we throw a
cricket ball, once with higher velocity and next time with lower velocity and try to stop then
it is found that more force is required to stop the cricket ball when it is moving with higher
velocity and less force is required to stop it when it is moving with lower velocity. So, the
quantity of motion in a body depends on the mass and velocity of the body. The measurement
of the motion in a body is done by the quantity known as momentum. Thus, the momentum
of a body can be defined as the product of its mass and velocity.

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

Momentum is a vector quantity. Its direction is same as the direction of velocity.

FACT WITH REASON

Momentum is called a vector quantity, why?
Momentum has both direction and magnitude. Its direction is in the direction of velocity. So, momentum is
called a vector quantity.
It is easier to stop a tennis ball in comparison to a cricket ball moving with the same speed, why?
Tennis ball is lighter than a cricket ball. We know that momentum is the product of mass and velocity. The
tennis ball moving with the same speed has less momentum than that of a cricket ball. So, it is easier to stop
a tennis ball in comparison to a cricket ball moving with the same speed.

Units of Momentum
The SI unit of momentum is kilogram-metre per second. It is written as kg m/s or kg m s-1.

The C.G.S. unit of momentum is gram-centimetre per second. It is also written as g cm/s or g cm s-1.

FACT WITH REASON

The total momentum of the gun and bullet before firing is zero, why?
Before firing, the bullet and the gun are at rest and their velocity is zero. As they are at rest, the total
momentum of the gun and bullet before firing is zero.

Solved Numerical 2.8

A body of mass 25 kg has momentum of 125 kgm/s. What is the velocity of the body?
Solution:

Mass of the body (m) = 25 kg

Momentum (p) = 125 kg m/s

Since, p = m.v

or, v = p = 125 = 5 m/s
m 25

Therefore, the velocity of the body is 5 m/s.

Modern Concept Science - 9 31

Newton's laws of motion

Sir Isaac Newton was an English physicist and mathematician. He put forward three laws on
motion in 1686 AD. These laws are popularly known as Newton's laws of motion. Newton's
first law of motion gives an accurate definition of force and inertia. The second law of motion
describes the relation of acceleration of a body with the force applied and mass of the body.
Newton's third law of motion establishes the relationship between 'action' and 'reaction' of
the forces.

Newton's First Law of Motion
Newton's first law of motion states, "every body continues to be in a state of rest or of uniform
motion in a straight line unless an external force is applied on it". This law defines the force.
This law is also called the law of inertia. Newton's first law of motion consists of three parts.

a) First part : A body at rest remains at rest unless some external force acts on it to change
its state of rest. For example, a football on the ground remains in the state of rest unless
a player kicks it.

b) Second part : A body in uniform motion continues to move uniformly in a straight
line unless some external force acts on it to change its state of motion. For example, a
moving bicycle continues in motion unless an external force is applied on it.

c) Third part : A body continues to move along the same straight line unless some external
force acts on it. For example, to turn a moving car over a straight road, we have to apply
a force on the steering wheel of the car.

We define force as a push or pull which changes or tries to change the state of a body from
rest to motion or vice versa. According to the first law of motion, only external force applied
on a body can change its state of rest or state of uniform motion along a straight path. Hence,
Newton's first law of motion defines force.

FACT WITH REASON

Newton's first law of motion is also called the law of inertia, why?
Newton's first law of motion states that every body continues to be in a state of rest or of uniform motion in
a straight line unless an external force is applied on it. This property of a body is also known as inertia. So,
Newton's first law of motion is also called the law of inertia.

Some examples related to Newton’s first law of motion:
1. A rotating fan continues rotating for a while although the switch is turned off. It is due

to inertia of motion. After some time, it comes to rest due to frictional force.
2. A book on the table remains in rest until and unless we displace or remove it by using

our muscular force or any other external force.
3. When a bullet is fired on a glass pane window, it makes a clear hole without causing

cracks in the glass. This is also due to inertia of rest of the glass pan.
4. A person jumping out from a moving bus falls forward and gets injured. This is due to

inertia of motion of the body.

32 Force

Newton's second law of motion

Newton's second law of motion shows a relationship between force and acceleration of a
body having certain mass. It is not possible to move an object fast without more force. We
need more force to move an object faster. It means that the acceleration produced on a body is
directly proportional to the force applied on it.

Mathematically, acceleration (a) α force (F) [When mass (m) remains constant]

A lighter object can be thrown faster, but it is difficult to throw a heavier one. Similarly, a
lighter object can be pushed faster than a heavier one. It means that the acceleration produced
on a body is inversely proportional to its mass.

