Green Science 9 Final PDF (2076)

Solved Numerical: 1

A load of 2000 N is lifted by a machine applying 500 N effort. Calculate the MA, VR and
h of the machine. The load distance and effort distance are 10 cm and 50 cm respectively.

Given,

Load = 2000 N

Effort = 500 N

Load distance = 10 cm

Effort distance = 50 cm

We know, = 2000N =4
MA = Load 500N

Effort

VR = Effort distance = 50 cm =5
Load distance 10 cm

h = MA × 100% = 4 × 100% = 80%
VR 5

\ The MA, VR and h of the machine are 4, 5 and 80% respectively.

Types of Simple Machine

There are six types of simple machines which are as follows:

1. Lever 2. Pulley 3. Inclined plane

4. Wheel and axle 5. Screw 6. Wedge

In this unit, we will study lever and its types, pulley, inclined plane and wheel and axle.

1. Lever

A lever is a rigid, straight or bent bar which is capable of turning about a fixed point or
an axis called its fulcrum. A lever consists of fulcrum, effort arm and load arm. See-saw,
scissors, beam balance, wheel-barrow, bottle-opener, fire-tongs and nut-cracker are some
examples of lever.

Fig. Load Fulcrum (F)
(L) Effort arm

Load arm

3.2 Effort (E)
A typical lever

The fixed point about which a lever can rotate freely is called fulcrum. The perpendicular
distance of the load from the fulcrum is called the load arm and the perpendicular distance
of the effort from the fulcrum is called the effort arm. We used different types of lever in
our daily life.

GREEN Science (Physics) Book-9 51

Principle of lever
When a lever is in equilibrium, the input work is always equal to the output work. In
other words, the product of load and load arm is equal to the product of effort and effort
arm.

In short,

Input work = Output work

or, Effort × Effort arm = Load × Load arm

Classification of lever

There are three classes of levers on the basis of the location of the fulcrum, load and effort.
They are as follows:

a. First class lever b. Second class lever c Third class lever

a. First class lever

The lever in which fulcrum is located in between load and effort is called first class lever.
Scissors, beam balance, crow-bar, nail-cutter, handle of water pump and pliers are some
common examples of first class levers used in our daily life.

Fig. Fig.3.3 Pliers Beam balance Handle of water
Scissors pump

First class levers are used to increase the rate of doing work, change the direction of force and
multiply the effort. The MA of first class lever may be more than one, one or less than one.

b. Second class lever

The lever in which load is located in between fulcrum and effort is called second class
lever. Nut-cracker, wheel-barrow, oar of a boat, bottle-opener, lemon-squeezer and
mango-cutter are some examples of second class lever.

3.4 Lemon squeezer Nut cracker Bottle opener
Wheel barrow

52 GREEN Science (Physics) Book-9

Since the load lies in between the effort and fulcrum, the effort arm is always longer than
the load arm in a second class lever. So, the MA of a second class lever is always more than
1. By applying less effort, a large load can be lifted by using these levers. Thus, second
class levers always act as force multipliers.

c. Third class lever

The lever in which effort is located in between fulcrum and load is called third class lever.
Fire tongs, human arm, fishing rod, shovel and broom are some examples of third class
lever.

Fig.3.5Fishing rodShovelHuman arm
Fig. Fire tongs

In third class lever, as effort lies in between the fulcrum 3.6
and load, the effort arm is always smaller than the load
arm. So the MA of third class lever is always less than 1.
Third class levers act as speed multipliers, e.g. a bread
knife cuts the entire bread slice by moving less effort
distance.

Activity 1

Name any ten levers that are used at your home.

Study the structure of each of them and identify the position of load, effort and
fulcrum in each of them.

Classify these levers on the basis of the position of fulcrum, load and effort.

Solved Numerical: 2

A load of 800 N is lifted by applying 200 N effort. If the distance between fulcrum and
load is 25 cm, calculate the effort distance.
Given,
Load = 800 N
Effort = 200 N
Load distance = 25 cm
Effort distance = ?
We know,
Effort × Effort distance = Load × load distance

GREEN Science (Physics) Book-9 53

or, Effort distance = Load × Load distance
Effort

= 800 × 25
200

= 4 × 25

= 100 cm

\ Effort distance = 100 cm

Solved Numerical: 3

One metre long lever is used to lift a load of 1500 N by applying 400 N effort. If the load
arm is 20 cm, calculate MA, VR and h of the lever.

Given,

Length of lever = 1 m = 100 cm

Load arm = 20 cm

\ Effort arm = (100 – 20) cm = 80 cm

Load = 1500 N

Effort = 400 N

We know, = 1500 = 3.75
MA = Load 400

Effort

VR = Effort arm = 80 = 4
Load arm 20

h = MA × 100% = 3.75 × 100% = 93.75%
VR 4

\ The MA, VR and h of the machine is 3.75, 4 and 93.75% respectively.

2. Pulley

In rural areas, people use pulleys to lift water from well. Pulleys are also used to lift
heavy loads in upstairs in large buildings. Have you seen people lifting water from a
well using a pulley? Have you observed the structure of a pulley? It consists of a circular
disc having a groove over which a rope is passed. A simple machine having a groove in
circular metallic disc or wooden disc over which a rope passes is called pulley. In a pulley,
the load is connected to one end of the rope and effort is applied at another end. When the
rope moves, the disc rotates.

54 GREEN Science (Physics) Book-9

Types of pulley
There are two types of pulleys on the basis of mobility. They are as follows:

i. Fixed pulley Do You Know
ii. Movable pulley
Pulley is commonly used to lift heavy loads.
i. Fixed pulley Pulley makes our work easier by changing the
direction of force applied.

If a pulley remains at a fixed point and does not move up and down along with load, it is
called a fixed pulley. The wheel of a fixed pulley rotates about an axle fixed to a support
and does not move as the load is raised.

In a single fixed pulley, a rope passes over the Fig. Load
groove of the pulley, one end of which is connected Fig.
to the load and effort is applied at the other end 3.7 Effort
of the rope. Effort is applied downward and the Single fixed pulley
load can be raised upward. So, it is used to change
the direction of applied force. A fixed pulley is
generally used to lift water from a well and in a flag
pole to raise the flag. In a single fixed pulley, the
effort distance is always equal to load distance. So,
VR of a single fixed pulley is 1.

ii. Movable pulley Effort
Rope
A movable pulley is the pulley which moves up and
down along with the load and is not fixed at a point. Pulley
In this pulley, one end of rope is fixed at a point and
the effort is applied at the another end. The load is Load
connected to the axle of the pulley. Single movable Single movable pulley
pulley acts as a force multiplier because in this pulley,
load is equal to twice the effort. In a single movable
pulley, the effort distance is two times more than that
of load distance. Therefore, the VR of a single movable
pulley is 2.

Do You Know 3.8

In a single movable pulley, the effort applied to
lift a load is shared equally by both parts of a rope
supporting the pulley. So, we can lift load two times
heavy by applying an effort on a single movable pulley.

In a movable pulley, downward effort can be used to overcome the load and pull upward.

GREEN Science (Physics) Book-9 55

iii. Block and tackle system or mixed pulley Fixed pulley block Spring balance reading
Fixed end of rope the effort force
In block and tackle system, two or more Fixed end of rope
pulleys are used in a combined form. This
system consists of two sets of pulleys and each
set has two or more pulleys. In this system, all
the pulleys of the same size are adjusted in a
common axle.

Block and tackle system makes our work Fig. Moving pulley block
easier and faster by:

i. multiplying the force applied. 3.9 Slotted masses Load

ii. changing the direction of the force Block and tackle system
applied.

The velocity ratio of block and tackle system is equal to the number of pulleys in the
system. For example, if a pulley system contains 4 pulleys, its VR is 4.

The MA, VR and efficiency of a pulley can be calculated by the given formulae.

MA (mechanical advantage) of a pulley

MA = Load
Effort

VR (velocity ratio) of a single fixed pulley

VR = 1

VR of a single movable pulley
VR = 2 (No. of rope segments that supports the load)

VR of a block and tackle system
VR = No. of pulleys in the system

Efficienty (h) of a pulley

Efficiency (h) = MA × 100%
VR

Solved Numerical: 4

In a block and tackle system of 6 pulleys, a load of 5000 N is lifted by an effort of 1000 N.
Calculate MA, VR and h of the pulley system.

Solution:

No. of pulleys in the system = 6

\ VR of the pulley system = 6

Load = 5000 N

Effort = 1000 N

\ MA = Load = 5000 = 5
Effort 1000

56 GREEN Science (Physics) Book-9

Now,

Efficiency (h) = MA × 100% = 5 × 100% = 83.33%
VR 6

\ The MA, VR and h of the pulley system are 5, 6 and 83.33% respectively.

Activity 2

Go to the science laboratory.
Take a single fixed pulley, a single movable pulley and a block and tackle system.
Collect a spring balance, thread, various weights and meter scale.
Calculate MA, VR and efficiency of these pulleys one by one.

