The intuitive meaning of work is quite different from the scientific definition of work. In everyday activity, the term 'work' is used equally for mental work and for physical work (involving muscular force) as is clear from the following examples.
(i) You may read a book or exert yourself mentally in thinking about a simple or difficult problem.
(ii) You might be holding a weight without moving.
(iii) You may be carrying a load and moving with uniform velocity.
(iv) You may be trying hard to move a huge rock which does not move despite your best efforts, though you may get completely exhausted in the process.
In all these cases, according to scientific definition, you are not doing any work.
In physics, the term work is used in a special technical sense and has a much more precise definition which follows from the following examples.
(i) When a box is pushed on a floor by applying a force and it moves through some distance, work is said to be done. In this case, the applied force displaces the box.
(ii) When we pull a trolley by applying a force and it moves through some distance, work is again said to be done.
(iii) When we lift a box through a height, we have to apply force. In this case, the applied force does work in lifting the box.
From all the examples given above, it follows that work is done if :
(a) a force is applied on the object and
(b) the object is displaced from its original position.
No work is said to be done if any of the two conditions is not satisfied.
Work done, W = Fd
In C.G.S. system the unit of work done is dyne x cm = erg.
Definition of 1 erg:
If F = 1 dyne and d = 1 cm
then, W = 1 × 1 = 1 erg.
If one dyne force is applied on a body and displacement in the body is 1 cm in the direction of force, then work done will be one erg.
S.I. unit of work done is newton × metre = joule
Definition of 1 joule:
If F = 1N and d = 1m
then, W = 1 × 1 = 1 joule (J)
If a force 1 Newton is applied on a body and displacement in the body is 1m in the direction of force then work done will be 1 joule.
Relation between joule and erg:
1 joule = 107 erg
Erg and joule are the absolute units of work done.
1. When s = 0, W = 0, i.e. work done by a force on a body is zero 
if the displacement of the body is zero. For example, when you push a
wall with a force F, then the displacement of the wall is zero.
Therefore, the work done by force F on the wall is zero.
2. When you sit on a chair and prepare a lesson in two hours, you may feel tired. But according to physics, no work is done.
3. If you hold a briefcase for one hour and do not move the briefcase, then s = 0. Therefore, work done by you on the briefcase is zero.
A body A is kept on a smooth horizontal surface. A force F is applied as shown. This force acts on the body for some time during which the displacement of the body is s. In such a case work is defined as follows.
Work done by a force on a body is the product of force and 
displacement of the body in the direction of the force.
Work = Force × Displacement
=> W = F × s
Work is a scalar quantity. This means that it has no sense of direction.
Let us consider a body A lying on a smooth horizontal surface. A constant force F acts at an angle q to the horizontal. The body is displaced through a distance s in the horizontal direction. Here the complete force F is not responsible to displace the body. A part of the force acting in the direction of displacement is responsible for displacing the body. This horizontal part is F cos q. Work done in this case is defined as 'work done by a constant force acting at an angle to the displacement is the product of component of force in the direction of displacement and the displacement of the body'.
Work = Component of force in the direction of displacement x Displacement
CASE-1 : Work done is positive when q is acute. This is because cos q is positive, Work done is maximum when q = 0°. This is because the maximum value of cos q = 1. This happens when force acts in the direction of displacement.
CASE-2 : When the angle between force and displacement is 90°, i.e. when q = 90°, then
cos 
= 0 cos 90° = 0
W= 0
Some examples where work done is zero because q = 90°
(a) WORK DONE BY CENTRIPETAL FORCE: When a stone is whirled in a horizontal circle, then centripetal force acts at 90° to the displacement. Therefore, work done by centripetal force is zero.
(b) WORK DONE BY COOLIE: When a coolie moves on a horizontal surface, he applies a force on the load kept on his head in vertically upward direction. Therefore, q = 90°. Therefore, work done by the force applied by coolie is zero.
(c) MOTION OF THE EARTH AROUND THE SUN: Work done by the centripetal force (which is the gravitational pull of sun on earth) acting on earth is zero. Because centripetal force is perpendicular to the displacement.
[Remember the displacement is always tangential and centripetal force is always radically inward. The angle between radius and tangent is 90°].
NOTE : Work may be positive, negative or zero depending on the angle .
When the angle between force and the displacement is acute (q < 90°), then work done will be positive because one component of force (F cosq) is in the direction of displacement so work done by this component will be positive (Fd cosq). Work done by the vertical component (i.e F sinq) will be zero (Q the angle between F sinq and displacement is 90°) so net work done will be positive.
(i) In lifting weight upward by applying an upward force the work done by the applied force will be positive.