Mathematically,

Acceleration (a) α 1 (m) [When the force applied (F) remains constant]
mass

From the above relations, Newton put forward the second law of motion. It states, "acceleration

produced on a body is directly proportional to the force applied on it and inversely proportional

to its mass.”

Derivation of Newton's Second Law of Motion

Newton's second law of motion states, "Acceleration produced on a body is directly proportional
to the force applied on it and inversely proportional to its mass.” From the statement,

Acceleration (a) α force (F) ......(i) [When mass (m) remains constant]

Acceleration (a) α 1 (m) ......(ii) [When the force applied (F) remains constant]
mass

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

a α F
m
or, F α ma

or, F = k ma .........(iii) Where 'k' is a proportionality constant.

When, m = 1 kg, a = 1 m/s2 then,

F=1N

In this condition, k = 1

Substituting the value of 'k' in equation (iii), we get

F = ma

One newton force

From the Newton's second law of motion,

We have, F = ma

or, 1 N = 1 kg × 1 m/s2

The force which produces 1 m/s2 acceleration on a body of mass 1 kg is called 1 newton force.

Modern Concept Science - 9 33

Solved Numerical 2.9

A car of mass 1000 kg is moving with a velocity of 72 km/h. It takes 2.5 seconds to stop after
the brakes are applied. Calculate the force exerted by the brakes on the car.

Solution:

Initial velocity of the car (u) = 72 km/h = 72 × 1000 m/s = 20 m/s
60 × 60

Final velocity of the car (v) = 0 [since the car comes to rest]

Mass of the car (m) = 1000 kg

Time taken to stop the car (t) = 2.5 seconds

According to Newton's second law of motion, we have

F=ma

or, F = m (v – u) = 1000 (0 – 20) = – 20000 = – 8000 N
t 2.5 2.5

Therefore, the force exerted by the brakes is 8000 N

The negative sign indicates that the force exerted by the brakes is opposite to the
direction of motion of the car.

Solved Numerical 2.10

A force of 500 N is applied on a moving bus of mass 1000 kg. Now the bus comes to rest
within a distance of 64 m. Find the initial velocity and the time taken by the bus to come
to rest.

Solution:

Force (F) = 500 N

Mass of the car (m) = 1000 kg

Distance covered (s) = 64 m

According to Newton's second law of motion,

F=ma

or, a = F = 500 = 0.5 m/s2
m 1000

Since, the car comes to rest by applying force on it. So, it has retardation.

Again,

Final velocity (v) = 0 m/s

Acceleration a = 0.5 m/s2

From the equation of motion,

v2 = u2 + 2as

or, 0 = u2 + 2 × – 0.5 × 64

or, u2 = 64

34 Force

or, u = 8 m/s

Again,

v = u + at

or, 0 = 8 – 0.5 × t

or, 0.5 × t = 8

∴ t = 16 seconds

∴ Initial velocity (u) = 8 m/s, time (t) = 16 s and retardation = 0.5 m/s2

FACT WITH REASON

While catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backward with
the moving ball, why?

According to Newton's second law of motion, F = ma, where 'm' is the mass of the object and 'a' is the
acceleration produced in it. In lowering the hands, the fielder increases the time duration in which the high
velocity of the ball decreases to zero. This also decreases the acceleration of the ball. Therefore, the impact
of catching the fast moving ball is reduced.

If the ball is caught suddenly without lowering the hands, then its high velocity decreases to zero in very
short interval of time. At this condition, acceleration of the ball will be very large. Thus, a large force would
have to be applied for holding the catch. This may hurt the palm of the fielder.

Newton's Third Law of Motion

ACTIVITY 4

1. Connect two spring balances together as shown in the given figure

2. Fix the end of spring balance "B" to a rigid support. B A

3. Pull the free end of spring balance "A" with the force of 5

N. Observe the readings on the spring balance "B". Do you

observe the reading of 5N in the spring balance "B"?

The force exerted by the spring balance "A" on the spring balance "B" (i.e. action) is equal but opposite in

direction to the force exerted by the spring balance "B" on the spring balance "A" (i.e. reaction).

ACTIVITY 5

1. Tie a nylon rope on two stands.
2. Insert a rope into a spool made from a piece of paper.
3. Inflate a balloon and fix on the spool.
4. Open the mouth of the balloon and observe its motion. Does the balloon move forward?
The force with which air rushes out from the balloon is equal to the force which pushes the balloon
forward.

