# ICSE Solutions for Chapter 2 Work, Energy and Power Class 10 Selina Physics

### Exercise 2 A

Question 1: An ox can apply a maximum force of 1000 N. It is taking part in a cart race and is able to pull the cart at a constant speed of 30 M
S-1 while making its best effort. Calculate the power developed by the ox.

Solution 1: Given, force = 1000N, velocity = 30m/s
Power, P = force × velocity
P = 1000 x 30 = 30,000W = 30kW

Question 2: If the power of a motor is 40 kw, at what speed can it raise a load of 20,000 N?

Solution 2: Power = 40kW
Force = 20,000N
Power = force × velocity
Velocity = Power/Force = 40 KW/20,000 = 40,000/20,000 = 2 m/s

### Exercise 2 B

Question 1: What are the two forms of mechanical energy?

Solution 1: Two forms of mechanical energy are:
(i) Kinetic energy
(ii) Potential energy

Question 2: Name the forms of energy which a wound-up watch spring possesses.

Solution 2: Elastic potential energy is possessed by wound up watch spring.

Question 3: Name the type of energy (kinetic energy K or potential energy U) possessed in the following cases:
(a) A moving cricket ball
(b) A compressed spring
(c) A moving bus
(d) The bob of a simple pendulum at its extreme position.
(e) The bob of a simple pendulum at its mean position.
(f) A piece of stone places on the roof.

Solution 3: (a) Kinetic energy (K)
(b) Potential energy (U)
(c) Kinetic energy (K)
(d) Potential energy (U)
(e) Kinetic energy (K)
(f) Potential energy (U)

Question 4: When an arrow is shot from a bow, it has kinetic energy in it. Explain briefly from where does it get its kinetic energy?

Solution 4: When the string of a bow is pulled, some work is done which is stored in the deformed state of the bow in the form of its elastic potential energy. On releasing the string to shoot an arrow, the potential energy of the bow changes into the kinetic energy of the arrow which makes it move.

Question 5: Define the term potential energy of a body. State its different forms and give one example of each.

Solution 5: Potential energy: The energy possessed by a body by virtue of its specific position (or changed configuration) is called the potential energy.
Different forms of P.E. are as listed below:

(i) Gravitational potential energy: The potential energy possessed by a body due to its position relative to the centre of Earth is called its gravitational potential energy.
Example: A stone at a height has gravitational potential energy due to its raised height.

(ii) Elastic potential energy: The potential energy possessed by a body in the deformed state due to change in its configuration is called its elastic potential energy.
Example: A compressed spring has elastic potential energy due to its compressed state.

Question 6: A ball is placed on a compressed spring. What form of energy does the spring possess? On releasing the spring, the ball flies away. Give a reason.

Solution 6: The compressed spring has elastic potential energy due to its compressed state. When it is released, the potential energy of the spring changes into kinetic energy which does work on the ball if placed on it and changes into kinetic energy of the ball due to which it flies away.

Question 7: What is meant by the gravitational potential energy? Derive an expression for it.

Solution 7: Gravitational potential energy is the potential energy possessed by a body due to its position relative to the centre of earth.
For a body placed at a height above the ground, the gravitational potential energy is measured by the amount of work done in lifting it up to that height against the force of gravity.
Let a body of mass m be lifted from the ground to a vertical height h. The least upward force F required to lift the body (without acceleration) must be equal to the force of gravity (=mg) on the body acting vertically downwards. The work done W on the body in lifting it to a height h is W = force of gravity (mg) × displacement (h) = mgh
This work is stored in the body when it is at a height h in the form of its gravitational potential energy.
Gravitational potential energy U = mgh

Question 8: Write an expression for the potential energy of a body of mass m places at a height h above the earth's surface.

Solution 8: The work done W on the body in lifting it to a height h is
W= force of gravity (mg) × displacement (h) = mgh
This work is stored in the body when it is at a height h in the form of its gravitational potential energy.
Gravitational potential energy U = mgh

Question 9: Name the form of energy which a body may possess even when it is not in motion. Give an example to support your answer.

Solution 9: Potential energy is possessed by the body even when it is not in motion. For example: a stone at a height has the gravitational potential energy due to its raised position.

Question 10: What do you understand by the kinetic energy of a body?

Solution 10: A body in motion is said to possess the kinetic energy. The energy possessed by a body by virtue of its state of motion is called the kinetic energy.

Question 11: A body of mass m is moving with a velocity v. Write the expression for its kinetic energy.

Solution 11:
Kinetic energy = ½ ×mass×(velocity)2 = ½ mv2

Question 12: State the work energy theorem.

Solution 12: According to the work-energy theorem, the work done by a force on a moving body is equal to the increase in its kinetic energy.

Question 13: A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity changes from u to v. How much work is being done by the force.