Types of pulley Load Effort VR Load Effort MA Efficiency
distance distance
1. Single fixed
pulley

2. Single
movable
pulley

3. Block and
tackle system

What can you conclude from this activity?

3. Inclined plane

We know that it is very difficult to climb up
hilly areas by vehicles without winding roads.
Similarly, it is very difficult to load a heavy drum
of kerosene into a truck. But it can be lifted easily
by using a wooden plank. So a plane (a wooden
plank) which makes an angle with the horizontal
plane and is used to push things upward is called
inclined plane. It is considered as a simple machine
because it makes work easier and comfortable by
carrying heavy loads.
Fig.3.10
Fig.

3.11 Steep road Children slide
Ladder
GREEN Science (Physics) Book-9 57

Steep road in the hilly region, children’s slide, ladder, wooden plank used to load and
unload, etc. are the examples of inclined plane.

In an inclined plane, the length of the plane acts as an effort distance and the height as
the load distance. So an inclined plane makes our worker easier by increasing the effort
distance since the effort distance in an inclined plane is always longer than the load
distance.

In an inclined plane, the mechanical advantage (MA) is the ratio of load to the effort, i.e.

MA = Load
Effort

The velocity ratio of an inclined plane is the ratio of effort distance (length of inclined
plane) to the load distance (height of the inclined plane).

VR = Length of inclined plane
Height of inclined plane

The MA and VR of an inclined plane increases on increasing the length of the inclined
plane keeping its height constant.

The efficiency (h) of inclined plane can be calculated by the given formula.

Efficiency (h) = MA × 100%
VR

Solved Numerical: 5

A load of 2400 N is lifted by an effort of 800 N by using an wooden plank. If the length
and height of the plank are 4 m and 1.2 m respectively. Calculate MA, VR and h of the
inclined plane.

Solution:

Given,

Load = 2400 N

Effort = 800 N

\ MA = ELfofoadrt = 2840000 = 3
Length of inclined plane = 4 m

Height of inclined plane = 1.2 m

\ VR = Length of inclined plane
Height of inclined plane

= 4
1.2

= 3.33

58 GREEN Science (Physics) Book-9

Now, h = MA × 100%
VR

= 3 × 100%
3.33

= 90.09 %

\ The MA, VR and h of the inclined plane are 3, 3.33 and 90.09% respectively.

Activity 3

Bring three wooden planks of 50 cm, 100 cm and 200 cm length.
Put these planks inclining on a bench. Measure the height of the bench with a ruler.
Take a kinetic trolley, spring balance and thread.
Measure the weight of the trolley with a spring balance.
Now, pull the kinetic trolley on the surface of wooden planks one by one and

measure the effort required in each case.
Calculate MA, VR and η in each case.

S.N. Slope of Height of VR Load Effort MA Efficiency

inclined plane inclined plane

1. 50 cm

2. 100 cm

3. 200 cm

What can you conclude from this activity? Discuss in your classroom.

4. Wheel and axle

You might have seen simple machines having two Wheel
Axle
cylinders of different radius like screw driver, knob Rope

of a tap, the steering of a car, bobbin of a kite, paddle Effort Load

of bicycle, etc. These simple machines are examples

of wheel and axle. Wheel and axle is an arrangement

of two co-axial cylinders of different radius attached

to each other. The cylinder which has longer radius Fig.

is called a wheel and that having a shorter radius is

called an axle. The rope is wound around the wheel

and axle. 3.12

If we rotate the wheel, the axle also rotates and when the wheel completes one rotation,
the axle also completes the same. But distance covered by the wheel is more than the axle
due to different radius. So the effort is applied to the free end of a rope wound around the
wheel and the load is connected to the free end of the rope wound around the axle. The

GREEN Science (Physics) Book-9 59

effort applied on the wheel is magnified and a heavy load of axle will be overcome by a
small effort applied on the wheel.

Fig.

3.13 Screw driver Bobbin of a kite Handle of sewing
Steering of a car machine

In a wheel and axle, mechanical advantage (MA) is calculated by the given formula.

MA = Load
Effort

In a wheel and axle, the ratio of the radius of wheel to that of axle is called velocity ratio
(VR). The VR of a wheel and axle is calculated by the given formula.

VR = Radius of wheel (R)
Radius of axle (r)

The efficiency (h) of wheel and axle is calculated by the given formula.

Efficiency (h) = MA × 100%
VR

In a wheel and axle, both wheel and axle rotate simultaneously around a common axis. In
this simple machine, the fulcrum lies in between the load and effort. So it can be considered
as a first class lever. Therefore, wheel and axle is called a continuous lever.

Solved Numerical: 6

An effort of 400 N is required to lift a load of 1200 N by using a wheel and axle. If the
radius of the wheel and axle are 20 cm and 5 cm respectively, calculate MA, VR and h of
the wheel and axle.
Solution:
Given,
Effort = 400 N
Load = 1200 N
\ MA = ELfofoadrt
= 1420000
= 3

60 GREEN Science (Physics) Book-9

Now, Radius of wheel (R) = 20 cm

Radius of axle (r) = 5 cm

\ VR = R
r

= 20
5

= 4

Now, h = MA × 100%
VR

= 3 × 100%
4

= 75 %

\ The MA, VR and h of the inclined plane are 3, 4 and 75% respectively.

Activity 4

Take a wheel and axle.
Lift various loads with the help of the wheel and axle.
Measure the effort applied to lift the load and using spring balance.
Measure the radius of the wheel and that of axle.
Calculate MA, VR and h of the wheel and axle.

Moment

We prefer a long spanner to unscrew a rusted nut than a short spanner. The long spanner
produces more turning effect which makes our work easier. This turning effect produced
by a force is called moment. So, moment can be defined as the turning effect produced by
a force.

The moment produced by a force depends on following two factors.

i. Amount of force (F)

ii. Moment arm (r)

Moment is the product of force and perpendicular distance between the force and axis of
rotation.

Moment can be calculated by the given formula.

Moment = Force × moment arm

The SI unit of moment is newton-metre (Nm)

GREEN Science (Physics) Book-9 61

Activity 5

Take a spanner.
Fit the spanner to a nut.
Apply force from another end of the spanner and try to unscrew.
Change the point of applying force at different distance till you reach at the middle

of the spanner.

Fig. Nut Effort
Fig. 3.14
Spanner

Where do you feel easy to apply force to unscrew the nut? What can you conclude
from this activity?

We feel easy to apply force at the end point of the spanner to unscrew the nut. It is
because the moment increases when the perpendicular distance between the force
and axis of rotation (moment arm) increases.

From above activity, it becomes clear that the moment increases when the moment arm
increases. Therefore, the probability of breaking a tall tree during storm is more than that
of a short one. Similarly, handles of doors are installed on another side of the hinges to
increase the momentum. The steering of a truck is made larger than that of a car to increase
the momentum. The handle of a screw-driver is made larger and wider to produce more
turning effect by increasing moment arm.

Law of moment

Law of moment states that, in an equilibrium condition, the sum of clockwise moments is
equal the sum of anti-clockwise moments.

In short,

Sum of clockwise moments = Sum of anti-clockwise moments

Distance 1 Distance 2

pivot

Force 1 Force 2
3.15

Solved Numerical: 7

A 25 cm long spanner is used to unscrew a rusted nut. If the effort applied is 20 N, calculate
the moment.

62 GREEN Science (Physics) Book-9

Solution: = 12050 = 0.25 m
Given, = 20 × 0.25 = 5 Nm

Moment arm (r) = 25 cm
Force or effort (F) = 20 N
Moment = ?
We know,
Moment = F × r
\ Moment = 5 Nm

Activity 6

Verification of law of moment
Take a stand with a clamp, a ruler (15 cm), loads of different weights and thread.
Set the apparatus as shown in the given picture.

Stand Scale (15 cm)
Load distance

Effort distance Load

Thread

Fig. Effort

3.16

Tie some loads and suspend them on both sides of the scale as shown in given
figure.

Shift the loads to different distance so that the scale remains in equilibrium.
Increase weights and repeat the above process for 5 times.
Measure the load, load distance, effort and effort distance in each case.

S.N. Load × Load distance Effort × Effort distance
1
2
3
4
5

Here, the product of load and load distance will be equal to the product of effort and
effort distance in each case in the equilibrium condition. This activity verifies the law
of moment.

GREEN Science (Physics) Book-9 63

Key Concepts

1. A simple machine is a device having simple structure which is used to make our
work easier, faster and to apply force in a convenient direction.

2. A simple machine is a mechanical device which is simple in structure and makes
our work easier and faster.

3. The ratio of the load to the effort applied is called mechanical advantage. It is
denoted by MA.

4. The ratio of the distance travelled by effort to the distance travelled by load is called
velocity ratio.

5. The efficiency of a machine is defined as the percentage ratio of output work to
input work.

6. The machine in which the output work is equal to the input work is called perfect
machine or ideal machine.

7. A lever is a rigid, straight or bent bar which is capable of turning about a fixed point
or an axis called its fulcrum.

