Science book class 8

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

MODERN CONCEPT

SCIENCE
AND ENVIRONMENT
8

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
AND ENVIRONMENT

8

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 our surrounding. Teaching science in the
classroom is not a rote learning process but it is a great achievement to the students for understanding the
facts, concepts, laws and principles. 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 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. So, teachers are the role model of the classroom.

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.
For the positive change in the concept, skill or attitude of the students and their performance in
their life, every activity is supposed to be an essential part for every teaching learning process.
Teachers are expected to make more and more involvement of the students in different activities
that help them to experience themselves for their further improvement.

vii. Management of teaching learning activities: For teaching learning activities, the weightage of
curriculum is determined 5. It is generally estimated that, in a year, the teaching learning activities
will be minimum 175 periods. Out of these, 140 periods (80%) are alloted for theory and 35
periods (20%) are alloted for practical. The period division of different areas of science and
environment is given in the following table.

S.N. Area Weighting (in %) Theory periods Practical periods

1. Physics 26 36 9

2. Chemistry 22.5 32 8

3. Biology 20 28 7

4. Geology and Astronomy 11.5 16 4

5. Environment education 20 28 7

Total 100 140 35

viii. 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 five branches of class 8 science and environment. They are as follows.

S.N. Branches Weighting (in %) Weighting (in marks)
1. Physics 33.3 25
2. Chemistry 20 15
3. Biology 20 15
4. Geology and Astronomy 6.7 5
5. Environment education 20 15
Total 100 75

b. Practical Test: Practical evaluation must be done on the basis of the following bases.

1. Drawings/Labellings/ Explaining characteristics
2. Record of practical work
3. Model Designing/ materials construction and their uses
4. Mini Project Work
5. Viva voce

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
25
Total

ix. 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.

Guidelines to make questions papers:

Area No. of No. of Sub- Full K 30% U 30% A 30% HA 10%
questions questions marks

Physics 5 10 25 7.5 10 5 2.5

Chemistry 3 6 15 4.5 6 3 1.5

Biology 3 6 15 4.5 6 3 1.5

Astronomy and 1 2 5 1.5 2 0 1.5
geology

Environment 3 6 15 4.5 6 3 1.5
education

Total 15 30 75 22.5 30 14 8.5

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
Understanding State, name, list, write, what, definition, What is….?, How many……?, Who…?, List
Application data, units, full forms, classification, the number of………..,State...?, Define.... , etc.
Higher Ability examples, labeling, etc. Write full form of......, Label the pars of......,Give
any two examples of....
Differentiate, Distinguish, Similarities,
Why, How, Explain, Parts of activity, Differentiate between…. and …., Write
Justify, compare, Short note, etc. similarities......, Write down characteristics......,
Give reason...... etc.
Uses, Application, Apply, Generalize,
Solve, Show, Use, Illustrate, Complete, Solve the given numerical problems. Complete
Examine, construct, Draw, Relate, the given chemical equations, Write down the
Transfer, etc. uses of, etc.

Derive, Verify, Argue, Discuss, Explain, Derive the formula……. , Explain an
Formulate, Criticize, Evaluate, Choose, experiment……, Analyse the....Formulate
Analysis, Determine, etc. the.....

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

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 then,
students are allowed to do exercise from step 1 to step 4.

PREFACE

Modern Concept Science and Environment for grade 8 is written to meet the objectives of the curriculum
of class eight science and environment developed by CDC (Curriculum Development Center), Sanothimi,
Bhaktapur. This edition of our textbook meets the criteria of basic knowledge in science and environment
for students who study in class 8. It will help students to achieve the goals of life by gaining of knowledge,
skills and values in Science and environment.

Logical placing of key points and well organized matter are given high priority throughout the textbook.
Appropriate pictures, matter in simplified language and organization of the content with new features are
our high expectation values about popularity of this textbook among the readers.

Features of Modern Concept Science and Environment

A notable concern of many teachers is to follow a well-organized textbook with step by step learnings
in a continuous flow. The organization of this textbook is logically designed to make the book's
information more accessible.
1. Top of the first page of each unit consists of syllabus issued by CDC (Curriculum Development

Center), Sanothimi, Bhaktapur for class 8.
2. Learning outcomes of each unit are given just below the syllabus issued by CDC to focus the

teaching learning goals.
3. The most important idea of writing terms and terminologies on the first page of each unit is

devoted to screen out the main content to be covered.
4. Highlighted definitions, catchy memory tips and bubble box on pages inside of a chapter for a

quick look on important points to be remembered are provided in the first page of each unit.
5. Activities and solved numerical problems are given in each unit of the same page with

corresponding to the topic to develop the scientific skill in the readers.
6. Sample questions of Knowledge, Understanding, Application, and Higher Ability with their

answer are given at the end of each unit under the title answer writing skill to get idea to solve the
questions given in the three steps exercise.
7. This text book focuses primarily on all three level questions to test students' skill under the title
three steps exercise.

With these all features in a well-organized content, the central focus of this book is to encourage students
and make the text user-friendly for all. The answer writing skill and three levels grid based exercise will
help teachers to set test papers for assessments. Students' interest will be peaked when they will find the
screen out terms and terminologies, the appropriate pictures and key points throughout the textbook. We
hope that this book will help teaching in learner-centered way.

We wish to express our sincere gratitude to Mr. Megh Raj Poudel, Managing director of Nova Publication
Pvt. Ltd. for publishing this book. Similarly, thanks are due to Mr. Umesh Bajagain (Sudip), for his valuable
help during the preparation and content editing of the book. Likewise, thanks are due to Mr. Romharsh
Panthi for his praiseworthy language editing.

Finally, we owe full responsibility of misprints and other technical errors, if any, found in this textbook in
spite of our best effort to make this book error-free. Constructive criticism and suggestions for improvement
of this book will be highly appreciated.

5 Poush 2076 Authors
Kathmandu, Nepal

Table of Contents

Physics 1 Measurement 1-13
2 Velocity and Acceleration 14-30
Chemistry 3 Simple Machine 31-43
4 Pressure 44-59
Biology 5 Work, Energy and Power 60-75
6 Heat 76-87
Environment Geology & 7 Light 88-103
Education Astronomy 8. Sound 104-115
9 Magnetism 116-123
10 Electricity 124-136
11 Matter 137-165
12 Mixture 166-175
13 Metal and Non-metal 176-187
14 Acid, Base and Salt 188-199
15 Some Useful Chemicals 200-210
16 Living Beings 211-238
17 Cell and Tissue 239-252
18 Life Process 253-282
19 Structure of the Earth 283-296
20 Weather and Climate 297-306
21 Earth and Space 307-317
22 Environment and its Balance 318-337

23 Environmental Degradation and its Conservation 338-357

24 Environment and Sustainable Development 358-368

Estimated teaching periods Theory MProadcetrincaCloncept Science and Environment – 8 1
3 1
UNIT
Measurement
1

Syllabus issued by CDC Sir Isaac Newton
 Physical quantities
 Fundamental and derived physical quantities
 Unit, fundamental units and derived units
 Measurement of mass
 Measurement of weight
 Measurement of time

LEARNING OBJECTIVES

At the end of this unit, students will be able to:
 define fundamental and derived units.
 identify the measurement of mass, weight and time.

Key terms and terminologies of the unit

1. Measurement : The comparison of an unknown physical quantity with a known
standard quantity of the same kind is called measurement.

2. Physical quantities : Those quantities which can be measured directly or indirectly by
using different devices or instruments are called physical quantities.

3. Non-physical quantities : Those abstract things which cannot be measured directly or
indirectly by using different devices or instruments are called non-
physical quantities.

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

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

6. Unit : The standard quantity which is used to measure an unknown
physical quantity of the same kind is called a unit.

7. SI units : The international system of measurement which is declared from
international convention of scientists held in France in 1960 AD is
called SI units.

8. Fundamental units : Those units which do not depend upon other units are called fundamental
units.

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

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

2 Measurement

11. Weight : The force with which a body is attracted towards the center of the earth
is called its weight.

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

13. Zenith : A particular point in the space directly above an observer standing on
the earth is called zenith.

14. Mean solar day : The average of time taken by the earth to complete one rotation on
15. One second its own axis is called mean solar day.

: One second is also defined as 86,1400 of a mean solar day.

1.1 Measurement

Measurement is an essential aspect of our daily life. We do various activities like export, import,
selling, buying in our day to day life. These activities are impossible without measurement.
Measurement of distance, time and mass is very necessary in every step of our daily life.
We use different kinds of measuring devices like meter rod, meter scale, beam balance, pan
balance, clock, thermometer to measure these physical quantities.

Measurement is a process of comparison. In order to measure a physical quantity, we assume
a standard known quantity of the same kind called ‘unit’. For example, to measure the length
of a piece of cloth, it is compared with a meter scale. The comparison of an unknown physical
quantity with a known standard quantity of the same kind is called measurement. In this unit,
we will discuss about the standard system of measurement and their units. Similarly, we also
discuss about the measurement of mass, weight and time.

1.2 Physical and Non-physical Quantities

There are two types of physical quantities, fundamental physical quantities and derived
physical quantities. Those quantities which can be measured directly or indirectly by using
different devices or instruments are called physical quantities. For example, mass, length,
area, volume, etc. Similarly, the abstract things like pain, sadness, happiness, anger, rudeness,
proudness, respcet, love, hate, stupidity, loyalty cannot be measured. So, those quantities
which cannot be measured directly or indirectly by using different devices or instruments are
called non-physical quantities.