Whenever two bodies interact, the forces that they exert on each other are always equal in
magnitude and opposite in direction. If a body "A" exerts a force "F" on the body "B" (an
action) then the body "B" also exerts a force "F" on the body "A" (a reaction). When we kick a
football, our foot exerts a forward force on the ball, but we also feel the force exerted by the

Modern Concept Science - 9 35

ball back on our foot. Action and reaction act on two different surfaces. Thus, they do not
cancel each other. Thus, according to Newton's third law of motion, for every action there is
an equal and opposite reaction

FACT WITH REASON

Action and reaction do not cancel each other even they have equal magnitude and opposite direction, why?
When two equal and opposite forces act on the same body then the resultant force is zero. But the action and
reaction forces act on two different bodies in two opposite directions. Thus, they do not cancel each other.

Some examples of Newton's third law of motion

a) An air filled balloon goes upward on releasing its mouth

When we release a balloon filled with air keeping its mouth downward, then
the air inside the balloon rushes out downward with high force called an action.
According to Newton's third law of motion, every action has equal and opposite
reaction. So, the air exerts an equal and opposite force on the balloon (reaction)
and it goes upward (reaction).

b) Rockets move forward with a great speed Reaction

In rockets, the fuel is burnt to produce a large quantity of gases. The hot gases come Action
out of a nozzle with a great force called an action. According to Newton's third
law of motion, there is an equal and opposite force exerted by the hot gases on the
rocket called reaction. This reaction pushes the rocket forward with a great speed.

c) Flying of a bird

When a bird flies, it pushes the air downward with its wings (action). At the same time, the air
exerts an equal and opposite force on the bird in the upward direction (reaction). As a result,
the bird flies in the air.

d) A gun recoils while firing a bullet Firing a bullet

Recoil of a gun means the sudden backward movement or jerk of the
gun when a bullet is fired from it. When a bullet is fired from a gun, the
forward force on the bullet (action) is equal to the backward force on the
gun (reaction). So, while firing bullets, the soldier gives support of his
shoulder to resist the recoil of the gun.

FACT WITH REASON

Action and reaction are equal in magnitude but they do not produce equal acceleration on the two bodies, why?

Two forces in an action-reaction pair act on different bodies which usually have different masses. The
acceleration produced is more on the body having less mass whereas the acceleration produced is less
in the body having more mass. For example, when a bullet is fired, the bullet gains high acceleration in
forward direction, but the gun moves only a little distance in backward direction. This is due to more mass
of the gun.

While swimming, a swimmer pushes the water backward. Why?

While swimming, a swimmer pushes water in backward direction with his hands. It is called an action.
According to Newton's third law of motion, water also pushes the swimmer with equal force in the forward
direction called reaction.

36 Force

A boatman ties his boat before allowing the passengers to get out of the boat. Why?
When the passengers get out of the boat, they push the boat in backward direction called an action. If the
boat is not tied, it slides backward without giving enough reaction force to the passengers. So, passenger

may fall in the water.

A rower pushes water backward while rowing a boat. Why?
While rowing, the rower pushes water in backward direction with oars. It is called an action. According to
Newton's third law of motion, every action has equal and opposite reaction. So, water also pushes the boat

with equal force in the forward direction. It is called reaction.

Why a rubber ball rebounds when struck against a hard floor?
When we strike a rubber ball against a hard floor, the ball exerts a force on the floor called an action.
According to Newton's third law of motion, the floor exerts an equal and opposite force on the ball (reaction).
So, the rubber ball rebounds when struck against a hard floor.
The simple act of walking depends on Newton's third law of motion, give reason.
To move forward, we push the ground backward with our foot. It is called an action. The ground also pushes
us forward on our foot with a force of the same magnitude called reaction. So the simple act of walking
depends on Newton's third law of motion.

ANSWER WRITING SKILL

1. What do you mean by rest? Give an example of an object at rest.

Ans: A body is said to be at rest if it does not change its position with respect to a fixed point called reference
point in its surrounding. For example, house, tree, electric pole.

2. What does it mean by v–u = 0? What would be the value of acceleration at this condition?

Ans: If v–u = 0 then, the object has uniform velocity and zero acceleration.

3. Which law of motion is represented by the equation “F = ma”?

Ans: The equation F = ma represents Newton’s second law of motion.