8. When a lever is in equilibrium, the input work is always equal to the output work.
In other words, the product of load and load arm is equal to the product of effort
and effort arm.

9. The lever in which fulcrum is located in between load and effort is called first class
lever.

10. The lever in which load is located in between fulcrum and effort is called second
class lever.

11. The lever in which effort is located in between fulcrum and load is called third class
lever.

12. In an inclined plane, the length of the plane acts as an effort distance and the height
as the load distance.

13. The velocity ratio of an inclined plane is the ratio of effort distance (length of
inclined plane) to the load distance (height of the inclined plane).

14. Wheel and axle is an arrangement of two co-axial cylinders of different radius
attached to each other.

15. If we rotate the wheel, the axle also rotates and when the wheel completes one
rotation, the axle also completes the same.

16. The effort applied on the wheel is magnified and a heavy load of axle will be
overcome by a small effort applied on the wheel.

17. In a wheel and axle, both wheel and axle rotate simultaneously around a common
axis. In this simple machine, the fulcrum lies in between the load and effort. So it can
be considered as a first class lever. Therefore, wheel and axle is called a continuous
lever.

18. The turning effect produced by a force is called momentum.

19. Law of moment states that, in an equilibrium condition, the sum of clockwise
moments is equal the sum of anti-clockwise moments.

64 GREEN Science (Physics) Book-9

Sequential General Exercise 1

1. Choose the best answer from the given alternatives.

a. Which of the following is a simple machine?

Car Aeroplane

Crow-bar Sewing machine

b. A load of 200 N is lifted by applying 50 N effort. What is the MA?

50 4 200 100

c. What is the VR of a single movable pulley?

1 2 3 4

d. What is the efficiency of an ideal machine?

50% 25% 100% 90%

e. What is the SI unit of moment?

Ncm N/m Nm N/M

2. Answer the following questions.
a. Define simple machine with any five examples.
b. What is mechanical advantage of a machine?
c. Define velocity ratio and efficiency.
d. What is meant by output work?
e. What is meant by input work?
f. What is a lever? State the principle of lever.
g. What is a pulley? Why is it used?
h. What is an inclined plane? Write down the formula to calculate MA, VR and h of
an inclined plane.
i. What is a wheel and axle? Why is it used?
j. What is moment? State the law of moment.

k. Write down the factors on which moment depends.

3. Derive the relation between MA, VR and h.
4. Describe the structure of a wheel and axle with a neat and labelled figure.

5. Differentiate between:
a. Practical machine and Perfect machine

GREEN Science (Physics) Book-9 65

b. MA and VR
c. Pulley and Wheel and axle
d. Single fixed pulley and Single movable pulley

6. Give reason.
a. VR has no unit.
b. The efficiency of a practical machine is always less than 100%.
c. Wheel and axle is called a continuous lever.
d. The probability of breaking of a tall tree is more than a short one during storm.
e. A long spanner is preferred to unscrew a rusted nut.

7. Numerical problems

a. By using a lever, a load of 1000 N is lifted by an effort of 400 N. If the load arm and
effort arm are 8 cm and 24 cm respectively, calculate MA, VR and efficiency.
[Ans: MA = 2.5, VR = 3, h = 83.33%]

b. In a single movable pulley, a load of 500 N is lifted by applying 300 N effort.

Calculate MA, VR and h. [Ans: MA = 1.66, VR = 2, h = 83.33%]

c. The length and height of an inclined plane are 25 m and 5 m respectively. If a

load of 6000 N is lifted by using 1500 N effort, calculate MA, VR and efficiency

of the inclined plane. [Ans: MA = 4, VR = 5, h = 80%]

d. Study the given figure and calculate MA, VR and efficiency of the given

machine. [Ans: MA = 3, VR = 4, h = 75%]

300 N

900 N 3m

12 m

e. There are four pulleys in a block and tackle system. If a load of 1200 N is lifted

by applying 400 N effort by using that pulley, calculate MA, VR and efficiency of

the pulley system. [Ans: MA = 3, VR = 4, h = 80%]

f. The radius of a wheel and that of an axle are 25 cm and 5 cm respectively. If an

effort of 300 N can lift a loaf of 1000 N. Calculate MA, VR and h of the wheel and

axle. [Ans: MA = 3.33, VR = 5, h = 66.66%]

g. An effort of 50 N is applied to unscrew a rusted nut by using a 30 cm long

spanner. Calculate the moment. [Ans: 15 Nm]

66 GREEN Science (Physics) Book-9

Grid-based Exercise 2

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

1. Define simple machine.

2. What is velocity ratio? Write down its formula.

3. What is mechanical advantage?

4. What is the velocity ratio of a single fixed pulley?

5. What are the factors that affect the efficiency of a pulley?

6. Define input work and output work.

7. What are the factors that affect the efficiency of a simple machine?

8. What is an inclined plane?

9. What is velocity ratio of an inclined plane?

10. What is a pulley? Why is it used?

11. State the law of moment.

12. What is a wheel and axle?

13. What is a movable pulley?

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

14. Write down the type of the pulley shown in the given figures and also write down the
velocity ratio of each.
Effort

Load

Effort Load
(b)
(a)

15. What is meant by mechanical advantage of a machine is 2? Velocity ratio has no unit.
Why ?

16. What is meant by the velocity ratio of a machine is 4? The efficiency of a machine is
always less than 100%, why ?

17. The efficiency of a machine can be increased by applying oil or grease. Why ?

18. Small spanner is made to open a small nut and long spanner is made to open a big
nut. Why ?

19. The probability of breaking a tree branch increases while moving towards the tip of
the branch. Give reason.

20. A nut is rusted and jammed. We have two wrenches one of length 10cm and another
of 20cm. Which wrench is preferred to unscrew the nut? Give reason also.

GREEN Science (Physics) Book-9 67

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

21. Write down two advantages of using simple machines. Why is it impossible to get a
perfect machine in practice?

22. Draw a neat and labelled figure of a block and tackle system.

23. How can we increase the efficiency of a simple machine? Give any two methods.
Write any two applications of simple machine.

24. What are two factors that affect the turning effect of force (moment)? No one machine
has 100% efficiency. Justify this statement.

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

25. A simple machine of velocity ratio 20 is used to lift a load of 600N by applying an
effort of 40N. Calculate the mechanical advantage and efficiency of the machine.

26. Draw a neat and labelled diagram of each of the given simple
machines.

a. pulley system having three pulleys

b. wheel and axle 350N

27. Study the given diagram and calculate the mechanical advantage, 500N Load
velocity ratio and efficiency.
25 N
28. A 15cm long spanner is used to open a rusted nut of a bicycle. If
the effort is 50N, calculate the moment produced. Write any two
differences between ideal machine and practical machine.

29. A load is lifted by using an inclined plane in the given diagram.
Answer the following questions.

a. What is the efficiency of the given
machine?

b. Calculate the output work and 200 N 0.5 m
input work when the load is raised
up. 5m

c. What should be the length of the
inclined plane if the same load is
lifted by an effort of 50N without changing the efficiency?

68 GREEN Science (Physics) Book-9

UNIT Energy, Work and

4 Power

Weighting Distribution Theory : 8 Practical: 2

Before You Begin

If a person can do a lot of work, we say the person is very energetic.
Energy of a body is the capacity or ability of a body to work. Living
beings cannot survive in the absence of energy. Similarly, energy
is required to operate machines in industries, to run automobiles
and so on. Work is said to be done when the force acting on a body
produces motion in it in the direction of the force. In SI system, work
is measured in joule (J). The rate of doing work is called power. Its
SI unit is watt (W). Energy, work and power are interrelated to each
other.

Learning Objectives Syllabus

After completing the study of this unit, students will be able to: • Introduction to energy, work
and power
i. introduce energy, work and power and explain the
relationship among them. • Relationship among energy,
work and power
ii. explain the transformation of energy and
demonstrate it. • Transformation of energy

iii. write the formula to calculate energy, work and • Simple numerical problems
power. related to energy, work and
power
iv. solve simple numerical problems related to energy,
work and power.

Glossary: A dictionary of scientific/technical terms

energy : the capacity of doing work
work : the product of force and displacement
power : the rate of doing work
potential energy : the form of energy that an object gains when it is lifted
kinetic energy : the form of energy that an object gains when it moves
transformation : conversion of one form of a substance into another
nuclear : related to nucleus of an atom
gravity : the force with which a body is pulled towards the surface of the earth or a

planet

GREEN Science (Physics) Book-9 69

Energy

We cannot work for a long time without having
food. We get energy from the food to do work.
The capacity or ability of a body to do work is
called energy. Living beings get energy from food.
So, plants and animals cannot survive without
food. In SI system, energy is measured in joule (J)
and in CGS system, it is measured in erg, where
1J = 107erg. Energy is a scalar quantity. There are
different forms of energy.