1.3 Classification of Physical Quantities

a) Fundamental Physical Quantities

Those physical quantities which are independent of each other are called fundamental
physical quantities. They are not derived from others. Fundamental quantities are also called
base quantities. There are a total of seven fundamental physical quantities. They are length,
mass, time, temperature, electric current, luminous intensity and amount of substance.

b) Derived Physical Quantities

Those physical quantities which are derived from the fundamental physical quantities are

Modern Concept Science and Environment – 8 3

called derived physical quantities. They are obtained by the combination of one or more
fundamental physical quantities. For example, area, volume, density, acceleration, force,
pressure, work, power, etc. Derived quantities are obtained by multiplying or dividing one
or more fundamental quantities. For example, density is a derived quantity because it can be
expressed as:

Density = Mass = length × Mass × height
Volume breadth

Here, density depends upon the fundamental quantities : mass and length. So, density is a

derived quantity.

FACT WITH REASON

Velocity is a derived quantity, why? displacement (s)
time (t)
The change in displacement is called velocity. i.e., velocity = . Here, velocity depends

upon two fundamental quantities: displacement and time. So, velocity is a derived physical quantity.

1.4 Expression of Measurement

In order to express the result of a measurement, we must know two things. They are:

a. The unit in which a physical quantity is measured.

b. The numerical value which expresses how many times a unit is contained in the given
physical quantity.

Physical Quantity Magnitude

Number Unit

Length 5 meter

Mass 2 kilogram

Area 4 square meter

So, a physical quantity can be represented by a number, followed by a unit.

i.e., Physical quantity = Numerical value × Unit

1.5 Unit

Unit is a fixed quantity. The standard quantity which is used to measure an unknown physical
quantity of the same kind is called a unit. The unit of a physical quantity should have the
following properties:

i) It should not change with time and place.

ii) It should be of convenient size.

iii) It should be reproducible.

iv) There should not be any doubt about the definition of a unit.

v) It should be applicable to measure derived quantities.

4 Measurement

FACT WITH REASON

Meter is considered as a standard unit, why?
The value of 1 meter length is same everywhere in the world. It is accepted throughout the world. So
meter is considered as a standard unit.

International system of units (SI units)

The specific system of measurement at one place gives the same result at another place. The
General Conference of Weights and Measures held in Paris, France in 1960 introduced a new
system of units known as ‘Le Systeme Internationale d’ Unites’, i.e. ‘International system
of units’ (SI units). It is an extended version of MKS system. The international system of
measurement which is declared from the international convention of scientists held in France
in 1960 AD is called SI units.

FACT WITH REASON

Standard units must be used in measurement, why?
To make the selling and buying accurate and acceptable in global trade, it is necessary to use the
standard units in measurement.

Need of SI units

People used certain units of measurement in their specific region. For example, pawa, pound,
sear, etc. are used for measuring mass. One pawa contains 200 grams in Kathmandu valley but
out of Kathmandu valley it contains 250 grams. Such types of variable systems of measurement
make the trade difficult. Therefore, scientist felt the need of standard units which should be
adopted all over the world. Later, SI units of measurement have been adopted in 1960 AD to
bring the uniformity in measurement throughout the world.

FACT WITH REASON

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

Types of Units

Units are classified into two groups. They are fundamental units and derived units.

a) Fundamental unit
Those units which do not depend upon other units are called fundamental units. In SI units,
there are seven fundamental units to measure seven fundamental physical quantities. The
seven fundamental quantities and their SI units with respective symbols are given in the table
below:

Modern Concept Science and Environment – 8 5

S. N. Fundamental quantity SI unit Symbol

1. Length metre m

2. Mass kilogram kg

3. Time second s

4. Temperature kelvin K

5. Current ampere A

6. Luminous intensity candela cd

7. Amount of substance mole mol

b) Derived unit Memory Tips

Except seven fundamental units, other units of measurement Speed is expressed as
depend upon fundamental units. Thus, those units which
are formed by the combination of two or more fundamental Speed = distance
units are called derived units. For examples, unit of area time
is m2, unit of volume is m3, unit of velocity is m/s, unit of unit of distance
acceleration is m/s2, unit of power is watt (W), unit of work or, unit of speed = unit of time
is joule (J), etc.
= m = ms–1
FACT WITH REASON s
So, the unit of speed (ms-1) depend

upon meter (m) and second (s).

Unit of density is a derived unit, why?

Density is expressed as

Density = mass
volume
unit of mass kg
or, unit of density = unit of volume = m3 = kgm–3

The unit of density (kg m-3) can be expressed in terms of kilogram (kg) and meter (m). So, the unit of

density is a derived unit.

Some derived physical quantities; their formula, SI unit, symbol and fundamental units
involved are given in the table below:

S. N. Physical Formula Derived SI unit Symbol Fundamental units
quantity involved

1. Area length × breadth square metre m2 m×m

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

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

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

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

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

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

8. Power work / time watt W kg×m×m/(s×s×s)

9. Pressure force/area pascal Pa kg/(m×s×s)

10. Frequency 1/time period hertz Hz 1/s

6 Measurement

Differences between fundamental units and derived units

SN Fundamental units SN Derived units

1 Those units of measurement which 1 Those units of measurement which

do not depend upon other units are are obtained from the fundamental

called fundamental units. units are called derived units.

2 These are the units of fundamental 2 These are the units of derived

quantities. quantities.

3 There are seven fundamental unit in 3 There are many derived unit in SI

SI units. Examples: meter, kilogram, Units. Examples: newton, joule, watt,

second, etc. pascal, etc.

1.6 Mass

The total amount of matter contained in a body is called its mass. Different substances have

different amount of matter. So, they have different mass. Mass is a scalar quantity. The mass

of a body remains the same all over the world. So, it is a constant quantity.

a) Relation between quantity of matter and mass: A Memory Tips

substance with less quantity of matter has less mass Total quantity of matter = mass of
and that with more quantity of matter has more mass. object.

b) Units of mass: The SI unit of mass is kilogram (kg) and its CGS unit is gram (g).

c) Standard one kilogram: Standard one kilogram is the mass of a
platinum-iridium cylinder having equal diameter and height kept at
00C at the International Bureau of Weights and Measures, held in Paris
in France. The accurate copies of standard one kilogram are prepared
to measure mass in different countries. One such copy is also present
in the Office of Weights and Measure at Balaju, Kathmandu.

d) Relation between multiples and submultiples of the kilogram Standard 1 Kg

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

e) Measurement of mass : The mass of a body can be measured by using a beam balance
or pan balance. While measuring mass in a beam balance having two pans on it, one of
its pans contains standard weight and another pan contains the substance whose mass
is to be measured. The substance is added on the pan of the beam balance until its beam
becomes horizontal.

Modern Concept Science and Environment – 8 7

Beam balance Physical balance Grocery balance Digital balance

f) Things to be remembered while measuring mass with the help of a beam balance

i) Raising and lowering of the beam must be done gently.

ii) The beam of a beam balance should be horizontal before

and after adding standard weight and the substance to be 5 KG

measured on its pans. 1 KG 2 KG

iii) Mass of the standard weight must be mentioned clearly on it. Weight

1.7 Weight

Each and every object is attracted towards the center of the earth with a certain force. This
force is called weight. Thus, the force with which a body is attracted towards the center of the
earth is called its weight. Force of gravity is the downward force. It acts on the objects whether
they are stationary, moving horizontally or moving vertically.

The force of attraction depends upon the mass (m) of the body and the
acceleration due to gravity (g) at that place. The weight of an object on the
moon is about one-sixth of that on the earth. The weight of a body at a place
on the earth is given by:

Weight (W) = mass (m) × acceleration due to gravity (g) Falling an apple
or W = mg

The SI unit of weight is newton (N) and its CGS unit is dyne. It is a vector quantity as it has
both magnitude and direction.

FACT WITH REASON

The weight of an object is more at pole and less at equator of the earth, why?

The value of acceleration due to gravity depends upon radius of the earth (R). The earth is not a perfect
sphere. Its polar radius is shorter than the equatorial radius. Due to this the value of acceleration due
to gravity at pole is 9.83 m/s2 and that at equator is 9.78 m/s2. Since weight of an object is directly
proportional to the acceleration due to gravity at a place, i.e. W α g ,the weight of an object is more at
pole and less at equator of the earth.

The weight of an object on the moon is about one-sixth the weight it would have on the earth, why?

The acceleration due to gravity on the moon is about 6 times less than that on the earth. So, the weight
of an object on the moon is about one-sixth the weight it would have on the earth.

8 Measurement

Measurement of Weight Memory Tips

Weight of an object is measured by using a spring balance. While measuring mass of an object
on the pan balance, the force of
In a spring balance, the extension of spring depends upon attraction on each of the mass and
the force with which it is pulled downward by the earth. So, standard weight is equal. Thus, a

spring balance gives us the weight of the object. pan balance measures mass. But

Weight of a 1 kg mass on the earth measuring mass is traditionally
called weight.

Since weight of a body is given by :

W = mg = 1 kg × 9.8 m/s2

∴ W = 9.8N 9.8 N

Thus, the weight of a 1 kilogram mass on the earth surface is 9.8 N. It means the
force acting on a mass of 1 kg on the earth's surface is 9.8 N.

FACT WITH REASON 1 Kg

Weight is a vector quantity, why?

Weight of a body always acts vertically downward, towards the center of the earth. As weight has
magnitude and direction, it is a vector quantity.

Differences between mass and weight.

SN Mass SN Weight

1 Mass of an object is the quantity of 1 Weight of an object is the force with

matter contained in it. which it is attracted towards the

center of the earth.

2 The SI unit of mass is kilogram (kg) 2 The SI unit of weight is newton (N).

3 The mass of an object is constant 3 The weight of an object changes with the

everywhere. change in acceleration due to gravity.