4. A moving bus moves a little distance forward even when brakes are applied on it. Which Newton's law
is working here?

Ans: A moving bus moves a little forward even when brakes are applied on it. It is due to inertia of motion of
5.
Ans: the bus. It explains Newton’s first law of motion.
6. Y

Name the type of velocity shown in the given graph. How much would be 25

acceleration in this condition and why? Velocity (m/s) 20
15

Uniform velocity is shown in the given graph. At this condition there is zero 10 234 5 X
acceleration because the change in velocity is zero. 5 Time (s)

Write any two differences between acceleration and retardation. 01

Ans: The differences between acceleration and retardation are:

S.N Acceleration S.N Retardation

1. Acceleration is a rate of change in velocity. 1. Retardation is a rate of decrease in velocity.

2. Acceleration exists when final velocity 2. Retardation exists when final velocity

increases. decreases.

Modern Concept Science - 9 37

7. Why is it difficult to walk on the sandy, muddy and swamp areas?
Ans:
8. The sand particles are loosely packed. When we step on it as an action, it gets pressed and cannot
Ans: provide us enough reaction to lift our legs. As a result, it is difficult to walk on the sandy, muddy and
9. swamp areas.
Ans:
It is difficult for a horse to pull a cart at rest at first but easier as cart starts to move. Explain the reason.
10.
Ans: At first the cart is at rest. So the horse has to apply more force upon the cart to overcome the inertia of
rest. But later the cart gains inertia of motion and sufficient momentum. Therefore, it is difficult for a
horse to pull a cart at rest at first but easier when the cart starts to move.

A ball of mass 1 kg is thrown with a force of 10 N. Calculate the acceleration and the final velocity of the
ball after 2 seconds.

Solution:

Mass of the ball (m) = 1 kg

Force applied (F) = 10 N

Initial velocity (u) = 0 m/s

Time (t) = 2 seconds

Acceleration (a) =?

Final velocity (v) =?

Using formula,

F = ma
a = F = 10 = 10 m/s2

m1
Again, v = u + at = 0 + 10 × 2 = 20 m/s

Draw a distance time graph to show a body at rest and a velocity-time graph to show a body moving
with uniform velocity.

Y Y

20 25
15 20
10 15
5 10
5

01 2 3 4 5
Time (s)

b) uniform velocity
Distance (m)01 2 3 4 5 X X
Velocity (m/s)Time (s)

Velocity (m/s)a) Body at rest

11. Study the given graph and answer the following questions. 6 BC
4
a) What is represented by line AB? 2 4 10 D
Time (s) 16
Ans: Line AB represents uniform acceleration. A
b) What is represented by line BC?
Ans: Line BC represents uniform velocity.
c) What is the value of acceleration at BC?
Ans: At BC acceleration is 0 m/s2.

38 Force

d) Which line shows retardation?

Ans: Line CD shows retardation.

e) What is the condition of the body at the point D?

Ans: The body at the point D is at rest.

12. A man of 72 kg runs with a uniform velocity of 5 m/s. Find his momentum.

Solution:

Mass of the man (m) = 72 kg

Velocity (v) = 5 m/s

Momentum (p) = m × v

Momentum (p) = 72 × 5 = 360 kg m/s

Therefore, momentum of the man is 360 kg m/s.

13. When brake is applied in a vehicle moving with velocity 25 m/s the retardation becomes 0.5 m/s2, how
far will it travel in 15 seconds?

Solution:

Initial velocity (u) = 25 m/s

Time taken (t) = 15 seconds

Acceleration (a) = - 0.5 m/s2

Using the equation of motion,

s = ut + 1 at2 = 25 × 15 + 1 × – 0.5 × 152 = 375 – 56.25 = 318.75
2 2
So, the vehicle will travel 318.75 m in 15 seconds.

14. A force of 10 N acts on a body of mass 2 kg. If the body was initially at rest, calculate the velocity acquired
by the body in 5 seconds.

Solution:

Force (F) = 10 N

Mass of the body (m) = 2 kg

Initial velocity (u) = 0 m/s

Time taken (t) = 5 seconds

According to Newton's second law of motion,

F = ma

or, F=m× v–u
t

or, 10 = 2 × v– 0
or, 5 m/s
v= 50
2 = 25

Therefore, the velocity acquired by the body in 5 seconds is 25 m/s.

15. A rock dropped from the top of a building reaches the ground with a velocity of 49 ms-1. If the acceleration
due to gravity is 9.8 m s-2, calculate the time for which the stone is falling freely.

Solution:

Initial velocity (u)= 0 m/s

Final velocity (v) = 49 m/s

Modern Concept Science - 9 39

Acceleration due to gravity= 9.8 m s-2

Now, from the equation of motion,

v = u + gt

or, t= v–u = 49 – 0 = 5 seconds
g 9.8

Therefore, the time taken by the stone is 5 seconds.