Energy provides force to do work. The object
having no energy cannot do work. Whenever work
is done, energy is consumed.
Fig.4.1
Fig.
Kinds of Energy

There are different forms of energy in nature. They are mechanical energy, chemical
energy, sound energy, heat energy, light energy, electrical energy, nuclear energy and
magnetic energy.

1. Mechanical energy

Mechanical energy is the energy possessed by a body due to its state of motion or of
position. It is of two types:

i. Kinetic energy (KE)

ii. Potential energy (PE)

i. Kinetic energy

We have seen that a moving hammer can do work on a nail it strikes. Similarly, running
water can rotate a turbine. It is possible due to kinetic energy. The energy possessed by
a body by virtue of its motion is called kinetic energy. Running water, blowing air, the
bullet fired from a gun, moving vehicle, rolling ball, etc. possess kinetic energy. Running
water and blowing air have kinetic energy. So we can rotate a turbine with the help of
running water and blowing air to generate electricity.

Formula for Kinetic Energy (KE = 1 mv2)
2

Let us consider a body of mass

'm' at rest (u = 0) is moving Football Football

with an acceleration 'a'. Let 'v' u=0
be the final velocity of the body F

in moving the distance 's'. 4.2 a
s
According to the equation of
motion,

70 GREEN Science (Physics) Book-9

v2 = u2 + 2as

or, v2 = 0 + 2as [ u = 0]
or, s = v2 ........................... (1)

2a
Now, Kinetic energy (KE) = Work done (W)

KE = F × s [ W = F × s]

KE = ma × v2 F=m×a r
2a q s = v2
2a
KE = mv2
2

\ 1
KE = 2 mv2

From the above relation, it becomes clear that the kinetic energy (KE) of the body is
directly proportional to the mass and square of the velocity of the moving body.

In short,

KE ∝ m ........................... (1)
KE ∝ v2 ........................... (2)

Activity 1

Take a volleyball. Throw it slowly and ask your friend to catch the ball. Repeat this
activity by increasing the speed of the ball while throwing. Ask your friend to say the
difference while catching the ball in both cases. More force is required to catch the ball
thrown at a high speed than that in a low speed.

Repeat the above activity with a tennis ball. The mass of a volleyball is more than
that of a tennis ball. So less force is required to catch a tennis ball than that to catch
a volleyball thrown at the same speed.

This activity proves that kinetic energy increases with increase in mass and velocity
of the moving body and vice-versa.

Solved Numerical: 1

A bullet of mass 20g is moving with the velocity of 200 km/h. Calculate the kinetic energy.

Given,
Mass of bullet (m) = 20 g

= 20 kg [ 1kg = 1000 g]
1000

= 0.02 kg

GREEN Science (Physics) Book-9 71

Velocity (v) = 200 km/h

= 200 × 1000 m/s 1 km = 1000 m
60 × 60
q 1 hr. = 60 min. r

1 min. = 60 sec.

= 55.55m/s

\ Kinetic energy (KE) = ?
1

KE = 2 mv2
1

= 2 × 0.02 × (55.55)2
= 30.85 J
\ Kinetic energy (KE) = 30.85 J

ii. Potential energy

The potential energy of a body is defined as the energy possessed by the body by virtue
of its position or configuration (change in shape or size). The energy stored in the stone
lifted from the ground, stored water in a dam, stretched spring, stretched elastic, etc. are
some examples of the objects having potential energy.

Formula of Potential Energy (PE = mgh) Football
Let us consider a body of mass 'm' is lifted to a height of Mass (m)
'h' from the surface of the ground.
Height (h)
Then,

Potential energy (PE) = Work done (W)

or, PE = F × s [ W = F × s]

or, PE = mg × h [ F = mg, s = h] Fig.

or, PE = mgh

\ PE = mgh 4.3

Solved Numerical: 2
A stone of mass 12 kg is located at a height of 25 m from the ground. Calculate the potential
energy stored in the stone. [Take g = 9.8 m/s2.]
Given,
Mass (m) = 12 kg

72 GREEN Science (Physics) Book-9

Height (h) = 25 m

Acceleration due to gravity (g) = 9.8 m/s2

Potential energy (PE) = ?

We know,

PE = mgh = 12 × 9.8 × 25 = 2940 J

\ Potential energy (PE) = 2940 J

Activity 2

Take a catapult. Stretch the elastic of the catapult and throw a pebble in an open
place. Be careful while throwing the pebble as it may hit birds, animals or people.
Which energy helps to throw the pebble? Name the type of energy present in the
stretched elastic of the catapult.

Differences between Potential energy and Kinetic energy

Potential energy Kinetic energy

1. It is the energy possessed by a body by 1. It is the energy possessed by a body by

virtue of its position or configuration. virtue of its motion.

2. It can be calculated by formula: 2. It can be calculated by the formula:
PE = mgh KE = 1mv²
2

2. Heat energy Fig. Fig.4.4
Burning coal
We get heat energy from hot objects. The form of
energy which gives the sensation of warmth is called 4.5
heat energy. Electric heater, sun, burning coal, etc. are The sun
some sources of heat energy. The burning of diesel
in a truck engine provides the energy needed to run GREEN Science (Physics) Book-9 73
the truck. Similarly, the heat energy produced from
burning fire is used to cook food.

3. Light energy

We cannot see objects in a dark room. So we need
light to see things. Light is a form of energy which
makes things visible. Light is produced by extremely
hot objects. The sun, lantern, torch light, electric bulb,
kerosene lamp, etc. are some sources of light energy.
The sun is the main source of light energy for the
earth. Green plans use sunlight to prepare food by
photosynthesis. Similarly, sunlight can be used to
produce electricity by using photo cell or solar panel.

4. Chemical energy

We get energy stored in the food we eat. When petrol is burnt in the engine of a car, the
chemical energy stored in petrol is used to run the car. The energy stored in a matter is
called chemical energy. Bread, coal, petrol, diesel, battery, wood, oil, etc. have chemical
energy stored in them. The chemical energy is released when chemical change takes place.
Some sources of chemical energy are given below:

Fig. Fig.4.6KeroseneCell
Fig. Bread

5. Electrical energy 4.7

The form of energy which is produced due to Lighting CFL
continuous flow of electrons is called electrical energy.
A cell, photocell, battery, generator, etc. are the sources
of electrical energy. Electrical energy is used to rotate
fans, drive trains, light bulbs, operate equipment
like television, computer, camera and mobile phone.
Electrical energy can be changed into heat, light,
sound, mechanical energy, etc. So, it is widely used
throughout the world.

6. Sound energy 4.8
Loudspeaker produces sound
When we ring a temple bell, it produces sound. Sound
energy is the form of energy which is produced due
to the vibration of a material medium. A vibrating
body possesses sound energy. Loudspeaker, radio,
television, horn of vehicles, temple bell, etc. are some
sources of sound energy.

Sound can be experienced as a form of energy when
the window panes shatter due to an explosion or when
loud sound is produced by a low-flying aeroplane.

74 GREEN Science (Physics) Book-9

7. Magnetic energy

The energy obtained from a magnet is called Fig.
magnetic energy. It is used in electric bell,
loudspeaker, mobile phone, television, radio, 4.9
etc. Similarly, magnetic energy is used to
generate electricity. A magnet attracts iron,
nickel, cobalt, etc. due to magnetic energy.
A magnet consists of numerous molecular
magnets.

Magnet attracting iron nails

8. Nuclear energy

The energy obtained from the nucleus of an atom is called nuclear energy. This energy
can produce a large amount of heat and light energy. Nuclear energy is used in atomic
power plants to produce electricity. Similarly, nuclear energy is used for making atom
bomb, hydrogen bomb, etc. Nuclear energy is produced due to nuclear fusion or nuclear
fission reaction.

Work

Work is said to be done when the force acting on a body produces motion in it in the direction
of the force. In other words, work done is defined as the product of force and displacement.
In the SI system, work is measured in joule (J) or newton-metre (Nm).

Formula of work done W=F×s
Work done (W) = Force (F) × Displacement (s) \

One joule work

When one newton force displaces a body through a distance of one metre, the work done
is called one joule.

In short,

1 joule = 1 newton × 1 metre [ W = F × s]

No mechanical work is done when a student studies for 2-3 hours sitting on a chair.
Similarly, no work is done by a teacher teaching a class. Work is said to be done only if
the force applied to a body succeeds in moving it. When a person pushes a wall, no work
is done because the wall does not cover distance. But work is done when a person pushes
a cart because the cart covers some distance. Therefore, the work done by a body depends
on:
a. The magnitude of force applied (F)
b. The distance covered in the direction of the force (s) applied

GREEN Science (Physics) Book-9 75

Fig.

4.10 A man pushing a cart (Some work is done)
A man pushing a wall (No work is done)

Types of Work 2. Work done against gravity

There are two types of work. They are:

1. Work done against friction

1. Work done against friction

The work done by pushing or pulling an object on a surface is called work done against
friction. For example, work done by pulling a wooden log on the road, work done by
pushing a cart, etc.