4 It is measured by using a beam 4 It is measured by using a spring

balance. balance.

ACTIVITY 1

Take a spring balance and measure the weight of different objects like pencil, pen, exercise book, book, etc.

1.8 Time

Time depends on some regular events, either natural or artificial. Sunrise and sunset are two
regular natural events. The interval between these two events gives the day time. Thus, the
duration between any two events is called time. For example, ringing of our school bell at the

Modern Concept Science and Environment – 8 9

beginning of the class and when the class is over are two events. The duration between these
two events is generally of 45 minutes.

Zenith Zenith

The particular point in the space directly above the head of an
observer standing on the earth is called zenith.

Mean Solar Day

The average of time taken by the earth to complete one rotation Zenith
on its own axis is called a mean solar day. Its duration is 24 hours.

a) Unit of time : The SI unit of time is second. Second is also
the unit of time in CGS and FPS system.

b) One second : From the definition of a mean solar day, we know that,

1 mean solar day = 24 hours = 24 × 60 minutes = 24 × 60 × 60 seconds

or 1 mean solar day = 86, 400 seconds

One second is defined as 1 of a mean solar day.
86,400

Relation between multiples and sub-multiples of a second

Multiples of time Sub-multiples of time

1 minutes = 60 seconds (s) Decisecond (ds) = 10-1 s

1 hour = 60 minutes (min) = 3600 seconds Centisecond (cs) = 10-2 s

1 day = 24 hours (hr) = 86,400 seconds Millisecond (ms) = 10-3 s

1 week = 7 days = 7 × 86,400 seconds Microsecond (µs) = 10-6 s

1 year = 365 days = 365 × 86,400 seconds Nanosecond (ns) = 10-9 s

Measurement of time

In our daily life, it is very essential to measure time. Time is measured using different
instruments. Thus, the instrument which measures time is called a clock.

Different time measuring devices

a) Pendulum clock

In a pendulum clock, the metallic bob is suspended from a rigid support
by a thread. The bob has a to and fro motion called simple harmonic
motion. One complete to and fro motion is called an oscillation. The time
taken by a pendulum for one oscillation is known as its time period. The
time period of a simple pendulum depends on its length.

The length of a pendulum changes with the change in temperature. So,

there is fluctuation in time measured by a pendulum clock. Pendulum clock

10 Measurement

FACT WITH REASON

There is fluctuation in time measured by a pendulum clock, why?

In a pendulum clock, time is measured by oscillation of the pendulum. Oscillation of a pendulum depends
on its length. The length of a pendulum changes with the change in temperature which affects the time
taken to complete one oscillation. So, there is fluctuation in the time measured by a pendulum clock.

b) Mechanical wristwatch

A mechanical wristwatch has a balance-wheel instead of a pendulum. It measures time
on the basis of motion of the balance-wheel.

c) Quartz watch (electronic wrist watch) Memory Tips
Quartz watch has crystals of quartz.

These crystals regularly vibrate very Quartz is a mineral mainly

fast. Quartz watch measures time composed of silicon dioxide. It is
on the basis of vibration of quartz the second most abundant mineral
crystals. A quartz clock is much more after feldspar on the earth. Quartz watch
accurate than a pendulum clock.

d) Atomic watch Automic watch

Atomic watch is the most accurate time measuring device. It works
on the basis of frequency associated with the emission of radiation
from Cs-133 atoms. One second is defined as the time taken by the
radiation from a cesium-133 atom to complete 9,192,631,770 cycles
of oscillation. Vibrations of cesium atoms are very regular. So, the
time measured by an atomic watch is very accurate. It is said that in
an atomic watch, there is a fluctuation of one second in 3000 years.

Memory Tips

In ancient times, sand clock and sundials were used to measure time. A sand clock works on the
principle that all the sand particles from upper chamber fall into the lower chamber in a fixed
time. This fixed duration was the unit to measure time.

Sundial was used long ago to measure the time of the day. It works on the principle that as the
position of the sun in the sky changes, the length of shadow cast by an object also gets changed.

ANSWER WRITING SKILL

1. What are fundamental and derived physical quantities? Write any three examples of each.

Ans: Those physical quantities which are independent of each other are called fundamental physical
quantities. For example, mass, length, time, etc.

Those physical quantities which are derived from the fundamental physical quantities are called
derived physical quantities. For example, area, volume, acceleration due to gravity, etc.

2. On which fundamental units does the unit of power depend?

Ans: Power = work (w) = force (f ) × displacement (s) = mass (m) × acceleration (a) × displacement (s)
time (t) time (t) time (t)

Modern Concept Science and Environment – 8 11

Unit of Power = unit of mass (m) × unit of acceleration (a) × unit of displacement (s)
unit of time (t)

or watt = kg u×nmits/so2f×pmow=ekr,gi.me.2/ws3a=ttk(gWm)2sd–e3pends upon the fundamental units : kilogram (kg),
Therefore, the

metre (m), and second (s).

3. The weight of an object is less on the moon and more on the earth, why?

Ans: The weight of an object depends upon the mass of the object and acceleration due to gravity. The
value of acceleration due to gravity on the earth is 9.8 m/s2 and that on the moon is 1.63 m/s2. Since
the value of acceleration due to gravity on the earth is more than on the moon. So, the weight of an
object on the earth is more than that on the moon.

4. Write any two differences between a mechanical watch and quartz watch.

Ans: Differences between a mechanical watch and quartz watch

S.N. Mechanical watch S.N. Quartz watch

1 Mechanical watch measures time on the 1 Quartz watches measure time on the

basis of motion of the balance-wheel. basis of vibration of quartz crystals

2 It is less accurate. 2 It is more accurate

5. Convert one day into seconds.
Ans: 1 day = 24 hours (hr) = 24×60 minutes = 24×60×60 seconds = 86,400 seconds
6. Convert 2.5 kg into gram
Ans: Given, mass = 2.5 kg

Now, we know that 1 kg = 1000 grams
So, 2.5 kg = 2.5 × 1000 = 2500 grams
7. Naina has a mass of 40 kg. Calculate her weight.
Ans: Given, mass (m)= 40 kg
Acceleration due to gravity (g) = 9.8 m/s2
Weight (W) = ?
Now, weight (W) = mass (m) × acceleration due to gravity (g) = 40 × 9.8 = 392 N
8. Convert 0.01 kg into gram.
Ans: We know that, 1 kg =1000 g. So, 0.01 kg = 0.01 × 1000 g = 10 g
9. Convert 1 year into seconds
Ans: 1 year = 365 days = 365 × 24 hours = 365× 24 × 60 minutes = 365× 24 × 60 × 60 seconds
= 31536000 seconds
10. Calculate the weight of a person having mass of 70 kg. (g = 9.8 m/s2)
Ans: Here, mass of the person (m) = 70 kg
Acceleration due to gravity (g) = 9.8 m/s2
Now, weight of the person,
W = mg = 70 × 9.8 = 686 N

12 Measurement

STEPS EXERCISE

STEP 1

1. Fill in the blanks with appropriate words.
a) Quantities such as length, area, volume are called …….. quantities.
b) …… is a particular point in the space directly above an observer.
c) Pendulum clock measures time on the basis of ……. of pendulum.
d) Quartz watches have …… of quartz.
e) …… clocks are the most accurate.
f) ……. is the force with which the earth pulls a body toward its center.

2. Write True for the correct and False for the incorrect statements.
a) The measurable quantities are called physical quantities.
b) Volume is an example of fundamental quantity.
c) Mole is the SI unit of amount of substance.
d) Mass of a body cannot be zero.
e) Weight of a given substance does not change with place.
f) The SI unit of weight is newton (N).

STEP 2

3. Answer the following questions in one word.

a) What types of quantities are pain, sadness, happiness, etc.

b) What is called to the standard quantity used for comparison while measuring a
substance?

c) What is SI unit of volume?

d) What type of quantity is frequency?
e) Which type of unit is meter/second?

4. Write any two differences between: b) Fundamental and derived unit
a) Fundamental and derived quantity d) Mass and weight
c) Pendulum clock and quartz clock

5. Give reasons.
a) Standard units are used in measurement.
b) Watt (W) is a derived unit.
c) The atomic clock is suitable for measuring time.
d) There is fluctuation in time measured by a pendulum clock.
e) The weight of an object is more at pole and less at equator of the earth.
f) The weight of an object on the moon is about one-sixth the weight it would have
on the earth.
g) In average, the weight of 1 kilogram mass on the earth surface is 9.8 N

Modern Concept Science and Environment – 8 13

6. Answer the questions with the help of the given figure.

a) Given figure shows the weight of a 1 kg mass 0N 1.6N 9.8N

measured in space, on the moon and on the earth. Space Moon Earth

i) How much is the weight on the earth, moon and

in space.

ii) Where is the weight measured maximum? Write with reason.

b) H ow much is the weight measured by the spring balance if the value of
acceleration due to gravity is 9.8 m/s2?

c) Name the instruments shown in the given figure and write their 1 kg
specific features.

STEP 3 i) ii)

7. Answer the following questions.

a) Define:

i) Mass ii) Standard one kilogram

iii) Weight iv) Time

b) What is measurement? Write down its importance in our daily life.

c) What are physical and non- physical quantities? Give any three examples of each.

d) What are fundamental and derived units? Write any two examples of each.

e) What is SI units? Give any two examples.

f) How is ‘standard one kilogram’ defined in SI units?

g) What are the fundamental units involved in a unit of the given derived quantities?

i) Density ii) Acceleration iii) Force

iv) Pressure v) Work

h) What is the relation between the quantity of matter and mass?

i) Write down the factors that affect weight of a body.