Solution 13: Body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity changes from u to v and produces an acceleration a in moving a distance S. Then,
Work done by the force = force x displacement
W = F × S --- (i)
From relation : v2 = u2 + 2aS
Displacement, S = (v2 – u2)/2a
And force, F = ma
From equation (i), W = ma ×(v2– u2)/2a
= 1/2m (v2 – u2)
= ki  - K1
Where K1 is the initial kinetic energy = 1/2 mu
And K1  is the final kinetic energy = ½ mv2
Thus work done on the body = increase in kinetic energy
W = ½ m (v– u2)

Question 14: A light mass and a heavy mass have equal momentum. Which will have more kinetic energy? (Hint: Kinetic energy K = P2/2m where P is the momentum)

Solution 14: Kinetic energy, k = p2/2m where p is the momentum.
Both the masses have same momentum p. The kinetic energy, K is inversely proportional to mass of the body.
Hence light mass body has more kinetic energy because smaller the mass, larger is the kinetic energy

Question 15: Name the three forms of kinetic energy and give on example of each.

Solution 15: The three forms of kinetic energy are:
(i) Translational kinetic energy-example: a freely falling body
(ii) (ii) Rotational kinetic energy-example: A spinning top.
(iii) (iii)Vibrational kinetic energy-example: atoms in a solid vibrating about their mean position.

Question 16: Differentiate between the potential energy (U) and the kinetic energy (K)
Solution 16:
 Potential Energy (U) Kinetic Energy (K) The energy possessed by a body by virtue of its specific position or changed configuration is called potential energy. The energy possessed by a body by virtue of its state of motion is called the kinetic energy. Two forms of potential energy are gravitational potential energy and elastic potential energy. Forms of kinetic energy are translational, rotational and vibrational kinetic energy. Example: A wound up watch spring has potential energy. Example: A moving car has kinetic energy.

Question 17: Complete the following sentences:
(a) The kinetic energy of a body is the energy by virtue of its.............
(b) The potential energy of a body is the energy by virtue of its .....

Solution 17: (a) Motion.
(b) Position.

Question 18: Is it possible that no transfer of energy may take place even when a force is applied to a body?

Solution 18: Yes, when force is normal to displacement, no transfer of energy takes place.

Question 19: Name the form of mechanical energy, which is put to use.

Solution 19: Kinetic energy.

Question 20: In what way does the temperature of water at the bottom of a waterfall differ from the temperature at the top? Explain the reason.

Solution 20: When water falls from a height, the potential energy stored in water at a height changes into the kinetic energy of water during the fall. On striking the ground, a part of the kinetic energy of water changes into the heat energy due to which the temperature of water rises.

Question 21: Name six different forms of energy?

Solution 21: The six different forms of energy are:
1. Solar energy
2. Heat energy
3. Light energy
4. Chemical or fuel energy
5. Hydro energy
6. Nuclear energy

Question 22: Energy can exist in several forms and may change from one form to another. For each of the following, state the energy changes that occur in:
(a) the unwinding of a watch spring
(b) a loaded truck when started and set in motion.
(c) (c) a car going uphill
(d) (d) photosynthesis in green leaves
(e) (e) Charging of a battery,
(f) (f) respiration,
(g) (g) burning of a match stick
(h) (h) the explosion of crackers.

Solution 22: (a) Potential energy of wound up spring converts into kinetic energy.
(b) Chemical energy of petrol or diesel converts into mechanical energy (kinetic energy)
(c) Kinetic energy to potential energy
(d) Light energy changes into chemical energy
(e) Electrical energy changes into chemical energy
(f) Chemical energy changes into heat energy
(g) Chemical energy changes into heat and light energy
(h) Chemical energy changes into heat, light and sound energy

Question 23: State the energy changes in the following cases while in use:
(a) loudspeaker
(b) a steam engine
(c) microphone
(d) washing machine
(e) an electric bulb
(f) burning coal
(g) a solar cell
(h) bio-gas burner
(i) an electric cell in a circuit
(j) a petrol engine of a running car
(k) an electric toaster
(l) a photovoltaic cell
(m) an electromagnet.

Solution 23: (a) Electrical energy into sound energy
(b) Heat energy into mechanical energy
(c) Sound energy into electrical energy
(d) Electrical energy to mechanical energy
(e) Electrical energy into light energy
(f) Chemical energy to heat energy
(g) Light energy into electrical energy
(h) Chemical energy into heat energy
(i) Chemical energy into electrical energy
(j) Chemical energy to mechanical energy
(k) Electrical energy into heat energy
(l) Light energy into electrical energy
(m) Electrical energy into magnetic energy.

Multiple Choice Type

Question 1: A body at a height possesses:
(a) kinetic energy
(b) potential energy
(c) solar energy
(d) heat energy

Solution 1: (b) Potential energy
Hint: P.E. is the energy possessed by a body by virtue of its position.

Question 2: In an electric cell which in use, the change in energy is from:
(a) electrical to mechanical
(b) electrical to chemical
(c) chemical to mechanical
(d) chemical to electrical

Solution 2: Chemical to electrical
Hint: When current is drawn from an electric cell, the chemical energy stored in it changes into electrical energy.

Numericals

Question 1: Two bodies of equal masses are placed at heights h and 2h. Find the ration of their gravitational potential energies.