2. Work done against gravity Do You Know

The work done by lifting a body vertically Friction is the force which opposes the
upward from the earth's surface is called work motion of a body moving on other body
done against gravity. For example, work done when they are in contact.
by a crane by lifting a wooden log vertically
upward from the ground.

Formula of work done against gravity
Work done against gravity (W) = Force × displacement
or, W = Weight × height [ Force = Weight (mg), Displacement = Height (h)]
\ W = mgh

Solved Numerical: 3

A force of 375 N displaces a body through 35 m. Calculate the work done.
Given,
Force (F) = 375 N
Displacement (s) = 35 m
Work done (W) = ?

76 GREEN Science (Physics) Book-9

Fig.We know,
W = F × s
= (375 × 35) Nm
= 13125 J
\ Work done (W) = 13125 J.

Solved Numerical: 4
A crane lifts a wooden log of 500 kg upto a height of 25 m from the earth's surface.
Calculate the work done against gravity. [Take g = 9.8 m/s2.]
Given,
Mass of wooden log (m) = 500 kg
height (h) = 25 m
Acceleration due to gravity (g) = 9.8 m/s2
Work done (W) = ?
We know,
W = mgh
= 500 × 9.8 × 25
= 122500 J
\ The work done against gravity (W) = –122500 J.

Transformation of Energy

We need different forms of energy in our day to day life. Therefore, we convert one form
of energy into another. A candle consists of chemical energy. When the candle is burnt,
chemical energy transforms into light and heat energy. So, the process in which one form
of energy is converted into another is called transformation of energy. An electric bulb
converts electrical energy into light and heat energy, a solar cell converts light energy into
electrical energy and a loudspeaker converts electrical energy into sound energy. These
are some examples of transformation of energy.

Light and heat
energy

Wax (Chemical
energy)

4.11

GREEN Science (Physics) Book-9 77

Some examples of energy transformation and the devices required are as follows:

S.N. Devices Energy transformation
1. Electric bulb Electrical energy → Light energy and heat energy
2. Cell or battery Chemical energy → Electrical energy
3. Loud speaker Electrical energy → Sound energy
4. Microphone Sound energy → Electrical energy
5. Television Electrical energy → Light and sound energy
6. Electric motor Electrical energy → Mechanical energy
7. Dynamo or generator Mechanical energy → Electrical energy
8. Electromagnet Electrical energy → Magnetic energy
9. Solar cell / panel Light energy → Electrical energy
10. Heater Electrical energy → Heat energy

1. Transformation of energy while lighting a torchlight

Battery Copper wire Bulb
Chemical energy Electrical energy
Light energy +
Heat energy

2. Transformation of energy in hydroelectric project

Water stored in Running water Rotating Electricity
a dam Kinetic energy turbine in coil

Potential energy Kinetic energy Electrical
energy

Law of conservation of energy

According to law of conservation of energy, “Energy can neither be created nor be
destroyed. Energy can only be changed from one form to another.”

Activity 2

Take a cell, two pieces of copper wire, a bulb and a bulb holder.
Connect these materials to light the bulb.
What type of transformation of energy occurs here? Discuss in your class.

Power

Power can be defined as the rate of doing work. The SI unit of work done is joule (J) and
that of time is second (s). So the SI unit of power is J/s or W (watt). Power is also measured
in kilowatt (kW), megawatt (MW), horsepower (h.p.), etc.

78 GREEN Science (Physics) Book-9

Formula to calculate power (P)
Power (P) = Work done (W)

Time taken (t)

\ W
P= t

From the above relation, it becomes clear that power (P) depends on two factors, viz.
amount of work done (W) and time taken (t).

Two machines that do the same amount of work can have different power. For example, machine
A completes 200 J work in 5 seconds. But machine B completes 200 J work in 10 seconds.

W 200
Power of machine A (PA) = t = 5 = 40 W

W 200
Power of machine B (PB) = t = 10 = 20 W

From the above calculation, it becomes clear that when a body takes lesser time to do a
particular work, the power is said to be greater and vice-versa.

One watt power

One watt power can be defined as the rate of doing one joule work in a time of one second.

In short, 1 joule
1 watt = 1 second

Meaning of 1000 W written on an electric heater: It means that the electric heater converts
1000 J of electrical energy into heat energy in 1 second.

\ 1000 J
1000 W = 1s

The relation among watt (W), kilowatt (kW), megawatt (MW) and horse power (h.p.):

1000 W = 1 kW
1000 kW = 1 MW
746 W = 1 h.p.

Solved Numerical: 5

A man pulls a cart of 80 kg and covers a distance of 40 m in 10 seconds. Calculate the
power of the man.
Given,
Mass (m) = 80 kg
\ Weight or Force (F) = m × g

GREEN Science (Physics) Book-9 79

or, Force (F) = 80 × 9.8 [ g = 9.8 m/s2]

= 784 N

Distance (s) = 40 m

time (t) = 10 s

We know,

W
P = t

F×s
= t

784 × 40
= 10
= 3136 W

\ Power of the man (P) = 1336 W

Solved Numerical: 6

A crane lifts a load of 80000 N upto a height of 50 m in 10 seconds. Calculate the power of
the crane in horsepower.

Given,

Load (F) = 80000 N

Height (h) = 50 m

Time (t) = 10 s

Power (P) = ?

We know,

W
P = t

F×h
= t [ W = F × h]

= 80000 × 50

10

= 400000 W

400000 [ 1 h.p. = 746 W]
= 746 h.p.
= 536.19 h.p.

\ Power of the crane (P) = 536.19 h.p.

80 GREEN Science (Physics) Book-9

Comparative study of energy, work and power

Energy Work Power

1. It is the capacity of 1. It is the product of force 1. It is the rate of doing

doing work. and displacement. work.

2. Its SI unit is J. 2. Its SI unit is J. 2. Its SI unit is W.

3. It is not affected by time. 3. It is not affected by time. 3. It is affected by time.

Relation Among Energy, Work and Power

There is a close relationship among energy, work and power. Energy is the capacity of
a body to do work. A person or object cannot do work without energy. Human beings
cannot do work without energy and they eat food to get energy. After digestion, the
chemical energy present in food changes into muscular energy. We use muscular energy
to do various types of work. Work is the product of force and displacement. It is the effect
of energy.

Power is the rate of doing work. It is the rate of transformation of energy. Work done does
not depend on the time taken but the time taken to do a particular work determines the
power. Two machines or person that perform the same amount of work can have different
power. The capacity of a body to do work is called energy and the rate of doing work is
called power. Therefore, energy, work and power are interrelated to each other.

Key Concepts

1. The capacity or ability of a body to do work is called energy.

2. Energy provides force to do work. The object having no energy cannot do work.

3. Mechanical energy is the energy possessed by a body due to its state of motion or
of position.

4. The energy possessed by a body by virtue of its motion is called kinetic energy.
Running water, blowing air, the bullet fired from a gun, moving vehicle, rolling
ball, etc. possess kinetic energy.

5. The potential energy of a body is defined as the energy possessed by the body by
virtue of its position or configuration (change in shape or size).

6. The form of energy which gives the sensation of warmth is called heat energy.

7. Light is a form of energy which makes things visible. Light is produced by extremely
hot objects.

8. The energy stored in a matter is called chemical energy.

9. The form of energy which is produced due to continuous flow of electrons is called
electrical energy.

GREEN Science (Physics) Book-9 81

10. A vibrating body possesses sound energy. Loudspeaker, radio, television, horn of
vehicles, temple bell, etc. are some sources of sound energy.

11. The energy obtained from a magnet is called magnetic energy. It is used in electric
bell, loudspeaker, mobile phone, television, radio, etc.

12. Nuclear energy is used in atomic power plants to produce electricity. Similarly,
nuclear energy is used for making atom bomb, hydrogen bomb, etc.

13. Work done is defined as the product of force and displacement. In the SI system,
work is measured in joule (J) or newton-metre (Nm).

14. The work done by pushing or pulling an object on a surface is called work done
against friction.

15. The work done by lifting a body vertically upward from the earth’s surface is called
work done against gravity.

16. Power can be defined as the rate of doing work. The SI unit of work done is joule
(J) and that of time is second (s). So the SI unit of power is J/s or W (watt).

17. There is a close relationship among energy, work and power.

Sequential General Exercise 1

1. Choose the best answer from the given alternatives.

a. Which of the following is the main source of heat energy?

heater moon bulb candle

b. ....................... energy is produced due to vibration of a material medium.

heat light sound chemical

c. Which of the following consists of kinetic energy?

burning coal runing wayer

light bulb ringing bell

d. Which of the given devices converts electrical energy into heat energy?

television battery heater bulb

e. The SI unit of power is .......................

J Nm W Js

2. Answer the following questions.
a. What is energy? Write down its SI unit.
b. Name any five forms of energy.
c. Define mechanical energy with any two examples.