8. Numerical Problems:

a) Convert the followings:

i) 0.25 kg into gram Ans: 250 g

ii) 2.5 kg into gram Ans: 2500 g

iii) 2500 kg into grams Ans: 2500000 g

b) Convert the followings:

i) 1 day into seconds Ans: 86400 s

ii) 1 week into seconds Ans: 604800s

iii) 1 month into second Ans: 2592000 s

c) Solve:

i) Calculate the weight of a person having mass of 50 kg. (g = 9.8 m/s2) Ans: 490 N

ii) What is the weight of your science book if its mass is 250 g. (g = 9.8 m/s2) Ans:2.45N

14 V e loc i t yEsatinmdatAecdcteealcehrinagtpi oerniods Theory Practical
UNIT 4 1

2 Velocity and Acceleration

Syllabus issued by CDC Body in motion
 Introduction to rest and motion
 Uniform motion and non-uniform motion
 Reference point, vectors and scalars
 Average velocity and relative velocity
 Acceleration and retardation
 Equations related to velocity and acceleration and numerical problems

LEARNING OBJECTIVES

At the end of this unit, students will be able to:
 explain average velocity and relative velocity.
 introduce acceleration and retardation.
 write and apply equations related to velocity and acceleration.
 solve numerical problems related to velocity and acceleration.

Key terms and terminologies of the unit

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

2. 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.

3. Reference point : The fixed point with respect to which rest and motion of an object can be studied
is called a reference point.

4. Uniform motion : A body is said to have a uniform motion when it covers equal distance in equal
interval of time.

5. Non-uniform motion : A body is said to have a non-uniform motion when it covers unequal distance in
equal interval of time.

6. Scalar quantity : A physical quantity which has only magnitude but no direction is called a scalar quantity.

7. Vector quantity : A physical quantity which has both magnitude and direction is called a vector quantity.

8. Distance travelled : The actual length of the path travelled by a moving body, irrespective of its direction
is called the distance travelled by the body.

9. Displacement : The shortest distance between the initial and final position of a moving body in a
particular direction is called displacement.

10. Speed : The total distance travelled in per unit time is called speed.

11. Velocity : The displacement of a body per unit time is called its velocity.

12. Average velocity : The arithmetic mean of the initial velocity and final velocity over a given period of
time is called average velocity.

Modern Concept Science and Environment – 8 15

13. Relative velocity : The velocity of a body relative to a second moving body is called relative velocity.

14. Acceleration : The rate of change of velocity of a body is called acceleration.

15. Retardation : The rate of decrease in velocity is called negative acceleration or retardation.

16. Equation of motion : The relationship between initial velocity (u), final velocity (v), distance travelled (s),
acceleration (a) and time taken (t) is called an equation of motion.

2.1 Introduction

Observe in your surrounding. You can see various things. Among them some can move and
some cannot. A body is said to be at rest if it does not change its position with respect to its
surrounding. For example, a book on the table does not change its position with respect to the
table. So, the book is said to be in a state of rest. Similarly, school, house, bench, desk, chair,
etc. are some examples of the resting objects. The fixed point with respect to which rest and
motion of an object can be studied is called a reference point.

Animals, human beings and other objects in our surrounding can move from one place to
another. They are called moving objects. Thus, a body is said to be in motion if it can change
its position with respect to its surrounding. For example, a football kicked by the player,
falling apple, moving vehicle, rainfall, flying birds, walking animals, etc. We need to apply an
external force to change the state of rest and state of motion. In this unit, we will discuss about
rest and motion, speed, velocity, acceleration and equation of motion.

ACTIVITY 1

Observe in your surrounding carefully and write down the name of any five objects which are in the
state of motion and in the state of rest.

Rest and motion are relative terms

When we are on the seat Memory Tips

of a moving bus, we are There is nothing at absolute rest. Rest and motion
in the state motion with Everything in this world, from the
respect to the trees or smallest particle to the largest
buildings present along galaxies is in motion. An object at
the road side. However, rest with respect to one reference
if we compare our point may be in motion with
position with respect to respect to another reference point.
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.

FACT WITH REASON

Rest and motion are called relative terms,why?
A body may be at rest with respect to one reference point and may in motion with respect to another
reference point at the same time. So, rest and motion are the relative terms.

16 Velocity and Acceleration

2.2 Uniform Motion and Non-uniform Motion

Uniform motion

A body is said to be in a uniform motion when it covers equal distance in equal interval of
time. For example, a car moving in a straight line with a constant speed has uniform velocity.

12m 1s 12m 12m 12m 4s
0s 2s 3s

A uniform motion

Non-uniform motion or variable motion

A body is said to be in a non-uniform motion when it covers unequal distance in equal interval
of time. For example, the motion of a freely falling object is in non- uniform.

8m 1s 20m 10m 3s 22m
0s 2s 4s

A non-uniform motion

FACT WITH REASON

Motion of a falling object towards the earth is a variable motion (neglecting the air resistance), why?

Gravity of the earth accelerates the falling body towards the earth's surface. In average, the acceleration
due to gravity of the earth is 9.8 m/s2. So, every second a falling body moves 9.8 m/s faster. So motion
of a falling object towards the earth is a variable motion.

ACTIVITY 2

Observe in your surrounding carefully and write down the name of objects which are in the state of
uniform motion and in non-uniform motion.

2.3 Scalar Quantities and Vector Quantities

Scalar quantity

Those physical quantities which have only magnitude are called scalars or scalar quantities.
For example, distance, speed, mass, work, energy, etc. A scalar quantity does not need a
direction to express it.

Vector quantity

Those physical quantities which have both magnitude and direction are called vectors or

vector quantities. A vector quantity requires both magnitude and direction for its complete
description. For example, displacement, force, weight, velocity, etc.

Modern Concept Science and Environment – 8 17

Differences between vectors and scalars

SN Vectors SN Scalars

1 Vector quantities have both magnitude 1 Scalar quantities have only magnitude.
and direction.

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

zero or negative.

3 Addition and subtraction of the vectors 3 Addition and subtraction of the scalars

can be done by vector algebra. can be done by simple algebra.

2.4 Distance and Displacement

Distance AD
8m

The actual length of the path travelled by a body is called distance. 4 m 4m

The SI unit of distance is meter (m). It is a scalar quantity. In

distance we measure actual length of the path covered by a B 8m C
moving body. We do not account direction. For example, If a man Distance

travels 8 m from point B to point C, 4 m from point C to point D and then 8 m from point

D to point A, then the total length of the path travelled by the man = BC + CD + DA

Or, Distance = 8 m + 4 m +8 m = 20 m.

Displacement

The shortest distance between the initial position and the final position of a moving body in a
particular direction is called its displacement. It is a vector quantity. Its value may be positive,
negative or zero. For example, when a man travels from a point B to another point A towards
the north, then the displacement (BA) of the man is 4 m towards north.

FACT WITH REASON

Is it possible to have a zero displacement but non-zero distance?

In case of a body moving in a circular track, after one complete revolution, the distance travelled
by the body is equal to the circumference of the track i.e.,2πr, where r is radius of the track. But the
displacement is zero.

Differences between distance and displacement.

SN Distance SN Displacement

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

by a body is called distance. position and the final position of a

moving body in a particular direction is

called its displacement.

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

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

18 Velocity and Acceleration

2.5 Speed and Velocity

Speed

The speed of a body gives an idea of how fast a body is moving. With the help of speed we can

compare the distance travelled by the two bodies in a given interval of time. For example, if a

car covers 1 km distance in one minute and another car covers the same distance in 2 minutes,

then the first car has more speed than the second car. Thus, the rate of change of distance is

called speed.

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

You might have seen a meter fitted on the dashboard of cars, buses and other vehicles, which

records the speed. It is called speedometer.

Its SI unit is m/s and CGS unit is cm/s. The speed of the fast moving bodies like cars, bus, trains,
aeroplanes, etc. is expressed in kilometer per hour written as km/h. When the speedometer in
a car indicates 72 km/h, it indicates that the car covers a distance of 72 kilometer in one hour.

FACT WITH REASON

Speed is a scalar quantity, why?
Speed has only magnitude but it does not have direction. So,speed is a scalar quantity.

Velocity

Velocity is same as speed except direction of motion. Velocity is a physical quantity which has
both direction of motion and the distance covered. Thus, the rate of change of displacement
is called velocity.

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

It is a vector quantity. The unit of velocity is same as that of speed, i.e. In SI system, unit of
velocity is m/s.

FACT WITH REASON

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

Differences between speed and velocity

SN Speed SN Velocity

1 Speed is the rate of change of distance. 1 Velocity is the rate of change of
displacement.

2 It is a scalar quantity. 2 It is a vector quantity.
3 It cannot be zero. 3 It can be zero.

Modern Concept Science and Environment – 8 19

Solved Numerical 2.1

Find the speed of a car which covers 800 m distance in 40 seconds.

Solution:

Distance covered by the car (s) = 800 m

Time taken = 40 s

Speed = ?

We know, speed = distance travelled (s) = 800 = 20 m/s
time taken (t) 40

∴ The speed of car is 20 m/s.

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. Thus, the mean of the initial velocity and final velocity over a given
period of time is called average velocity.

Velocity (vav) = Initial velocity (u) + Final velocity (v)
2

But if the velocity of a body in a particular direction does not change continuously at a uniform
rate the average velocity is given by

Average velocity (v) = Total displacement
Total time taken

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

In the given figure, total displacement (s) = 3 m + 4 m + 2 m + 4 m = 13 m

Total time (t) = 4 s

∴ The average velocity = Total displacement (s) = 13 = 3.25 m/s
Total time taken (t) 4
Solved Numerical 2.2

Calculate the average velocity of a bus which covers 7500 m distance towards east in 5
minutes.