Solution 1: Height H1 = h
Height H2 = 2h
Mass of body 1 = m
Mass of body 2 = m
Gravitational potential energy of body 1 = mgH1  = mgh
Gravitational potential energy of Body 2 = mgH2 = mg (2h)
Ratio of gravitational potential energies = mgh/mg(2h) = mgh/2mgh = 1/2 = 1 : 2

Question 2: Find the gravitational potential energy of 1 kg mass kept at a height of 5 m above the ground if g = 10 ms-2?

Solution 2: Mass, m = 1kg
Height, h = 5m
Gravitational potential energy = mgh
= 1 × 10 × 5 = 50J

Question 3: A box of weight 150 kgf has gravitational potential energy stored in it equal to 14700 J. Find the height of the box above the ground. (Take g = 9.8 N kg-1)

Solution 3: Gravitational potential energy = 14700 J
Force of gravity = mg = 150 9.8N/kg = 1470N
Gravitational potential energy = mgh
14700 = 1470 × h
h = 10m

Question 4: A body of mass 5 kg falls from a height of 10 m to 4 m. Calculate: (i) the loss in potential energy of the body, (ii) the total energy possessed by the body at any instant? (Take g = 10 m s-1 )

Solution 4: (i) Mass of the body = 5 kg
P.E. at height 10m = mgh = 5 × 10 × 10 = 500 J
P.E. at height 4 m = mgh = 5 × 10 × 4 = 200 J
Loss in P.E. = (500 – 200) J = 300 J

(ii) The total energy possessed by the body at
It is equal to the sum of P.E. and K.E.
∴  At height 10m, i.e., at top most point, K.E. = 0
∴  Total energy = P.E. + K.E.
Total energy = 500 + 0 = 500J

Question 5: Calculate the height through which a body of mass 0.5 kg is lifted if the energy spent in doing so is 1.0 J. Take g = 10 m s-2

Solution 5: Mass = 0.5 kg
Energy = 1 J
Gravitational potential energy = mgh
1 = 0.5 × 10 × h
1 = 5h
Height, h = 0.2 m

Question 6: A boy weighing 25 kgf climbs up from the first floor at height 3 m above the ground to the third floor at height 9m above the ground. What will be the increase in his gravitational potential energy? (Take g = 10 N kg-1)

Solution 6: Force of gravity on boy = mg = 25 × 10 = 250N
Increase in gravitational potential energy = Mg (h2 – h1)
= 250 × (9 – 3)
= 250 × 6 = 1500 J

Question 7: A vessel containing 50 kg of water is placed at a height 15 m above the ground. Assuming the gravitational potential energy at ground to be zero, what will be the gravitational potential energy of water in the vessel? (g = 10 ms-2 )

Solution 7: Mass of water, m = 50kg
Height, h = 15m
Gravitational potential energy = mgh
= 50 × 10 × 15
= 7500 J

Question 8: A man of mass 50 kg climbs up a ladder of height 10 m. Calculate: (i) the work done by the man, (ii) the increase in his potential energy. (g = 9.8 ms-2 )

Solution 8: Mass of man = 50kg
Height of ladder, h2 = 10m
(i) Work done by man = mgh2
= 50 × 9.8 × 10 = 4900J

(ii) increase in his potential energy:
Height, h2 = 10m
Reference point is ground, h2  = 0m
Gravitational potential energy = Mg (h2 - h1)
= 50 × 9.8 ×  (10 - 0)
= 50 × 9.8 × 10 = 4900J

Question 9: A block A, whose weight is 200 N, is pulled up a slope of length 5 m by means of a constant force F (= 150 N) as illustrated in Fig

(a) what is the work done by the force F in moving the block A, 5 m along the slope?
(b) By how much has the potential energy of the block A increased?
(c) Account for the difference in work done by the force and the increase in potential energy of the block.

Solution 9: F = 150N
(a) Work done by the force in moving the block 5m along the slope = Force x displacement in the direction of force = 150 x 5 = 750 J

(b) The potential energy gained by the block
U = mgh where h = 3m
= 200 × 3 = 600 J

(c) The difference i.e., 150 J energy is used in doing work against friction between the block and the slope, which will appear as heat energy.

Question 10: Find the kinetic energy of a body of mass 1 kg moving with a uniform velocity of 10 ms-1 .

Solution 10: Mass, m = 1kg
Velocity, v = 10m/s
Kinetic energy  = 1/2 ×mass×(velocity)2
= ½ × 1 × (10)
= ½  × 1 × 100
= 50J

Question 11: If the speed of a car is halved, how does its kinetic energy change?

Solution 11: If the speed is halved (keeping the mass same), the kinetic energy decreases, it becomes one-fourth (since kinetic energy is proportional to the square of velocity).

Question 12: Two bodies of equal masses are moving with uniform velocities v and 2v. Find the ratio of their kinetic energies.