82 GREEN Science (Physics) Book-9

d. What is potential energy? Write down the formula to calculate potential energy.
e. Name the factors on which potential energy depends.
f. Name the factors which affect kinetic energy.
g. Define kinetic energy with any two examples.
h. What is chemical energy? Name any three objects having chemical energy.
i. Define heat energy and light energy. Write any two sources of heat energy.
j. What is nuclear energy? Write its two applications.
k. What is meant by work done? Define one joule work.
l. Define work against friction.
m. What is meant by work done against gravity? Give one example.
n. What is meant by transformation of energy? Give any two examples.
o. What is power? Write its SI unit.
p. Define one watt power.
q. Write down the relation between energy and power.

3. Name the devices that convert the following.
a. Electrical energy into light energy
b. Electrical energy into mechanical energy
c. Light energy into electrical energy
d. Mechanical energy into sound energy

e. Electrical energy into sound energy

f. Electrical energy into heat energy

g. Sound energy into electrical energy

h. Electrical energy into magnetic energy

4. Prove that: b. KE = 1 mv2
a. PE = mgh 2

5. Differentiate between:
a. Kinetic energy and Potential energy
b. Work and Power
c. Heat energy and Sound energy
d. Energy and Power
e. Light energy and Magnetic energy

6. Name the form of energy present in the given objects/devices.

a. Photo cell b. Petrol

c. Running water d. Water stored in a dam

e. Stretched catapult f. Bullet fired from a gun

GREEN Science (Physics) Book-9 83

g. Lighting bulb h. Ringing bell
i. Tuning radio
k. Coal j. Battery
m. Kerosene
o. Compressed spring l. Bread
n. Rolling football

7. Numerical Problems

a. A bicycle of 15 kg is moving with the velocity of 10 m/s. Calculate the kinetic

energy. [Ans: 750 J]

b. Calculate the potential energy stored in a metal ball of a mass of 80 kg kept at a
height of 15 m from the earth's surface. What will be the potential energy when
the metal ball is kept on the earth's surface. [Take g = 9.8 m/s2] [Ans: 11760 J, 0J]

c. Study the given figure and calculate the potential energy. 200 kg
50 m
[Take g = 9.8 m/s2] [Ans: 98000 J]

d. A bullet of mass of 50 g is moving with the velocity of 200 km/h. Calculate the

kinetic energy of the bullet. [Ans: 77.16 J]

e. A bullet moving with the velocity of 200 km/h has the kinetic energy of 77.16 J.

Calculate the mass of the bullet. [Ans: 50 g]

f. A man lifts a load of 40 kg to a height of 16 m. Calculate the work done against

gravity. [Ans: 6272 J]

g. A person carries an object 20 m away by applying 500 N force. Calculate the

work done. [Ans: 10000 J]

h. How much work is done while pushing a box of mass of 35 kg at a distance of 20
m? [Ans: 6860 J]

i. A crane lifts a load of 6000 N at the height of 20 m in 5 seconds. Calculate the

power of the crane in horse power. [Ans: 32.17 h.p.]

j. Suman with a mass of 45 kg climbs a 3m high ladder in 10 seconds. Calculate her

power. [Ans: 132.3W]

k. A person carries a load of 150 N and covers a distance of 40 m in 40 minutes.

Calculate his power. [Ans: 2.5 W]

l. Calculate the work done when a body of mass 100 kg is displaced 10 m with the

acceleration of 5 m/s². [Ans: 5000 J]

m. Ramita of 50 kg mass climbs a stair of 20 steps in 40 s. If each step has 25 cm

height, calculate her power. [Ans: 62.25 W]

84 GREEN Science (Physics) Book-9

Grid-based Exercise 2

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

1. What is energy? In which unit is it measured?

2. What is work done? Write down its formula and SI unit.

3. Define 1 joule work done.

4. What are the conditions required for work to be done?

5. Write the “law of conservation of energy”.

6. Name any two sources of electrical energy.

7. Define power and write its SI unit.

8. What is “one watt power”?

9. What is transformation of energy?

10. Name the equipment which converts energy as indicated below:

a. Electrical energy into heat energy

b. Sound energy into electrical energy

11. Which factors does the power of a body depend on?
12. What is chemical energy?
13. Write down the formula to calculate the work done against gravity.

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

14. Write any two differences between work and power.

15. No work is done when a person is standing by carrying a load of 50kg for one hour.
Give reason.

16. Electrical energy is widely used among the various types of energy. Give reason.

17. What is meant by the statement that the power of an electric bulb is 60W?

18. How much potential energy is present in a stone kept on the earth’s surface? Why?

19. The cricket player which catches the ball wears gloves. Give reason.

20. What is meant by the statement that the power of an electric heater is 1500W?

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

21. How is atomic energy produced? Write. Which factors does the kinetic energy of a
body depend on?

22. What happens to the kinetic energy when the velocity of a moving body is doubled?
Which factors does the power of a body depend on?

23. Write down the transformation of energy while using a microphone and a loudspeaker
in a programme.

24. What is transformation of energy? Write with examples. What is the relation between
work done and power? Write.

GREEN Science (Physics) Book-9 85

25. Write down the transformation of energy while lighting a bulb in a torchlight by
using cells. What are the conditions required for work to be done?

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

26. A man of mass 70 kg climbs the Nautale Durbar of Basantapur. He climbs 15 steps in 1
minute. If the height of 1 step is 15 cm, calculate his power, (g = 9.8 m/s2) Differentiate
between force and work in any two points.

27. Prove that:

a. PE = mgh b. KE = 1 mv2
2

28. How does transformation of energy take place in each of the given actions?

a. Producing electricity in a hydropower station

b. Producing electricity in a nuclear furnace

c. While stopping a moving vehicle by applying brakes

d. Lighting a bulb by using a battery

29. The velocity of a body of mass 60kg reaches 15m/s from 0 m/s in 12 seconds. Calculate

the kinetic energy and power of the body. Stone
30. The potential energy of a stone kept on the earth’s surface 30 kg

is zero, give reason. Study the given diagram and calculate

the potential energy stored in the stone. What is the potential

energy when the stone reaches the ground surface? 25 m

Ground

86 GREEN Science (Physics) Book-9

UNIT Light

5

Weighting Distribution Theory : 3 Practical: 1

Before You Begin

We get light from various sources like the sun, lighting bulb, burning
candle, kerosene lamp, etc. In a dark room, we cannot see the things
kept there although our eyes are open. We need light to see the things
kept there. So, light is a form of energy which makes things visible. It
is produced from extremely hot objects. The objects which emit light
are called the sources of light. The sun is the main source of light on
the earth. Some other sources of light are light bulb, burning candle,
kerosene lamp, etc. In this unit, we will study light, refraction of light,
laws of refraction of light, dispersion of light and electromagnetic
spectrum.

Learning Objectives Syllabus

After completing the study of this unit, students will be able to: • Indtroduction to light
i. introduce light. • Refraction of light
• Law of refraction of light
ii. define refraction of light and state the laws of • Total interal relection of light
refraction of light. • Dispresion of light
• Electromagnetic spectrum
iii. explain dispersion of light and demonstrate the
spectrum of light.

iv. describe the electromagnetic wave with its nature.

v. explain the frequency and wavelength of
electromagnetic waves.

Glossary: A dictionary of scientific/technical terms

light : the form of energy which makes things visible
refraction : the process of bending light when it passes from one medium to another
denser medium : the medium having more density
rarer medium : the medium having less density
dispersion : the splitting of something into its constituent parts

GREEN Science (Physics) Book-9 87

Light

Light is the form of energy which causes the sensation of sight. Light makes things visible.
So we can see things around us. Light does not require a material medium (like solid,
liquid or gas) for its propagation.

Objects such as the sun, a lighting bulb and a burning candle emit light and make things
visible. We can see objects when light from a luminous body falls on them. The objects
that emit light are called sources of light, e.g. the sun, lighting bulb, burning candle, etc.
All luminous objects are the sources of light.

Fig.5.1Lighting bulbBurning coal
Fig. Sun

Refraction Light

Light travels in a straight path as long as it travels in a
vacuum or the same medium. But it bends when passes
from one medium to another. This process is called
refraction of light. So, the bending of light when it passes
from one medium to another is called refraction of light.

Light travels through different media like glass, air, water, 5.2
plastic, etc. The medium through which light can pass is
called an optical medium. Different optical media have Refraction of light
different densities. On this basis, there are two types of
optical media, viz. rarer medium and denser medium.

Rarer medium Do You Know

The optical medium having relatively The speed of light is more in a rarer
lower density is called rarer medium. For medium and less in a denser medium.
example, out of glass and air media, air is
rarer medium. The speed of light is maximum in a
vacuum, i.e. 3 × 108 m/s.
Denser medium

The optical medium having relatively higher density is called denser medium. For
example, out of air and glass media, glass is denser medium.