Solution:
Total displacement = 7500 m

Total time taken = 5 minutes = 5 × 60 second = 300 s

We know, average velocity (v) = Total displacement (s) = 7500 = 25 m/s
Total time taken (t) 300

∴ The average velocity of the bus is 25 m/s.

20 Velocity and Acceleration

Relative velocity

The calculated value of a velocity depends upon the observer when one is moving with respect
to another. For example, when two cars are moving in the same direction at a high speed on
the highway, then the observer along the road side observes that both the cars are moving
with high velocity. But relative to one another, the two cars hardly move at all. Thus, the
velocity of one body with respect to another body is called relative velocity.

Relative velocity

a) Relative velocity for the bodies moving in the same direction

When two bodies A and B are moving along a straight
line in the same direction, the magnitude of the relative
velocity of A with respect to (w.r.t.) B is given by

VAB = VA – VB Bodies moving in the same direction
VAB is the relative velocity of the object A as seen from
the object B. Memory Tips

In the given figure, the If the bodies are moving with the
same velocity (i.e. VA = VB, their
velocity of the police car relative velocity will be zero.

with respect to the sport car 150km/hr 120km/hr i.e. VAB = VA – VB = VA – VA = 0

is given by VPS = VP – VS Bodies moving in the same direction

VPS = 150 – 120 = 30 kmh–1

Thus, the velocity of the police car as seen from the sport car is 30 kmh–1.

FACT WITH REASON

When two buses are moving in the same direction with the same velocity then a passenger in one bus
finds another bus at rest, why?

When two buses are moving in the same direction with the same velocity then the relative velocity is
zero. In this condition, one bus does not change its position with respect to another. So, a passenger in
one bus finds another bus at rest.

b) For the bodies moving in the opposite direction

When two bodies A and B are moving along a straight
line in the opposite direction, the magnitude of the
relative velocity of A w.r.t. B is equal to the sum of the
magnitude of their velocities.

i.e. VAB = VA – (–VB) = VA + VB Bodies moving in the opposite direction

Modern Concept Science and Environment – 8 21

In the given figure, the velocity of helicopter 180km/hr
with respect to the sport car is given by
150km/hr 120km/hr
VHS = VH + VS
VHS = 180 + 120 = 300 kmh–1

Thus, the velocity of the helicopter as seen from the sport car is 300 kmh–1.

Solved Numerical 2.3

The velocity of car A is 10 m/s towards north and the velocity of the car B is 15 m/s towards

south. If both the cars start from the same line, calculate: A B

i) the distance travelled by each of them in 2 minutes

ii) the relative velocity 10 m/s 15 m/s
iii) the distance between them after 1 minute

Solution:

Velocity of car A (VA) = 10 m/s

Velocity of car B (VB) = 15 m/s

i) Time (t) = 2 minutes = 2× 60 = 120 s

Distance travelled by the car A in 2 minutes = VA × t = 10 × 120 = 1200 m
Distance travelled by the car B in 2 minutes = VB × t = 15 × 120 = 1800 m
ii) Relative velocity

VAB = VA + VB = 10 + 15 = 25 m/s
iii) Time (t) = 1 minute = 60 s

The distance between two cars after 1 minutes

= Relative velocity × time = 25 × 60 = 1500 m

2.6 Acceleration

A moving object may not have uniform velocity all the time. Sometimes, its velocity increases
and sometimes decreases. For example, a bus starts from the rest and after a certain interval
of time 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 and the bus stops. In this example, the bus is under acceleration. That is, the
velocity of the bus changes with time. Thus, the rate of change in velocity is called acceleration.

Acceleration = Change in velocity
Time taken

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

or, a = v – u
t

The SI unit of acceleration is m/s2 and it is a vector quantity.

22 Velocity and Acceleration

Meaning of positive acceleration Memory Tips

An object has acceleration of 2 m/s2 means the velocity of When the velocity of an object

the object increases by 2 m/s in every second. increases (i.e., v > u), it is under

FACT WITH REASON positive acceleration.

A body in a uniform linear motion is not under acceleration but that in a uniform circular motion is
under acceleration, why?

In a uniform linear motion, the change in velocity is zero and the direction of motion
is fixed. But, in case of a uniform circular motion, the direction of motion changes
continuously. So, a body in a uniform linear motion is not under acceleration but
that in a uniform circular motion is under acceleration.

The motion of an athlete running in a circular track with a constant speed is an accelerated motion, why?

When an athlete runs in a circular track with a constant speed, then the direction of athlete in the track
changes continuously. Such motion is called an accelerated circular motion.

Solved Numerical 2.4

A car moving with a speed of 15 m/s speeds up to 30 m/s in 5 seconds. Calculate its
acceleration.

Solution:

Initial velocity of the car (u) = 15 m/s Final velocity of the car (v) = 30 m/s

Total time taken = 5 s Acceleration (a) = ?
From the formula, acceleration (a) = v – u = 30 – 15 = 3 m/s2

t5
∴ Acceleration of the car is 3 m/s2.

Negative acceleration or Retardation

If final velocity (v) of a moving body is less than the initial velocity (u), then the acceleration
comes in negative. It can be expressed as:

Acceleration (a) = Final velocity (v) – Initial velocity (u) = Negative quantity
Time taken (t) Time taken

= Negative quantity

The decrease in velocity of a body in motion with time Memory Tips

causes negative acceleration. Thus, the rate of decrease in When the velocity of an object
velocity is called negative acceleration, or retardation. For decreases (i.e., v < u), it is
example, a ball thrown vertically upward from the earth under negative acceleration, or
has a negative acceleration; a football rolling on the plane retardation.

football ground also has a negative acceleration.

Meaning of negative acceleration
An acceleration of – 7 m/s2 means that the velocity of the body decreases by 7 m/s in every second.

Modern Concept Science and Environment – 8 23

Solved Numerical 2.5

A car has an initial speed of 45 m/s at a point A. When brakes are applied then after 4
seconds its speedometer records a speed of 15 m/s. Find acceleration of the car.

Solution:

Initial velocity of the car (u) = 45 m/s Final velocity of the car (v) = 15 m/s

Total time taken = 4 s Acceleration (a) = ?
From the formula, acceleration (a) = v – u = 15 – 45 = – 30 = – 7.5 m/s2

t 44

∴ Retardation of the car is 7.5 m/s2.

2.7 Equations of Motion

When an accelerated body travels in Memory Tips
a straight line, then the relationship
between the initial velocity (u), final To solve the numerical problems based on motion, we
velocity (v), distance travelled (s), should remember that:
acceleration (a) and time taken (t) is
called the equation of motion. There are 1. If a body starts from rest, its initial velocity, u = 0
three equations of motion. They are:
2. If a body comes to rest, its final velocity, v = 0
i) v = u + at
3. If a body moves with a uniform velocity, its
ii) s = ut + 1 at2 acceleration, a = 0.
2
4. Acceleration due to gravity on a freely falling object
iii) v2 = u2 + 2as towards the earth surface = 9.8 m/s2.

Derivation of the first equation of motion: v = u + at

(Relationship between initial velocity ‘u’, final velocity ‘v’, acceleration ‘a’ and time ‘t’)

Suppose a body has initial velocity ‘u’ and uniform acceleration ‘a’ for time’t’. After some time
if its final velocity becomes ‘v’, then,

From the definition of acceleration, we have,

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

or, at = v – u

∴ v = u + at
Solved Numerical 2.6

The retardation of a car due to brakes is 2.5 m/s2 and the car stopped in 10s by applying
brakes. Calculate the initial velocity of the car.

Solution:
Retardation = 2.5 m/s2 (i.e. acceleration (a) = -2.5 m/s2)
Final velocity (v) = 0 [Since the car comes to rest]

24 Velocity and Acceleration

Time taken (t) = 10 s

Initial velocity (u) = ?

We have, v = u + at

or, 0 = u + (– 2.5) × 10

or, 0 = u – 25

or, u = 25

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

Derivation of second equation of motion : s = ut + 1 at2
2
(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’. Then,

Distance travelled = Average velocity × Time

or, s = v + u × t
2

Substituting the value of ‘v’ from the first equation of motion,

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

or, s = 2u + at × t
2

or, s = 2u + at × t
22

or, s = 2ut + at2
22

∴ s = ut + 1at2
2

It gives the distance travelled by a body in time ‘t’.

Solved Numerical 2.7

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

Solution:

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

Acceleration (a) = 5 m/s2

Time taken (t) = 5 seconds

Distance travelled (s) = ?
We have, s = ut + 1at2 = 0 × 5 + 1 × 5 × 52 = 62.5 m

22
∴ The distance travelled by the body in 5s is 62.5 m.

Modern Concept Science and Environment – 8 25

Derivation of 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’. Then,

Distance travelled = Average velocity × Time

or, s = v + u × t ............................. (i)
2

From the definition of acceleration,

a=v–u
t
v – u
or, t = a

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

or, s= v+u × v–u
2 a

or, s = v2 – u2
2a

or, 2as = v2 – u2

∴ v2 = u2 + 2as
Solved Numerical 2.8

A car was moving with an initial velocity of 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:

Initial velocity (u) = 27 m/s

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

Acceleration (a) = - 0.9 m/s2

Distance covered (s) = ?

We have,

v2 = u2 + 2as

or, s = v2 – u2 = 0 – (27)2
2a 2 × (–0.9)

or, s = – 729 = 405 m
– 1.8

∴ The distance covered by the car before coming to rest is 405 m.