Solution 12: Given, velocity of first body v1  = v
And velocity of second body, v2 = 2v
Since masses are same, kinetic energy is directly proportional to the square of the velocity.
Hence, ratio of their kinetic energies is:
k1/k2  = (v1)2 /(v2)2 = v/(2v) = v2/4v
= ¼ = 1 : 4

Question 13: A car is running at a speed of 15 km h-1  while another similar car is moving at a speed of 30 km h-1. Find the ration of their kinetic energies.

Solution 13: Given, velocity of first car, v1 = 15 km/h
And velocity of second car, v2 = 30 km/h
Since masses are same, kinetic energy is directly proportional to the square of the velocity (Kav)
Hence, ratio of their kinetic energies is:
k1/k= (v1)2 /(v2)2 =   152/(30)2 = (15 × 15)/(30 × 30) = ¼ = 1 : 4

Question 14: A bullet of mass 0.5 kg slows down from a speed of 5 m s-1 to that of 3 m s-1. Calculate the change in kinetic energy of the ball.

Solution 14: Mass of ball = 0.5kg
Initial velocity = 5m/s
Initial kinetic energy = ½ × mass × (velocity)2
= ½ × 0.5 × (5)2
= ½ × 0.5 × 25 = 6.25J
Final velocity of the ball = 3m/s
Final kinetic energy of the ball = ½ × mass × (velocity)2
= 1/2 × 0.5 × (3)2
= ½ × 0.5 × 9 = 2.25J
Change in the kinetic energy of the ball = 2.25 J – 6.25J = – 4J
There is a decrease in the kinetic energy of the ball.

Question 15: A cannon ball of mass 500 g is fired with a speed of 15 m s. Find: (i) its kinetic energy and (ii) its momentum.

Solution 15: Mass of canon ball = 500g = 0.5 kg
Speed, v = 15m/s
(a) Kinetic energy of ball = ½ × mass × (velocity)2
= ½ × 0.5 × (15)2
= ½ × 0.5 × 225 = 56.25J

(b) Momentum of the ball = mass × velocity
= 0.5 × 15 = 7.5 kgm/s

Question 16: A bullet of mass 50 g is moving with a velocity of 500 m s. It penetrated 10 cm into a still target and comes to rest. Calculate: (a) the kinetic energy possessed by the bullet, (b) the average retarding force offered by the target.

Solution 16: Mass of bullet = 50g = 0.05kg
Velocity = 500m/s
Distance penetrated by the bullet = 10cm = 0.1m
(a) Kinetic energy of the bullet =1/2 × mass × (velocity)2
= ½ × 0.05 × (500)2
= ½ × 0.05 × 500 × 500 = 6250 J

(b) Work done by the bullet against the material of the target = resistive force x distance
6250 = resistive force × 0.1m
Resistive force = 62500 N

Question 17: A body of mass 10 kg is moving with a velocity 20 m s-1. If the mass of the body is doubled and its velocity is halved, find the ratio of the initial kinetic energy to the final kinetic energy.

Solution 17: Let initial Mass, m1  = 10kg and velocity, v1 = 20 m/s
Final mass, m2 = 2×10 = 20 kg and velocity, v2 = 20/2 = 10m/s
Initial kinetic energy, KÄ± = ½ x mass x (velocity)2
=1/2 × 10 × (20)2
= 1/2 × 10 × 20 × 20
= 2000 J
Final kinetic energy, K2  = ½ x mass × (velocity)2
= 1/2 × 20 × (10)2
= ½ × 20 × 10 ×10
= 1000J
k1/k2 = 2000/1000
= 2/1
= 2 : 1

Question 18: A truck weighing 1000 kgf changes its speed from 36 km h-1 to 72 km h-1in 2minutes. Calculate:
(i) the work done by the engine and
(j) (ii) its power/ (g = 10 m s-2)

Solution 18: U = 36 km/h = (36 × 1000m)/3600s = 10m/s
and v = 72km/h = (72 × 1000m)/3600s = 20m/s
mass of the truck = 1000 kg
(i) W = ½  × 1000 × (202 - 102)
W = 500 × (400 - 100)
W = 500 × 300 = 150000J
W = 1.5×105 J

(ii) Power = workdone/time taken
= (1.5×105J)/120 s = 1.25×103 w

Question 19: A body of mass 60 kg has the momentum 3000 kg m s-1. Calculate: (i) the kinetic energy and (ii) the speed of the body.

Solution 19: Mass of body = 60kg
Momentum, p = 3000kgm/s
(i) Kinetic energy = p2/2m
= (3000)2/(2 × 60)
= (3000 × 3000)/120 = 75000J
= 7.5 ×104 J

(ii) Momentum = mass x velocity
3000 = 60 x velocity
Velocity = 50m/s

Question 20: How much work is needed to be done on a ball of mass 50 g to give it s momentum of 500 g cm s-1 ?

Solution 20: Momentum, p = 500 gcm/s = 0.005 kgm/s
Mass of ball = 50 g = 0.05kg
(a)Kinetic energy of the ball = p2 /2m
= p2/2m = (0.005)2/(2 × 0.05)
= 2.5 × 10-4 J

Question 21: How much energy is gained by a box of mass 20 kg when a man
(a) carrying the box waits for 5 minutes for a bus?
(b) runs carrying the box with a speed of 3 m s-2 to catch the bus?
(c) Raises the box by 0.5 m in order to place it inside the bus? (g = 10 m s-2)

Solution : Mass of box = 20 kg
(a) Zero work is done as there is no displacement of the man.