STEPS EXERCISE

STEP 1

1. Define

a) Force b) Balanced forces
c) Unbalanced forces d) Rest
e) Motion f) Reference point
g) Scalar quantities h) Vector quantities
i) Distance j) Displacement
k) Speed l) Velocity
m) Uniform velocity n) Non-uniform velocity
o) Acceleration p) Positive acceleration
q) Negative acceleration r) Distance-time graph
s) Velocity-time graph t) Equation of motion
u) Inertia v) Inertia of motion
w) Inertia of rest x) Inertia of direction
y) Momentum z) One newton force

2. Very Short Answer Questions
a) Write the effects of force.
b) What is SI and CGS unit of force?
c) Write the relationship between SI unit and CGS unit of force.
d) Name any three scalar quantities and three vector quantities.
e) Identify the following quantities as vectors or scalars:
i) mass ii) weight iii) acceleration

iv) momentum v) time vi) velocity

f) Write the SI unit of followings
i) velocity ii) acceleration iii) momentum

g) Give two examples of non-uniform velocities.
h) What is the acceleration of a body moving with uniform velocity?
i) Give one example of a body moving with uniform acceleration.
j) What is retardation? Give one example having retarded motion of a body.

40 Force

k) What type of motion a particle has, if its
i) velocity-time graph is parallel to the time axis
ii) velocity-time graph is a straight line passing through the origin and
having constant slope.

l) On what factors does inertia of a body depend?
m) Name the type of inertia in each of the following cases

i) A passenger jumping out of a moving bus falls forward.
ii) On taking a sharp turn the driver feels a sideway jerk.
iii) Dust particles are removed when a carpet is beaten with a stick.
iv) When a bus is stopped suddenly, the passengers experience a forward

jerk.
n) On what factors does momentum of a body depend?
o) State Newton's first law of motion.
p) State Newton's second law of motion.
q) State Newton's third law of motion.
r) Identify the action-reaction forces in the following cases.

i) A boy walking on the ground
ii) Firing a bullet from the gun
iii) A boy swimming in a swimming pool
iv) Launching of a rocket from the earth surface

STEP 2

3. Short Answer Questions
a) What are the balanced forces and unbalanced forces? Write with an example of
each.
b) A body is moving with a uniform acceleration of 2 m/s2. What does it mean?
c) Under what condition a body travels a certain distance but the net displacement
is zero. Explain with an example.
d) A satellite goes around the earth with constant speed in a circular orbit. Does it
have acceleration? Explain.
e) Explain the inertia of rest, inertia of motion and inertia of direction with
appropriate examples.
f) What is the relation of inertia with mass?
g) Which of the following has larger inertia? Write with reason
i) A tennis ball or a cricket ball.
ii) A car or a bicycle.
iii) A man or a boy.

Modern Concept Science - 9 41

h) Two similar vehicles are moving with same velocity on the roads and one of them
is loaded and the other one is empty. Which of the vehicle will require larger force
to stop it? Give reason.

i) 'Newton's first law of motion is also called the law of inertia.' Explain this
statement.

j) Explain the motion of a rocket with the help of Newton's third law of motion.
k) Write relation between force, mass and acceleration.

4. Differentiate Between:

a) Balanced forces and unbalanced forces
b) Vector quantities and scalar quantities
c) Distance travelled and displacement
d) Speed and velocity
e) Uniform velocity and variable velocity
f) Inertia of rest and inertia of motion

5. Give reason:

a) In 'coin on card' experiment a smooth card is used.
b) A person getting out of the moving bus falls in the direction of motion of the bus.
c) A passenger falls backward when the bus suddenly starts moving.
d) Passengers experience a forward push when a running bus stops suddenly.
e) It is dangerous to jump out from a fast moving vehicle.
f) A tree is shaken to get its fruits down.
g) Dusts come out of a carpet when we hit it with a stick.
h) A cricket player lowers his hands while holding a catch.
i) Swimmers push water backward while swimming.
j) A rubber ball rebounds when it hits a wall.
k) A gun recoils on firing.
l) It is difficult to walk on slippery road.

6. Study the given graph and answer the following questions.

a) Identify the positive slope, constant slope and negative slope of the figure.

b) Identify slope for acceleration, no acceleration and retardation in the given graph.

c) Calculate the acceleration.

d) Calculate the retardation. Velocity (m/s) 6A B

e) Why is path AB parallel to x-axis? 4

2

D EC

f) What happens to the body at C? [Hint rest/motion] O4 10 16

Time (s)

STEP 3

7. Numerical Problems

42 Force