26 Velocity and Acceleration

ANSWER WRITING SKILL

1. What is a reference point?
Ans: The fixed point with respect to which rest and motion of an object can be studied is called a

reference point.
2. Define acceleration and retardation with their SI unit.
Ans: The rate of change in velocity is called acceleration. Its SI unit is m/s2. The negative acceleration, or

the rate of decrease in velocity is called retardation. Its SI unit is also m/s2.
3. Write any two differences between acceleration and retardation.
Ans: Differences between acceleration and retardation are:

S.N. Acceleration S.N. Retardation

1 The rate of change in velocity is 1 The negative acceleration, or the rate of

called acceleration. decrease in velocity is called retardation.

2 It is represented by ‘a’. 2 It is represented by‘-a’.

4. Write any two differences between average velocity and relative velocity.

Ans: Differences between average velocity and relative velocity are:

S.N. Average velocity S.N. Relative velocity

1 The mean of the initial velocity and 1 The velocity of one body with respect to

final velocity over a given period of another body is called relative velocity.

time is called average velocity.

2 Average velocity depends upon the 2 Relative velocity depends upon the

initial and final velocity of the body. velocity and direction of the moving

bodies.

5. Distance, speed, mass, time, work, etc. are called scalar quantities, why?

Ans: Distance, speed, mass, time, work, etc. are called scalar quantities because they have magnitude
but no direction.

6. What are constant and variable velocities?

Ans: If a body covers equal displacement in equal interval of time, the velocity of the body is called
constant velocity. It is also called a uniform velocity. If a body does not cover equal displacement
in equal interval of time, the velocity of the body is called variable velocity.

7. Under what condition the acceleration of a moving object becomes zero?

Ans: Acceleration of a moving object becomes zero if it is moving with a uniform velocity.

8. Acceleration of an object with uniform velocity is zero. Why?

If an object is moving with a uniform velocity, then there is no change in velocity. It means that
initial velocity is equal to the final velocity of the body. Hence, acceleration becomes zero.

Modern Concept Science and Environment – 8 27

9. A running horse covers a distance of 1200 m in 3 minutes. What is the speed of the horse?

Solution: Total distance travelled(s) = 1200 m

Total time taken (t) = 3 minutes = 3 × 60 second = 180 s

Speed of the horse = ?

From the formula, speed = Total distance = 1200 = 6.667 m/s
Total time taken 180

∴ The speed of the horse is 6.667 m/s.

10. A bus starts from rest and attains a velocity of 20 m/s after 5 seconds. Find its acceleration.

Solution: Total time taken = 5 s

Initial velocity of the bus (u) = 0 m/s

Final velocity of the bus (v) = 20 m/s

Acceleration of the bus (a) = ?

From the formula,

∴Ac celAercacteiolenra(ati)o=nvof–ttuhe=b2u0s5–is04=m4 /s2.

11. A ‘car A’ is moving towards east with a velocity of 70 km/h and another ‘car B’ is moving towards
west with a velocity of 50 km/h. Find their relative velocity. Also, find their relative velocity if they
move in the same direction.

Solution: Velocity of car A (VA) = 70 km/h
Velocity of car B (VB) = 50 km/h
Relative velocity (VAB) = ?
When both the cars are moving in the opposite direction

Relative velocity (VAB) = VA + VB = 70 + 50 = 120 km/h
When both the cars are moving in the same direction

Relative velocity (VAB) = VA – VB = 70 – 50 = 20 km/h

STEPS EXERCISE

STEP 1

1. Fill in the blanks with appropriate words.
a) Velocity………… in freely falling body.
b) The distance covered by a body in unit time in a specified direction is called…….
c) ……. is produced on a body whenever there is change in its velocity.
d) The SI unit of acceleration is …….....
e) If a body is moving with a constant velocity then it has ……. acceleration.
f) The negative acceleration is called …….....
g) The velocity of a body A with respect to another body B in motion is denoted
by......... .

28 Velocity and Acceleration

2. Write True for the correct and False for the incorrect statements.
a) A freely falling stone towards the earth has a uniform velocity.
b) Two cars A and B are moving with the same speed in the same direction. A
passenger in the car A finds that the car B is at rest.
c) In SI system the acceleration due to gravity is 8.9 m /s2.
d) When a body starts from rest, its final velocity is zero.
e) The SI unit of speed is m/s.
f) A ball thrown vertically upward is under retardation.
g) Acceleration is a scalar quantity.

STEP 2

3. Answer the following questions in one word.
a) How much is the relative velocity of two cars moving along a straight path with
same velocity?
b) Which type of motion is of clock's needle?
c) What is called to the total distance travelled by a body per unit time?
d) What is called to the rate of change of velocity?
e) What is the rate of decrease of velocity of a body called?
f) How much is the initial velocity of a body which is dropped from a certain height
from the earth surface?

4. Write any two differences between:
a) Scalar quantities and vector quantities
b) Distance travelled and displacement
c) Speed and velocity
d) Uniform velocity and variable velocity
e) Positive acceleration and negative acceleration

5. Give reasons.
a) Rest and motion are relative terms.
b) Motion of a falling object towards the earth is a variable motion (neglecting the
air resistance).
c) It is possible to have a zero displacement but non-zero distance travelled.
d) Speed is a scalar quantity.
e) Velocity is a vector quantity.

Modern Concept Science and Environment – 8 29

f) When two buses are moving in the same direction with the same velocity then a
passenger in one bus finds another bus at rest.

g) Motion of an athlete running in a circular track with a constant speed is an
accelerated motion.

6. Answer the questions with the help of the given figure. Ans: 5 m/s
a) Find the relative velocity of the jeep with respect to the cyclist.

STEP 3

7. Answer the following questions.

a) What are rest and motion?

b) What do you mean by a reference point?

c) Write down SI unit of the followings:

i) Distance ii) Displacement

iii) Velocity iv) Acceleration

d) Define:

i) Uniform velocity ii) average velocity

iii) relative velocity

e) When does a body have:

i) positive acceleration ii) negative acceleration

iii) zero acceleration

f) How is the relative velocity calculated when:

i) the two bodies A and B are moving in a straight line in the same direction.

ii) the two bodies A and B are moving in a straight line in the opposite
direction.

g) In which condition the relative velocity of the two bodies moving in the same
direction becomes zero?

h) Derive the following equations of motion:

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

a) A tiger covers a distance of 600 m in 1.5 minutes. What is the speed of the tiger?
Ans: 6.67 m/s

b) A motor bike covers a distance of 1.5 km on a straight road in 2 minutes. Find

average velocity of the motor bike. Ans: 12.5 m/s

30 Velocity and Acceleration

c) A car is moving with a speed of 15 ms-1. How long does it take to cover a distance

of 1.2 km? Ans: 80 seconds

d) A car starts from rest and gains a velocity of 20 m/s in 10 s. Calculate

acceleration. Ans: 2m/s2

e) A vehicle accelerates with 0.4 m/s2. Calculate the time taken by the vehicle to

increase its speed from 20 m/s to 40 m/s. Ans: 50 s

f) A bike is moving with a velocity of 10 m/s. If its acceleration is 1.2 m/s2 for 10 s,

calculate the final velocity of the bike. Ans: 22 m/s

g) A bus starts from rest and attains an acceleration of 2 m/s2 after 10 seconds. Find

the distance covered by the bus in that time. Ans: 100 m

h) A train is moving with the velocity 10 m/s. It attains an acceleration of 4 m/s2 after

5 seconds. Find the distance covered by the train in that time. Ans: 10 m

i) A car moving along a straight highway at a speed of 144 km/h is brought to a stop
within a distance of 200 m.

i) What is the retardation of the car? Ans: 4m/s2

ii) How long does it take for the car to stop? Ans: 10 s

j) A bus ‘A’ is moving towards east with a velocity of 170 km/h and another bus ‘B’
is moving towards west with a velocity of 70 km/h. Find their relative velocity.
Also, find their velocity if both are moving in the same direction. Ans: 240 km/h, 100

km/h.

k) A motorcycle ‘A’ and another motorcycle ‘B’ are moving in the same direction

with the velocities 60 km/h and 80 km/h respectively. Find the relative velocity of

the motorcycle B with respect to car A. Also, find their velocity if both motorcycles

move in the opposite direction. Ans: 20 km/h, 140 km/h.

l) A body moves in the east with the velocity of 25 25 m/s 10 m/s
m/s. Another body B moves in the same direction
with a velocity of 10 m/s. If both of them had
started from the same point then find:

i) the velocity of A w.r.t. B. Ans: 15 m/s

ii) the distance covered by each in 30 seconds. Ans: 750m, 300m

ii) the distance between them after 1 minute. Ans: 900 m

Estimated teaching periods Theory MProadcetrincCaloncept Science and Environment – 8 31
3 1
UNIT
Simple Machine
3

Syllabus issued by CDC Fishing

 Introduction to simple machines
 Advantages of simple machines
 Basic principle of simple machines
 Lever and its types
 Mechanical advantage (MA), Velocity ratio (VR) and Efficiency (η) of simple machines
 Numericals related to MA, VR and η of lever

LEARNING OBJECTIVES

At the end of this unit, students will be able to:
 introduce lever and state its principle.
 explain the types of lever and introduce mechanical advantage (MA), velocity ratio (VR) and

efficiency (η) of lever.
 calculate MA, VR and η of lever.

Key terms and terminologies of the unit

1. Simple machine : The device which makes our work easier, faster and more convenient is
called a simple machine.

2. Compound machine : The machine which has a complex structure and made from two or more
simple machines working together is called a compound machine.

3. Load : Load is the weight which has to be lifted by a simple machine.

4. Load distance : The distance moved by the load in a simple machine is called load distance.

5. Effort : Effort is the force applied directly to a simple machine to move the load or to
do work.

6. Effort distance : The distance moved by effort in a simple machine is called effort distance.

7. Mechanical advantage (M.A.) : The ratio of the load lifted to the effort applied in a simple machine is called

mechanical advantage.