(b) Work done, kinetic energy of man
= ½ × mass × (velocity)2
= ½ × 20 × (3)2
= ½ × 20 × 9
= 90 J

(c) Work done in raising the box, Potential energy = mgh
U = 20 × 10 × 0.5 = 100 J

Question 22: A spring is kept compressed by a small trolley of mass 0.5 kg lying on a smooth horizontal surface as shown in the adjacent fig. when the trolley is released, it is found to move at a speed v = 2 m s-1. What potential energy did the spring possess when compressed?

Solution 22: Mass of trolley = 0.5 kg
Velocity = 2 m/s
When the compressed spring is released, its potential energy is converted into kinetic energy completely.
Potential energy of compressed spring = kinetic energy of moving trolley
Kinetic energy of trolley = ½ × mass × (velocity)2
= ½ × 0.5 × (2)2
= 1 × 0.5 × 2 × 2 = 1J
Hence, potential energy of compressed spring = 1.0J

### Exercise 2 C

Question 1: State two characteristic which a source of energy must have.

Solution 1: Two characteristics which a source of energy must have are as listed below:
i. It should provide an adequate amount of useful energy at a steady rate over a longer period
of time.
ii. It should be safe and convenient to use and economical.

Question 2: Name the two groups in which various sources of energy are classified. State on what basis are they classified

Solution 2: Sources of energy are classified as shown below:
1. Renewable or non-conventional sources
2. Non-renewable or conventional sources
The above classification is done on the basis of availability of the energy sources.

Question 3: What is meant by the renewable and non-renewable sources of energy? Distinguish between them giving two examples of weach.

Solution 3:
 Renewable Sources Non-renewable Sources These are the sources from which energy can be obtained continuously over a very long period of time. These are the sources from which energy cannot be obtained continuously over a very long period of time. They are the non-conventional sources. They are conventional sources. These resources can be regenerated. These resources cannot be regenerated These are the natural sources which will not get exhausted. These are the natural sources which will soon get depleted. Examples: solar energy, wind energy, nuclear energy etc. Examples: coal, petroleum and natural gas.

Question 4: Select the renewable and non-renewable sources of energy from the following:
(a) Coal
(b) Wood
(c) Water
(d) Diesel
(e) Wind
(f) Oil

Solution 4:
 Renewable Sources Non-renewable Sources Wood Coal Water Diesel Wind Oil

Question 5: Why is the use of wood as a fuel not advisable although wood is a renewable source of energy?

Solution 5: A tree usually takes more than 15 years to grow fully; therefore renewal of wood as energy source takes a long time. Further, the cutting of trees on a large scale causes depletion of forests which results in environmental imbalance. Hence use of wood as a fuel must be avoided.

Question 6: Name five renewable and three non-renewable sources of energy.

Solution 6:
Five renewable sources of energy:
1. Sun
2. Wind
3. Flowing water
4. Bio-mass
5. Tides
Three non-renewable sources of energy:
1. Coal
2. Petroleum
3. Natural gas

Question 7: What is (i) tidal, (ii) ocean and (iii) geo thermal energy? Explain in brief.

Solution 7:
(i) Tidal energy: The energy possessed by rising and falling water in tides is known as tidal energy.
Dams are constructed across a narrow opening to the sea to harness tidal energy and produce electricity. However, it is not a major source of energy as the rise and fall of seawater during tides is not enough to generate electricity on a large scale.

(ii) Ocean energy: Water in the oceans possesses energy in two forms:
(a) Ocean thermal energy- The energy available due to the difference in temperature of
water at the surface and at deeper levels of ocean is called the ocean thermal energy. This energy is harnessed for producing electricity by a device called ocean thermal energy conversion power plant (OCTEC power plant).
(b) Oceanic waves energy - The kinetic energy possessed by fast moving oceanic (or sea)
waves is called oceanic waves energy. Though models have been made to generate electricity from oceanic waves, but so far it has not been put to practical use.

(iii) Geo thermal energy: The heat energy possessed by the rocks inside the Earth is called geothermal energy. The hot rocks present at the hot spots deep inside the Earth, heat the underground water and turn it into steam. This steam is compressed at high pressure between the rocks. Holes are drilled deep into the Earth up to the hot spots to extract the steam through pipes, which is utilized to rotate the turbines connected to the armature of an electric generator to produce electricity.

Question 8: What is the main source of energy for earth?

Solution 8: Sun is the main source of energy on earth.

Question 9: What is solar energy? How is the solar energy used to generate electricity in a solar power plant?

Solution 9: The energy obtained from sun is called the solar energy. A solar power plant is a device in which heat energy of sun is used to generate electricity. It consists of a large number of concave reflectors, at the focus of which there are black painted water pipes. The reflectors concentrate the heat energy of the sun rays on the pipes due to which water inside the pipes starts boiling and produces steam. The steam thus produced is used to rotate a steam turbine which drives a generator producing electricity.