88 GREEN Science (Physics) Book-9

Cause of Refraction of Light

The density of different optical media is different. Due to this, the speed of light differs
in different media. The change in the speed of light when it passes from one medium to
another is the main cause of refraction of light. The velocity of light in air is 3 × 108 m/s,
that in water is 2.25 × 108 m/s passes from air to glass medium or water medium, it bends.
On their hand, when light passes from glass medium to air medium, it also bends.

Refraction of Light through a Glass Slab

When a ray of light IO strikes a glass slab PQRS, it bends at O and travels along OE. The
ray OE again refracts and emerges out.

IN

i Air (Rarer medium)
Q
P
O
r

N’ N Glass slab (Denser
medium)

r

Fig. S E R
5.3 e B’

Lateral shift
N’ F

Refraction of light through a glass slab

The terms related to refraction of light are given below.

1. Incident ray

The ray of light which strikes a transparent medium is called incident ray. In this figure,
IO is an incident ray.

2. Refracted ray

The ray of light that passes in the second medium after refraction is called refracted ray.
In the figure, OE is the refracted ray.

3. Angle of incidence

The angle made by incident ray to the normal is called angle of incidence. It is denoted by
∠i or i. In the figure, ∠ION is the angle of incidence.

4. Normal

The perpendicular drawn at the point on incidence is called normal. In the figure, NN’ is
the normal.

GREEN Science (Physics) Book-9 89

5. Angle of refraction

The angle made by refracted ray to the normal is called angle of refraction. It is denoted
by ∠r or r. In the figure ∠N’ROE is the angle of refraction.

6. Emergent ray

The ray of light which emerges out of the second medium is called emergent ray. In the
figure, EF is the emergent ray.

7. Emergent angle

The angle made by emergent ray to the normal is called emergent angle. It is denoted by
∠e or e. In the figure ∠N'EF is emergent angle.

8. Lateral displacement

The perpendicular distance between emergent ray and incident ray is called lateral
displacement or lateral shift.

Laws of Refraction of Light

1. The incident ray, normal and refracted ray all lie in the same plane at the point of
incidence.

2. When a ray of light travels from a rarer medium to a denser medium, it bends towards

the normal and when a ray of light travels from a denser medium to a rarer medium,
it bends away from the normal. The ratio of sine of angle of incidence to the sine of
angle of refraction is constant for a given pair of media. It is called refractive index. It
is denoted by the Greek letter m (mew).

IN Air (Rarer medium) Glass
iO (Denser medium)
r Glass
(Denser medium)

N' I N

R iO

Fig. Air (Rarer medium) r R

5.4 N'

In short, Sin i = m (refractive index)
Sin r

90 GREEN Science (Physics) Book-9

Refractive index can also be calculated by given formula.

Refractive (index (m) = Speed of light in air (vacuum)
Speed of light in a medium

3. The ray of light does not bend 90° Air
when it passes normally from one
medium to another.

Glass

Fig.

5.5 90° Air

Refractive Index

The refractive index can be defined as the ratio of sine of angle of incidence to the sine of
angle of refraction for a given pair of media. It is denoted by ‘m’. Refractive index (m) has
no unit as it is a ratio of two similar quantities.

Formula:

Refractive index (m) = sin i
sin r

When a ray of light travels from air medium to water medium, then the ratio of sin i/sin r
is called the refractive index of water with respect to air, i.e.

sin i = air m
sin r
water

Solved Numerical: 1

Calculate the refractive index of glass medium if the angle of incidence is 45° and angle
of refraction is 28°.
Solution:
Angle of incidence (i) = 45°
Angle of refraction (r) = 28°
Refractive index (m) = ?

We know,

Refractive index (m) = sin ri = sin 2485°° = 1.5
sin sin

\ The refractive index of glass with respect to air medium is 1.5.

GREEN Science (Physics) Book-9 91

The refractive index of a medium can also be defined as the ratio of speed of light in
vacuum to the speed of light in the medium, i.e.

Refractive index (m) = Speed of light in vacuum (c)
Speed of light in medium (v)

Solved Numerical: 2

The speed of light in water is 2.2 × 108 m/s and that in vacuum is 3 × 108 m/s. Calculate the
refractive index of water.
Solution:
Speed of light in vacuum (c) = 3 × 108 m/s
Speed of light in water (v) = 2.2 × 108 m/s
Refractive index (m) = ?

We know, = 1.36

Refractive index (m) = vc = 23.2××110088
\ The refractive index of water is 1.36.

Real depth and Apparent depth

When a ray of light travelling in a denser medium enters a rarer medium, it bends away
from the normal. Due to this, a coin lying at the bottom of the cup full of water appears to
be raised. Similarly, the bottom of a swimming pool appears to be raised and the depth
seems to be less than that of the actual one. So, the actual depth of a pond is the real depth
and the virtual depth at which a body appears due to refraction of light is called apparent
depth.

Eye N

Fig. Apparent depth Real depth N' Coin (apparent
position)
Water
5.6 Coin (real
position)

The refractive index in terms of real depth virtual depth can be calculated by the given
formula:

Refractive index (m) = Real depth
Apparent depth

92 GREEN Science (Physics) Book-9

Solved Numerical: 3

The apparent depth of a pond appears to be 4.4 m. If the real depth of the pond is 6m,
calculate the refractive index of water.
Solution:
Real depth = 6 m
Apparent depth = 4.4 m
Refractive index (m) = ?

We know,

Refractive index (m) = 46.4 = 1.33

\ The refractive index of water (m) = 1.33

Activity 1

Demonstration of refraction of light through a glass slab
Take an A4 size paper and fix it on a drawing board with push pins.
Take a glass slab and put it on the middle of the paper and draw an outline PQRS.
Draw a line A at a certain angle that meets PQ at point B. Draw a normal NM at point B.
Fix two pins P1 and P2 on the line AB as shown in the figure.
Now, observe the pins P1 and P2 in a straight position from another side of the glass

slab and fix two pins P3 and P4.
Remove the glass slab and join B and C with the line CD.
Now, measure the angle of incidence, angle of refraction and angle of emergence.
This activity shows the refraction of light through a glass slab.

Activity 2

Take a beaker and fill it half with water. Take a glass rod and immerse half portion of
the glass rod into water. What do you observe? Does the glass rod appear bent? Why?

Glass rodFig. Water
5.7 Beaker

GREEN Science (Physics) Book-9 93

The glass rod immersed in water appears to be bent at the surface water due to refraction
of light. Similarly, a coin placed at the bottom of a beaker full of water appears to be raised
due to refraction of light. We observe a number of phenomena due to refraction of light.
Some of them are mentioned below.
1. We cannot kill a fish when we spear a fish where it appears in a pond.
2. A swimming pool or a pond appears less deep than its actual depth.
3. The legs of a person standing in a pond appear shorter.
4. The letter on a paper lying at the bottom of the glass slab appears to be raised when

viewed through the glass.

Activity 3

Take an empty beaker and place a coin into it. Observe the coin in the beaker. Does
it appear raised or not?

Now, fill the beaker with water and observe the position of the coin.
What is the conclusion of this activity?

Critical angle

When light travels from a Rarer medium

denser medium to a rarer 90° Refracted ray
medium, it bends away

from the normal. When Incident ray 42°
the angle of incidence
is further increased, the
corresponding angle of
Fig.
Fig.refraction also increases Glass Denser medium
and for a certain angle
of incidence, the angle of 5.8
refraction becomes 90°. In
Critical angle for glass medium

this condition, the angle of incidence in the denser medium is called critical angle.

Critical angle for a certain medium can be defined as the angle of incidence in a denser
medium when the corresponding angle of refraction in rarer medium becomes 90°. It is
denoted by C. For example, the value of critical angle for glass medium is 42°, for water
medium is 49°, for ice is 50° and for diamond is 24°.

Following figures show the critical angle for different media.

90° Rarer 90° Rarer 90° Rarer
42° 49° 50°

5.9 Denser Denser Denser
Glass Water Ice

94 GREEN Science (Physics) Book-9

Critical angle and refractive index of some media with respect to air

S.N. Medium Critical angle Refractive index
1. Glass 42° 1.5
2. Water 49° 1.33
3. Diamond 24° 2.42
4. Ice 50° 1.31
5. Glycerine 43° 1.47

Relation between the Refractive index and Critical angle

When a ray of light passes from a denser medium to a rarer medium, then according to
Snell’s law;

glass = sin i
mair sin r

For the incident ray moving from a denser medium to a rarer medium, the angle of

refraction is 90° and the refracted ray is parallel to the glass-air interface.

Thus, i = ic (critical angle) and r = 90°.

Then, glassmair = sin ic
sin 90°

= sin ic [ sin90° = 1]

But, glass = 1
mair airmglass

\ sin ic = air 1
mglass

or, glassmair = 1 ic
sin

Here, glassmair is the refractive index of denser (glass) medium with respect to rarer (air)
medium. So, if the refractive index of the denser medium with respect to rarer medium is
known, the critical angle can be calculated.