8. Velocity ratio (V.R.) : The ratio of the distance moved by effort to the distance moved by load in a

simple machine is called velocity ratio.

9. Input work : The work done on a simple machine by a given effort is called input work.

10. Output work : The work done by a simple machine on the load is called output work.

11. Efficiency : The percentage ratio of output work to input work is called efficiency of a
machine.

12. Practical machine : he machine which is useful in our daily life is called a real or practical
machine.

13. Perfect simple machine : Ahypothetical frictionless machine in which total input work is converted into output
work without wastage of energy is called an ideal or a perfect simple machine.

32 Simple Machine

14. Lever : A lever is a rigid bar which is capable of rotating about a fixed axis called
15. Principle of lever fulcrum.

: The principle of lever states that, “at an equilibrium condition the product
of effort and effort arm is equal to the product of load and load arm.”

3.1 Introduction

Present age is the age of tools and machines. They make our work easier and faster. Varieties
of tools are used in our daily life. Among them some machines are simple in structure while
others are complex. Those machines which are simple in structure are called simple machines.
For example, sharp knife is used for cutting things, pulley is used to lift loads, wheel and axle
is used to multiply effort, slanted surface is used to load and unload the things easily, etc.
Thus, those devices which make our work easier, faster and more convenient are called simple
machines. Examples: scissors, knife, nut cracker, bottle opener, spoon, pulley, screw. These
machines need muscular energy to work.

Scissors Beam balance Wheelbarrow Pulley Screw Axe

Some simple machines

Most of the modern machines are compound in their structure. They are made by the
combination of two or more simple machines. So, the machine which has complex structure
and made from two or more simple machines working together is called a compound machine.
For example, bicycle, motor bike, sewing machine, etc. Compound machines use different
types of energy like electrical energy, chemical energy, etc. In this unit, we will describe about
the lever.

3.2 Advantages of Simple Machines

Simple machines make our work easier, faster and more convenient by the following ways:
a) Simple machines help to multiply effort.
b) They help to change the direction of effort.
c) They help to increase the speed of work.
d) They transfer the applied force.
e) They help to do work safely.

3.3 General Terms Used in the Study of Simple Machines

1. Load and Load Distance

Load is the weight which has to be lifted by a simple machine. The SI unit of load is newton
(N). It is represented by ‘L’. The distance moved by the load in a simple machine is called load
distance. Its SI unit is meter (m). It is represented by ‘Ld’.

Modern Concept Science and Environment – 8 33

2. Effort and effort distance

Effort is the force applied directly to a simple machine to move the load or to do work. The SI
unit of effort is newton (N). It is represented by ‘E’. The distance moved by the effort applied
in a simple machine is called effort distance. Its SI unit is meter (m). It is represented by ‘Ed’.

3. Mechanical advantage

The ratio of the load to the effort is called mechanical advantage, i.e.

MA = Load (L) Memory Tips
Effort (E)
MA does not have unit as it is a simple ratio of two forces. MA is affected by friction and

If the load lifted by a machine is greater than the effort weight of the machine. If friction
applied, the mechanical advantage becomes greater than increases, MA decreases and vice-
1. Similarly, if the load lifted by the simple machine is less versa. In the world, no machine

than the effort applied, the mechanical advantage becomes is frictionless. So, large amount of

less than 1. effort is lost to overcome friction

FACT WITH REASON and weight of the machine.

Mechanical advantage of a simple machine is 2. What does it mean?

Mechanical advantage of a simple machine is 2 means that this simple machine multiplies the effort
applied by 2 times.

4. Velocity ratio

Velocity ratio is a measure that shows how many times the effort distance is longer than the
load distance. Thus, the ratio of the distance travelled by effort to the distance travelled by
load in a simple machine is called velocity ratio.
VR = Distance moved by effort (Ed)

Distance moved by load (Ld)

VR does not have unit as it is a simple ratio of two distances.

FACT WITH REASON

Velocity ratio of a simple machine is 4. What does it mean?
Velocity ratio of a simple machine is 4 means that the effort applied moves 4 times longer distance
than the distance moved by the load.

a) Velocity ratio of a simple machine is independent of friction
Velocity ratio is the simple ratio of effort distance to the load distance. So, friction does
not affect velocity ratio.

b) Velocity ratio of a simple machine is always greater than its mechanical advantage
Mechanical advantage of a simple machine is affected by the friction and weight of the
simple machine but the velocity ratio is not affected by friction and weight of the simple
machine. So, velocity ratio of a simple machine is always greater than mechanical advantage.

34 Simple Machine

FACT WITH REASON

M.A. and V.R. of simple machines do not have unit, why?

MA = Load ((LE)), it is a simple ratio of two forces. Similarly, VR = Effort ddiissttaannccee, it is a simple ratio
Effort Load

of two distances. So, M.A. and V.R. of a simple machines do not have unit.

5. Input work

The work done on a simple machine is called input work. It is the energy supplied to the
machine. Input work is calculated by :

Input work = Effort (E) × Effort distance (Ed)

The SI unit of input work is joule (J).

6. Output work

The work done by a simple machine on the load is called output work. It is calculated by

Output work = Load (L) × Load distance (Ld)

The SI unit of output work is joule (J).

7. Efficiency

The percentage ratio of output work to input work is called efficiency of a machine, i.e.
Efficiency (η) = Output work × 100%

Input work
Efficiency doesn’t have unit as it is a simple ratio of two works.

FACT WITH REASON

Efficiency of a simple machine is 80%. What does it mean?
Efficiency of a simple machine is 80% means that, only 80% of the total energy applied to this
machine is utilized to do useful work and the remaining 20% energy is changed into other forms of
energy while overcoming frictional force.

a) Effect of friction in efficiency of a machine
Frictional force converts the energy supplied to a machine into other forms of energy
like heat. So, the efficiency of a machine decreases as the frictional force increases.
Frication should be reduced to increase efficiency of a machine.

b) Methods of reducing friction in a machine
i) Use of grease or lubricants: Proper greasing or lubrication between sliding parts
of a simple machine reduces friction.

ii) Use of ball bearing: Sliding friction can be reduced by rolling friction with the
help of ball bearings.

Modern Concept Science and Environment – 8 35

iii) Designing smooth surfaces: There is less frictional force between two smooth
surfaces. So, surfaces are made smooth to reduce friction.

c) Real or practical machine
The machine which is used in our daily life is called a real machine or a practical machine.
A real simple machine is never 100 % efficient because of the following reasons:

i) The real machine is affected by friction. In a real machine, total input work does
not change into output work. Some of the input energy is changed into other
forms of energy like heat, sound, etc.

ii) The real machine has weight. No machine is weightless. So, weight of the simple
machine affects its efficiency.

FACT WITH REASON

A real simple machine is never 100 % efficient, why?
No machine is weightless and frictionless. The total input work in a real machine does not change
into output work. Some of the input energy changes into other forms of energy like heat, sound etc.
Therefore, output work becomes less than input work in a real simple machine. Hence, a real simple
machine is never 100 % efficient.

d) Ideal or perfect simple machine

A hypothetical weightless and frictionless machine in which total input work is
converted into output work without wastage of energy is called an ideal or a perfect
simple machine.

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

In case of an ideal simple machine, Input work = Output work,

Efficiency (η) = 1 × 100% = 100%

So an ideal simple machine has 100 % efficiency.

FACT WITH REASON

It is not possible to have an ideal machine, why?

Construction of weightless and frictionless machine is impossible. Ideal or perfect simple machine is
a hypothetical concept. So, it is not possible to have an ideal machine.

Differences between Real simple machines and Ideal simple machines

S.N. Real simple machines S.N. Ideal simple machines

1 The efficiency of a real simple machine is 1 The efficiency of an ideal simple machine

always less than 100%. is always equal to 100%.

2 In real simple machines, output work is 2 In ideal simple machines, output work is

less than input work. equal to input work.

3 In a practical machine, MA is less than VR. 3 In an ideal machine, MA is equal to VR.

36 Simple Machine

3.4 Relation between MA, VR and Efficiency

Efficiency of a simple machine is given by:

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

or, Efficiency (η) = Load × Load distance × 100%
Effort × Effort distance

Load

or, Efficiency (η) = Effort × 100%
Effort distance

Load distance

or, Efficiency (η) = MA × 100%
VR

From the above relation, efficiency of a machine can also be defined as the percentage ratio of
mechanical advantage (MA) to the velocity ratio (VR) of the machine.

3.5 Types of Simple Machines

1. Lever 2. Pulley 3. Wheel and axle

4. Inclined plane 5. Wedge 6. Screw

Memory Tips

All six types of simple machines are basically from two types MACHINE

of simple machines. They are : i) Lever ii) Inclined plane LEVER INCLINED PLANE

The modified forms of lever are pulley and wheel and axle. Whereas PULLEY WHEEL AND WEDGE SCREW
AXLE
the modified form of inclined planes are wedge and screw.

3.6 Lever

A lever is a rigid bar which is capable of rotating about a fixed axis called fulcrum. The weight
to be lifted by using a lever is called load (L) and the force applied on the lever to lift a load is
called effort(E). The distance of effort from the fulcrum is called Effort distance (Ed) and the
distance of load from the fulcrum is called load distance (Ld).

Principle of lever

The principle of lever states that, “when a lever Effort Load
is in equilibrium condition then the product of
effort and effort arm is equal to the product of Effort arm Load arm
load and load arm.”
Fulcrum

i.e. In an equilibrium condition,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld)

Modern Concept Science and Environment – 8 37

Types of lever

a) First class lever
The lever in which fulcrum lies in between load and effort is called first class lever.
Examples: crow bar, see-saw, scissors, dhiki, pliers, nail cutter, etc.