Question 10: What is a solar cell? State two uses of solar cells. State whether a solar cell produces a.c. or d.c. Give one disadvantage of using a solar cell.

Solution 10: A solar cell is an electrical device that converts light energy directly into electricity with the help of photovoltaic effect. Solar cells are usually made from semiconductors like silicon and gallium with some impurity added to it. When sunlight is made incident on a solar cell, a potential difference is produced between its surface, due to which a current flows in the circuit connected between the opposite faces of the semiconductor.
Two uses of solar cells are as listed below:
(i) They do not require maintenance and last over a long period of time at zero running cost.
(ii) They are very useful for remote, inaccessible and isolated places where electric power lines cannot be laid.
Solar cell produces d.c. (direct current).
One disadvantage of solar cell is listed below:
i. The initial cost of a solar panel is sufficiently high.

Question 11: State two advantages and two disadvantages of producing electricity from solar energy.

Solution 11: Advantages of using solar panels:
1. They do not cause any pollution in the environment.
2. Running cost of solar panel is almost zero.
3. They last over a long period of time.
4. They do not require any maintenance.
5. They are suitable for remote and inaccessible places where electricity power lines cannot be laid.
1. The initial cost of a solar panel is sufficiently high.
2. The efficiency of conversion of solar energy to electricity is low.
3. A solar panel produces d.c. electricity which cannot be directly used for many household purposes.

Question 12: What is wind energy? How is wind energy used to produce electricity? How much electric power is generated in India using the wing energy?

Solution 12: The kinetic energy of the moving large masses of air is called the wind energy. Wind energy is used in a wind generator to produce electricity by making use of wind mill to drive a wind generator.
At present in India, more than 1025MW electric power is generated using the wind energy.

Question 13: State two advantages and two disadvantages of using wind energy for generating electricity.

Solution 13: Advantages of using the wind energy:
1. It does not cause any kind of pollution.
2. It is an everlasting source.
1. The establishment of a wind farm is expensive.
A large area of land is needed for the establishment of a wind farm.

Question 14: What is hydro energy? Explain the principle of generating electricity from hydro energy. How much hydroelectric power is generated in India?

Solution 14: The kinetic energy possessed by the flowing water is called the water or hydro energy. Principle of a hydroelectric power plant is that the water flowing in high altitude rivers is collected in a high dam (or reservoir). The water from dam is then allowed to fall on a water turbine which is located near the bottom of the dam. The shaft of the turbine is connected to the armature of an electric generator or dynamo.
At present only 23% of the total electricity is generated by the hydro energy.

Solution 15: Advantages of producing the hydroelectricity:
1. It does not produce any environmental pollution.
2. It is a renewable source of energy.
1. Due to the construction of dams over the rivers, plants and animals of that place get
destroyed or killed.
2. The ecological balance in the downstream areas of rivers gets disturbed.

Question 16: What is nuclear energy? Explain the principle of producing electricity using the nuclear energy.

Solution 16: When a heavy nucleus is bombarded with slow neutrons, it splits into two nearly equal light nuclei with a release of tremendous amount of energy. In this process of nuclear fission, the total sum of masses of products is less than the total sum of masses of reactants. This lost mass gets converted into energy. The energy so released is called nuclear energy.
Principle: The heat energy released due to the controlled chain reaction of nuclear fission of uranium-235 in a nuclear reactor is absorbed by the coolant which then passes through the coils of a heat exchanger containing water. The water in heat exchanger gets heated and converts into steam. The steam is used to rotate the turbine which in turn rotates the armature of a generator in a magnetic field and thus produces electricity.

Question 17: What percentage of total electrical power generated in india is obtained from nuclear power plant? Name two places in india where electricity is generated from nuclear power plants.

Solution 17: At present only about 3% of the total electrical power generated in India is obtained from the nuclear power plants. Tarapur in Maharashtra and Narora in Uttar Pradesh are the places where electricity is produced by use of nuclear energy

Question 18: State two advantages and two disadvantages of using nuclear energy for producing electricity.

Solution 18: Advantages of using nuclear energy:
1. A very small amount of nuclear fuel can produce a tremendous amount of energy.
2. Once the nuclear fuel is loaded into nuclear power plant, it continues to release energy for several years.
1. It is not a clean source of energy because very harmful nuclear radiations are produced in process.
2. The waste causes environmental pollution.

Question 19: State the energy transformation on the following:
(i) Electricity is obtained from solar energy.
(ii) electricity is obtained from wind energy
(iii) Electricity is obtained from hydro energy.
(iv) Electricity is obtained from nuclear energy.

Solution 19: (a) Light energy into electrical energy
(b) Mechanical energy into electrical energy.
(c) Mechanical energy into electrical energy.
(d) Nuclear energy(or heat energy) into electrical energy.

Question 20: State four ways for the judicious use of energy.