Solved Numerical: 4

Calculate the refractive index of water medium with respect to air if the refractive index
of water is 1.33.
Solution:
Refractive index (m) = 1.33

Critical angle (ic) = ?

GREEN Science (Physics) Book-9 95

We know,
1

m = si1n ic
or, 1.33 = sin ic

or, sin ic = 1
1.33
= sin–1o1.133p
or, ic = 48°45° ≈ 49°

\ The critical angle of water medium with respect to air is 49°.

Total Internal Reflection in a Glass Prism

The refractive index of glass medium is about 1.5. So, the critical angle of glass medium
with respect to air is about 42°. Therefore, a ray of light travelling from glass medium to air
medium and incident on glass-air interface at an angle greater than 42° suffers total internal
reflection. A prism having an angle of 90° between two refracting surfaces and remaining
angles 45° is called total reflecting prism. This type of prism is generally used to

(i) deviate a ray of light through 90°.

(ii) erect the inverted image without deviation and

(iii) deviate ray of light through 180°.

Prism 45° 45° 45°
5.10 45°
45°
90° 45°
Fig.45°90°
Fig. 45°
Prism
45°

45°

Total Internal Reflection of Light

When the angle of incidence in a denser medium is more than the critical angle, the ray of
light reflects in the same medium. This process is called total internal reflection of light.

For example,

The critical angle for glass medium is 42°. If the angle of 45° 45°
incidence in glass medium becomes more than 42°, the ray
of light reflects in the same medium. This process is called 5.11 Glass
total internal reflection. Total internal refection
in glass
Similarly, the critical angle for water medium is 49°. When
the angle of incidence is more than 49°, total internal
reflection takes place.

96 GREEN Science (Physics) Book-9

Fig. 50° 50°
Fig.
5.12 Water
Fig. Total internal reflection
in water medium

Conditions required for total internal reflection of light

1. The ray of light should pass from a denser medium to a rarer medium.

2. The angle of incidence should be more than the critical
angle.

Applications of total internal reflection of light

1. Sparkling of a cut diamond
The value of critical angle for diamond is very low, i.e. 5.13
24°, when a ray of light enters a piece of diamond cut into
various surfaces, the ray of light suffers repeated total internal reflection. As a result, a cut
diamond sparkles.

2. Mirage
Mirage is seen in hot deserts
or coal-tarred roads in hot
days due to total internal
reflection of light. Mirage
is an optical illusion which
can be observed as if there
is a pond on hot desert or
coal-tarred road. A mirage
is formed when an inverted
image of the distant object is
formed on the desert or coal- 5.14
tarred road. The image can be seen along with the object.

Mirage is formed on a very hot day when the surface of the coal-tarred road or desert
is heated and the air molecules above it become hot. As a result, different layers of air
having different density are formed. The density increases from the surface of the road.
The air with high density acts as a denser medium. So the light travelling down from
upper layer of air bends away from the normal as it goes down from cold layers to hot
layers of air. After coming down through a number of layers, the rays of light suffer total
internal reflection and start going in upward direction. As a result, mirage is seen in coal-
tarred road or desert in hot sunny days.

GREEN Science (Physics) Book-9 97

3. Light pipe

Light pipe is a transparent pipe or rod made of glass or plastic fibres. The light ray that
falls on each optical fibre suffers total internal reflection as show in the figure. A light pipe
is used to view the internal organs of human body. It is based on total internal reflection
of light. It is also used for telecommunication for transmitting signals. It is also used to
transmit images of the objects.

Do You Know Fig.
Fig.
The internal parts of human body can be seen
with the help of light pipe or endoscope due
to total internal reflection of light. The light
pipe is made of optical fibres. When light
pipe is inserted inside the human body, the
light rays coming from internal parts of body
suffer total internal reflection. As a result, the
internal parts of the body can be seen.

5.14

Dispersion of light

In some rainy days, we can see

rainbow in the sky. Do you know

how rainbow is formed? A rainbow

is formed due to dispersion of light.

When the sunlight passes through R
rainwater, it gets dispersed into its
spWehcittreulimght
seven constituent colours. These White light
colours are violet (V), indigo (I), blue beam

(B), green (G), yellow (Y), orange (O), 5.15 Glass prism V
and red (R). So, dispersion of light
can be defined as the phenomenon Dispersion of light

in which white light splits into seven colours. Dispersion of light can be observed by

passing sunlight through a glass prism. The dispersion of light through a prism in shown

in the given figure.

Activity 4

Take a glass prism and go to a sunny place. Allow sunlight to pass through the
prism.

What do you observe?

Does the sunlight split into seven colours?

Write down the conclusion of this activity.

When the sunlight passes through a prism, it splits into seven colours. This process is
called dispersion of light.

98 GREEN Science (Physics) Book-9

From the above activity, it becomes clear that the sunlight is made of seven different
colours. The pattern of seven colours that can be seen on the screen is called spectrum of
light.

Causes of dispersion of light

The major cause of dispersion of light is the difference in speed of light of different colours
in the same medium. The speed of different colours in glass medium is different.

When white light strikes the surface of the prism, different colours move with different
speed. Due to difference in speed, they bend by making different angles. Out of seven
colours of light, the speed of red colour is maximum, so it suffers less deviation and the
speed of violet colour is minimum and surfers more deviation. As a result, a colourful
band of seven colours is formed on the screen which is called spectrum.

The wavelength of red ray has longest wavelength and hence it has minimum frequency.
Similarly, the violet colour has shortest wavelength and hence it has maximum frequency.
Pleases note that the wave length of red ray is 8 × 10–7 m and its frequency is 2.75 × 1014
Hz. Similarly, the wavelength of violet ray is 4 × 10–7 m and its frequency is 7.5 × 1014 Hz.

Electromagnetic wave

The wave which is not affected by electric field and magnetic field is called electromagnetic
wave. Electromagnetic waves can propagate through vacuum or without medium.
Sunlight is an example of electromagnetic wave. It consists of different types of rays. But
our eyes can detect only seven types of rays. These rays are called visible rays and the
spectrum is called visible spectrum.

Radio Microwave Sub- Infrared Ultraviolet X-ray Gamma-ray
mm 800 nm
Wavelength 10 cm 1 mm 10 nm Atoms
0.1 mm
0.1 nm3,00,00,000 K
400 nm

Fig.
Size scale Hand Pin Width at a Single cells Molecules
width head Human hair

0.01 K 3 K 30 K 300 K 5000 K 300,000 K
–273°C –270°C –243°C –27°C

5.16

Different types of spectra are found above the red ray and below the violet ray during
dispersion of light. But we cannot see other spectra. These spectra are called invisible
spectra.

Infrared rays, microwaves and radio waves are the electromagnetic waves having longer
wavelength than that of red rays. Similarly, ultraviolet rays (UV- rays), X-rays, and gamma
rays are the electromagnetic waves having less frequency than that of violet ray. These
waves are harmful for human beings and other animals. However, these waves are utilized
for radiotherapy, radiography and transmission of radio, telephone, television, etc.

GREEN Science (Physics) Book-9 99

X-rays

X-ray are harmful rays for human beings having wavelength from 0.01nm to 10 nm. They
cannot penetrate through bones but can easily penetrate through skin and muscle.

Use of X-rays Do You Know
1. X-rays are used to know about fracture
The exposure to x-rays for a long time is
and cracks in bones. harmful which causes cancer.

2. They are used in radiotherapy.

3. They are used to study molecular
structure and structure of crystals.

4. They are also used in security checking like in airports, custom offices, and other
security threatened zones.

Ultraviolet rays

Ultraviolet rays are commonly known as UV-rays. They are harmful rays having wave
length 10nm to 400 nm. Over exposure to UV-rays may cause eye disease (cataract) and
skin cancer.

Uses of UV-rays

1. UV-rays are used for sterilizing of medical equipment.
2. They are used to check the purity of food items like eggs, ghee, etc.
3. They are used to check the purity of jewelleries.
4. They are used to generate vitamin D.

Key Concepts

1. Light is the form of energy which causes the sensation of sight.
2. Light does not require a material medium (like solid, liquid or gas) for its

propagation.
3. The bending of light when it passes from one medium to another is called refraction

of light.
4. Different optical media have different densities. On this basis, there are two types

of optical media, viz. rarer medium and denser medium.
5. The optical medium having relatively lower density is called rarer medium.
6. The optical medium having relatively higher density is called denser medium.
7. The change in the speed of light when it passes from one medium to another is the

main cause of refraction of light.
8. The angle made by incident ray to the normal is called angle of incidence.
9. The perpendicular drawn at the point on incidence is called normal.
10. The perpendicular distance between emergent ray and incident ray is called lateral

displacement or lateral shift.
11. When a ray of light travels from a rarer medium to a denser medium, it bends

towards the normal and when a ray of light travels from a denser medium to a rarer
medium, it bends away from the normal.

100 GREEN Science (Physics) Book-9