Crowbar See-saw Scissors Pliers Nail cutter
First class lever

Mechanical advantage of first class lever
From the principle of lever,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld)

or, L = Ed
E Ld

∴ MA = Ed
Ld

Thus, the mechanical advantage of the first class lever depends upon the position of
fulcrum in between load and effort. On the basis of length of effort distance and load
distance, we can summarize the following conditions:

i) When Ed >Ld, M.A. > 1

ii) When Ed <Ld, M.A. < 1

iii) When Ed = Ld, M.A. = 1 Crow bar

Application of first class lever to multiply effort Load Effort
From the principle of lever, Input work = Output work

or, E × Ed = L × Ld

Fulcrum

Thus, when effort distance (Ed) is greater than the load distance (Ld), then effort gets

multiplied. Less effort (E) can lift a heavy load (L) as shown in the given figure.

b) Second class lever

The lever in which load lies in between fulcrum and effort is called a second class lever.
Examples: wheel barrow, nutcracker, lemon squeezer,bottle-opener, etc.

Wheelbarrow Nutcracker Bottle opener
Second class lever

In this lever, load lies at any point in between effort and fulcrum.

38 Simple Machine

Mechanical advantage of second class lever
From the principle of lever,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld)
or, L = Ed

E Ld
or, MA = Ed

Ld
In case of second class lever, effort distance (Ed) is always
greater than the load distance (Ld).

i.e. Ed > Ld

∴ MA > 1

Thus, by using the second class lever, a greater load can be lifted with lesser effort, i.e.
the second class levers are used as force multipliers.

FACT WITH REASON

Cracking of nut shells becomes easier with the help of a nutcracker, why?
Nutcracker is a second class lever in which the effort distance is longer than the load distance. So,
effort gets multiplied. As a result, the nut can be cracked with lesser effort with the help a nutcracker.

Solved Numerical 3.1

The efficiency of a wheelbarrow shown in the given figure is 80%. Calculate the effort
required to carry sand with the help of this wheelbarrow.

Solution: Effort
Load (L) = 450 N

Load distance (Ld) = 0.4m Sand

Effort distance (Ed) = 1.5m

Efficiency of the wheelbarrow (η) = 80% 1.5m

According to the formula, 0.4m

Efficiency (η) = Output work × 100% Pivot
Input work Weight of sand 450N

or, 80% = 450 × 0.4 × 100%
E × 1.5

or, E = 180 × 100% = 180 × 100% = 150
80 × 1.5 120
The effort required to carry sand with the help of the wheelbarrow is 150 N.

c) Third class lever

The lever in which effort lies in between load and fulcrum is called third class lever.
Examples, shovel, fishing rod, fire tongs, broom, etc.

Modern Concept Science and Environment – 8 39

Shovel Fishing rod Fire tongs Broom

Third class lever

Mechanical advantage of third class lever
From the principle of lever,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld)

or, EL = Ed
Ld

or, MA = Ed
Ld

In case of third class lever, effort distance (Ed) is always less
than the load distance (Ld).

i.e. Ed < Ld

∴ MA < 1

Thus, by using a third class lever, a greater load cannot be lifted with lesser effort, i.e.
the third class levers cannot be used as force multipliers. Instead, the third class levers
are used as a speed multiplier.

FACT WITH REASON

Cleaning becomes faster by using a broom, why?

In case of a broom, the effort distance is less than the load distance. It does not multiply effort. But a
small movement of our arm pushes the dust a longer distance. So, cleaning becomes faster by using a
broom.

Solved Numerical 3.2

Calculate the force with which the dust is pushed by a broom shown in the given figure.

Solution: 25N Fulcrum
Effort applied (E) = 25 N Input force
Force on dust, i.e. load (L) = ?
30cm
Effort distance (Ed) = 30 cm = 0.3 m

Load distance (Ld) = 1.2 m

Now, from principle of lever,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld) 1.2m

or, 25 × 0.3 = L × 1.2

or, L = 7.5 = 6.25 Output force
1.2
The dust is pushed by a force of 6.25 N.

40 Simple Machine

ANSWER WRITING SKILL

1. What is mechanical advantage (M.A.)? Write down its formula?

Ans: The ratio of load lifted to the effort applied in a simple machine is called mechanical advantage.

MA = Load (L)
Effort (E)

2. Define velocity ratio (V.R.) with its formula.

Ans: The ratio of the distance moved by effort to the distance moved by load in a simple machine is
called velocity ratio.

VR = Effort distance (Ed)
Load distance (Ld)

3. What do you mean by efficiency? Write down its formula.

Ans: The percentage ratio of output work to input work is called efficiency of a machine.

VR = Output work × 100%
Input work
4. No machine has equal amount of output work to the input work (100%efficiency), why?

Ans: In a machine, some amount of input work is lost due to friction and weight of the simple machine.
So, no machine has equal amount of output work to the input work.

5. The cutting edge of the cloth cutting scissors is much longer than the cutting edge of the metal sheet

cutting scissors, why?

Ans: Metal is harder than clothes. It needs more effort to cut metals. So, to increase effort to cut metals
easily, the cutting edge of the cloth cutting scissors is much longer than the cutting edge of the
metal sheet cutting scissor.

6. Write any two differences between Mechanical advantage and Velocity ratio.

S.N. Mechanical advantage S.N. Velocity ratio

1 The ratio of load lifted to the effort 1 The ratio of the distance moved by

applied in a simple machine is called effort to the distance moved by load in a

mechanical advantage. simple machine is called velocity ratio.

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

7. A machine has MA 4. What does it mean?

Ans: MA of a machine is 4 means that while using this machine, the load lifted is 4 times than the effort applied.

8. It becomes easier to carry a load in a wheelbarrow when the load is shifted towards its wheel,how?

Ans: A wheelbarrow is a second class lever. It has load in between effort and fulcrum. The wheel works as
a fulcrum. If we shift the load towards wheel, the load distance decreases and effort gets multiplied.
So, it becomes easier to carry a load in a wheelbarrow when the load is shifted towards its wheel.

9. An effort of 100 N is used to lift a load of 400 N by using a lever. If the load is at a distance of 20 cm
from the fulcrum then find the effort distance.

Solution: Effort applied (E) = 100 N Load lifted (L) = 400 N

Load distance (Ld) = 20 cm = 0.2 m Effort distance (Ed) = ?

Modern Concept Science and Environment – 8 41

Now, from the principle of lever,

Effort (E) × Effort arm (Ed) = Load (L) × Load arm (Ld)

or, 100 × Ed = 400 × 0.2

∴ Ed = 400 × 0.2 = 0.8 m = 80 cm
100

10. A worker lifts a load of 200 N with the help of a lever by applying an effort of 50 N. The load is

kept at a distance of 20 cm and the effort is applied at a distance of 1m from the fulcrum. Find the

mechanical advantage, velocity ratio, and efficiency of the lever used.

Solution: Load lifted (L) = 200 N

Effort (E) = 50 N

Effort distance (Ed) = 1 m

Load distance (Ld) = 20 cm = 20 = 0.2 m
100

Now, MA = Load (L) = 200 = 4 VR = Effort distance (Ed) = 1 = 5
Effort (E) 50 Load distance (Ld) 0.2

Efficiency = MA × 100%= 4 × 100 = = 80 %
VR 5

STEPS EXERCISE

STEP 1

1. Fill in the blanks with appropriate words.
a) A ……. machine is made from the several simple machines working together.
b) In a …… class lever, the effort distance is always smaller than the load distance.
c) A nail cutter is an example of ……. class lever.
d) In third class lever, mechanical advantage is always……. than one.
e) The ratio of the load lifted to the effort applied is called ……..
f) An …….. machine must be frictionless and weightless.
g) ……. reduces the efficiency of a simple machine.

2. Write True for the correct and False for the incorrect statements.
a) Sewing machine is an example of a simple machine
b) Output work is the useful work done by a machine.
c) The ratio of output work to the input work is called velocity ratio.
d) Mechanical advantage is a ratio of effort arm to the load arm.
e) A crowbar makes our work easier by multiplying effort.
f) A nut-cracker is an example of second class lever.
g) Friction increases the efficiency of a machine.

42 Simple Machine

STEP 2

3. Answer the following questions in one word.
a) How many types of lever are there?
b) What is called to the point about which a lever rotates?
c) What is the SI unit of input work?
d) Which class lever has VR always less than one?
e) 15% input work is lost due to friction, then what is the efficiency of machine?

4. Write any two differences between:
a) A simple machine and a complex machine
b) Mechanical advantage and velocity ratio
c) an ideal machine and a practical machine
d) second class lever and third class lever

5. Give reasons.
a) Mechanical advantage has no unit.
b) MA of a first class lever can be one or greater than one or less than one.
c) MA of a second class lever is always greater than one.
d) MA of a third class lever is always less than one.
e) The cutting edge of the scissors used for cutting cloth is much longer than the
cutting edge of the shears used for cutting metals.
f) A practical machine cannot be 100 % efficient.
g) It becomes easier to carry a load in a wheelbarrow when the load is shifted
towards its wheel.

6. Answer the questions with the help of the given figures.
a) Label the parts A, B, and C in the given figures.

b) Copy the given diagram of forearm and indicate the
position of load, effort and fulcrum.

STEP 3

7. Answer the following questions
a) What is a simple machine?
b) State four ways in which the machines are useful to us.
c) Define the following terms related to the simple machines:
i) load ii) effort iii) mechanical advantage
iv) velocity ratio v) efficiency vi) input work
vii) output work