Solution 20: Four ways for the judicious use of energy:
(a) The fossil fuels such as coal, petroleum, natural gas should be used only for the limited purposes when there is no other alternative source of energy available.
(b) The wastage of energy should be avoided.
(c) Efforts must be made to make use of energy for community or group purposes.
(d) The cutting of trees must be banned and more and more new trees must be roped to grow.

Multiple Choice Type

Question 1: The ultimate source of energy is:
(a) wood
(b) wind
(c) water
(d) sun

Solution 1: Sun

Question 2: Renewable source of energy is:
(a) Coal
(b) fossil fuels
(c) natural gas
(d) sun

Solution 2: Sun

### Exercise 2 D

Question 1: State the law of conservation of energy.

Solution 1: According to the law of conservation of energy, energy can neither be created nor can it be destroyed. It only changes from one form to another.

Question 2: What do you understand by the conservation of mechanical energy? State the condition under which the mechanical energy is conserved.

Solution 2: According to the law of conservation of mechanical energy, whenever there is an interchange between the potential energy and kinetic energy, the total mechanical energy (i.e., the sum of kinetic energy K and potential energy U) remains constant i.e., K + U = constant when there are no frictional forces.
Mechanical energy is conserved only when there are no frictional forces for a given system (i.e. between body and air). Thus, conservation of mechanical energy is strictly valid only in vacuum, where friction due to air is absent.

Question 3: Name two examples in which the mechanical energy of a system remains constant.

Solution 3: Motion of a simple pendulum and motion of a freely falling body.

Question 4: A body is thrown vertically upwards. Its velocity keeps on decreasing. What happens to its kinetic energy as its velocity becomes zero?

Solution 4: Kinetic energy of the body changes to potential energy when it is thrown vertically upwards and its velocity becomes zero.

Question 5: A body falls freely under gravity from rest. Name the kind of energy it will possess.
(a) at the point from where it falls.
(b) while falling
(c) on reaching the ground.

Solution 5: (a) Potential energy
(b) Potential energy and kinetic energy
(c) Kinetic energy

Question 6: Show that the sum of kinetic energy and potential energy (i.e., total mechanical energy) is always conserved in the case of a freely falling body under gravity (with air resistance neglected) from a height h by finding it when (i) the body is at the top, (ii) the body has fallen a distance x, (iii) the body has reached the ground.

Solution 6: Let a body of mass m be falling freely under gravity from a height h above the ground (i.e., from position A). Let us now calculate the sum of kinetic energy K and potential energy U at various positions, say at A (at height h above the ground), at B (when it has fallen through a distance x) and at C (on the ground).

(i) At the position A (at height h above the ground):
Initial velocity of body = 0 (since body is at rest at A)
Hence, kinetic energy K = 0
Potential energy U = mgh
Hence total energy = K + U = 0 + mgh = mgh ....(i)

(ii) At the position B (when it has fallen a distance x):
Let v1 be the velocity acquired by the body at B after falling through a distance x.
Then u = 0, S = x, a = g
From equation v= u2+ 2As
v1= 0 + 2gx = 2gx
Hence, Kinetic energy K = ½ mv12 = mgx
Now at B, height of body above the ground = h – x
Hence, potential energy U = mg (h – x)
Hence total energy = K + U
= mgx + mg (h - x) = mgh  ...(ii)

(iii) At the position C (on the ground):
Let the velocity acquired by the body on reaching the ground be v.
Then u = 0, S = h, a = g
From equation: v= u2+ 2aS
v= 02+ 2gh
v= 2gh
Hence, kinetic energy K = 1/2 mv2
=1/2 m (2gh) = mgh
And potentiall energy U = 0 (a the ground when h = 0)
Hence total energy = K + U = mgh + 0 = mgh ---- (iii)
Thus from equation (i), (ii) and (iii), we note that the total mechanical energy i.e., the sum of kinetic energy and potential energy always remain constant at each point of motion and is equal to initial potential energy at height h.

Question 7: A pendulum is oscillating on either side of its rest position. Explain the energy changes that takes place in the oscillating pendulum. How does the mechanical energy remains constant in it? Draw the necessary diagram.

Solution 7: When the bob swings from A to B, the kinetic energy decreases and the potential energy becomes maximum at B where it is momentarily at rest.
From B to A, the potential energy again changes into the kinetic energy and the process gets repeated again and again.
Thus while swinging, the bob has only the potential energy at the extreme position B or C and only the kinetic energy at the resting position A. At an intermediate position (between A and B or between A and C), the bob has both the kinetic energy and potential energy, and the sum of both the energies (i.e., the total mechanical energy) remains constant throughout the swing.

Question 8: A pendulum with bob of mass m is oscillating on either side from its resting position A between the extremes B and C at a vertical height h and A. what is the kinetic energy K and potential energy U when the pendulum is at position (i) A, (ii) B and (iii) C?

Solution 8: (a) At position A, pendulum has maximum kinetic energy and its potential energy is zero at its resting position. Hence, K =  mgh and U = 0.
(b) At B, kinetic energy decreases and potential energy increases. Hence, K = 0 and U = mgh
(c) At C also, kinetic energy K = 0 and potential energy U = mgh.

Question 9: What do you mean by degradation of energy? Explain it by taking two examples of your daily life.

Solution 9: The gradual decrease of useful energy due to friction etc. is called the degradation of energy.
Examples:
1. When we cook food over a fire, the major part of heat energy from the fuel is radiated out in the atmosphere. This radiated energy is of no use to us.
2. When electrical appliances are run by electricity, the major part of electrical energy is
wasted in the form of heat energy.

Multiple Choice Type

Question 1: A ball of mass m is thrown vertically up with an initial velocity so as to reach a height h. The correct statement is: (a) Potential energy of the ball at the ground in mgh. (b) Kinetic energy imparted to the ball at the ground is zero. (c) Kinetic energy of the ball at the highest point is mgh. (d) potential energy of the ball at the highest point is mgh.

Solution 1: Potential energy of the ball at the highest point is mgh.
Hint: At the highest point, the ball momentarily comes to rest and thus its kinetic energy becomes zero.

Question 2: A pendulum is oscillating on either side of its rest position. The correct statement is:
(a) It has only the kinetic energy.
(b) it has the maximum kinetic energy at its extreme position.
(c) it has the maximum potential energy at its rest position.
(d) The sum of its kinetic and potential energies remains constant throughout the motion.

Solution 2: The sum of its kinetic and potential energy remains constant throughout the motion. Hint: In accordance with law of conservation of mechanical energy, whenever there is an interchange between the potential energy and kinetic energy, the total mechanical energy remains constant.

Numericals

Question 1: A ball of mass 0.20 kg is thrown vertically upwards with an initial velocity of 20 m s-1 .Calculate the maximum potential energy it gains as it goes up.

Solution 1: Potential energy at the maximum height = initial kinetic energy
= ½ mv2
= ½ × 0.20 × 20 × 20 = 40J

Question 2: A stone of mass 500g is thrown vertically upwards with a velocity of 15 m s-1 Calculate: (a) the potential energy at the greatest height, (b) the kinetic energy on reaching the ground, (c) the total energy at its half-way point.

Solution 2: (a) Potential energy at the greatest height = initial kinetic energy
or, mgh = ½ mv2
= ½ × 0.500 × 15 × 15 = 56.25J
(b) Kinetic energy on reaching the ground= potential energy at the greatest height = 56.25 J
(c) Total energy at its half-way point = 1/2(K + U) = 56.25J

Question 3: A metal ball of mass 2 kg is allowed to fall freely from rest from a height of 5m above the ground. (Take g = 10 m s-2)
(a) Calculate the potential energy possessed by the ball when initially at rest.
(b) what is the kinetic energy of the ball just before it hits the ground?
(c) what happens to the mechanical energy after the ball hits the ground and comes to rest?

Solution 3: (a) Potential energy of the ball = mgh
= 2 x 10 x 5 =100J
(b) Kinetic energy of the ball just before hitting the ground = Initial potential energy = mgh = 2 × 10 × 5 = 100J
(c) Mechanical energy converts into heat and sound energy.

Question 4: The diagram given below shows a ski jump. A skier weighing 60 kgf stands at A at the top of ski jump. He moves from A to B and takes off for his jump at B.

(a) Calculate the change in the gravitational potential energy of the skier between A and B. (b) If 75% of the energy in part (a) becomes kinetic energy at B. Calculate the speed at which the skier arrives at B.
(Take g = 10 m s-2)

Solution 4: (a) Mass of skier = 60kg
Loss in potential energy = mg(h1 - h2)
= 60 × 10 × (75 -15)
= 60 × 10 x 60
= 3.6 × 104J

(b) Kinetic energy at B = 75/100 × 3.6 ×104 = 27000 J
= 2.7 × 104 J
Kinetic energy = ½ mv2
27000 = ½ mv2
27000 = ½ × 60 × v2
v2 = 27000/30 = 900
v = 30m/s

Question 5: A hydroelectric power station takes its water from a lake whose water level if 50 m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1 MV.

Solution 5: Potential energy = mgh
Efficiency = 40%
Useful work done = 40% of potential energy
= 40/100 (mgh)
= 0.4 × (m × 10 × 50)
= 200m
Power = work done pr second
1MW = 200 x mass of water flowing each second
1 × 106w = 200 × mass of water flowing each second
Mass of water flowing each second = (1 × 10)6/200 = 5000kg

Question 6: The bob of a simple pendulum is imparted a velocity 5 m s-1when it is at its mean position. To what maximum vertical height will it rise on reaching to its extreme position if 60% of its energy is lost in overcome friction of air?

Solution 6: Potential energy at the extreme position = 40% of kinetic energy at the resting position.
mgh = 40/100 × (1/2 mv2)
40/100 × (1/2 mv2) = mgh
0.4 × 0.5 × m × v2 = mgh
0.2 × v2 = 10 × h
0.2 × 5 × 5 = 10h
H = 5/10 =  0.5m