(ii) In stretching a spring, the work done by the external force will be positive.
When the angle between the force and the displacement is obtuse, (q > 90°), then work done will be negative because work done by the horizontal component of force (i.e. F cosq) is negative (–Fd cosq) and the work done by the vertical component (F sinq) will be zero, so net work done will be negative.
Conservative forces are defined by following three ways.
(i) Work done by a conservative force in moving a body from one position to another depends only on the initial and final positions and not on the length of the path followed between to positions.
(ii) Work done by conservative force in moving a complete round is always Zero.
(iii) Energy of the body after one complete round remain unchanged, then the force by which this work is held will be a conservative force.
Examples of Conservative forces:
Gravitational force, Restoring force, Electrical force, Lorenz force etc.
If work done by the force depends on the path then force is called non conservative force.
E.g.: Frictional force, Viscous force, etc.
When a car runs, the engine of the car generates a force which displaces the car. In other words, work is done by the car. This work is done on the expense of fuel. Fuel provides the energy needed to run the car. Had the petrol tank been empty, car could not be run. The conclusion is that, if there is no source of energy, no work will be done.
Let us take another example. Suppose a lift takes some persons from ground floor to second floor. Then the lift performs work. If you enquire, you will find that the lift is operated by an electrical motor. Thus, electrical energy does the work. If there is no electricity the lift will not operate. Again if there is no source of energy, no work will be done.
The above statement is not just true for the above two examples, but is true for all processes.
Therefore, energy is defined as the capacity to do work. Energy is the ability to do work. More the energy, more the work that can be performed and vice-versa.
Energy is a scalar quantity.
The S.I. unit of energy is joule (J). (Bigger units is 1 kJ = 1000 J, 1 MJ = 106 J)
The C.G.S. unit of energy is erg.
² NOTE:
(i) kilo Watt × hour (kWh) is commercial unit of energy.
1 kWh = 1000 watt × 60 × 60 sec
= 3.6 × 106 watt × sec.
1 kWh = 3.6 × 106 J.
(ii) Electron volt (eV) is also the unit of energy. The energy of an electron, when it is accelerated by a potential difference of 1 volt, is known as one eV
1eV = 1.6 × 10–19J
Nature-has been very kind to us in providing us energy in various forms. These forms of energy are as follows.
1. Solar energy. The energy radiated by the Sun is called solar energy. Plants collect and store this energy to make food through photosynthesis.
2. Heat energy. It is the energy released when coal, oil, gas or wood burn and it produces in us the sensation of warmth.
3. Light energy. It is the form of energy which produces in us the sensation of light. Sun is the natural source of light.
4. Chemical energy. It is the energy possessed by fossil fuels (coal; petroleum and natural gas) and is also called the fuel energy. The food that we eat has chemical energy stored in it.
5. Hydro energy. The energy possessed by water flowing in rivers and streams is called hydro energy. This energy is used to generate electricity in hydroelectric power plants.
6. Wind energy. The energy possessed by moving air is called wind energy.
7. Ocean thermal energy (OTE). Solar energy stored in the oceans in the form of heat is called ocean thermal energy.
8. Geothermal energy. It is the heat energy of the Earth and is found within rock formations and the fluids held within those formations.
9. Biomass energy. It is the energy obtained from biomass (i.e., living matter or its residues).
10. Tidal energy. It is the energy derived from the rising and falling ocean tides.
11. Sound energy. It is the energy possessed by vibrating objects and it produces in us the sensation of hearing.
12. Mechanical energy. It is the energy possessed by a body due to its position (or configuration) or motion. The energy possessed due to position or configuration is called potential energy and that due to motion is called kinetic energy. The sum of these two energies is called the mechanical energy.
13. Electric energy. The energy possessed by charges (either at rest or in motion) is called electric energy.
14. Magnetic energy. It is the energy possessed by magnetised bodies e.g. a magnet.
15. Electromagnetic energy. It is the general name for electric and magnetic energies.
16. Nuclear energy. The energy produced in the processes of fission and fusion is called nuclear energy.
A moving object is capable of doing work because of it" motion. Hence, we say that the object has kinetic energy. "Kinetikos" in Greek means "to move". Hence, kinetic energy means energy due to motion. The energy is stored in the object when work is done to change its velocity from a lower value to a higher value, or from rest to certain velocity.
Kinetic energy of an object is defined as the energy which it possesses by virtue of its motion, and is measured by the amount of work that the object can do against an opposing force before it comes to rest.
Kinetic energy of an object moving with a certain velocity is equal to the work done on it to enable it to acquire that velocity.
1. A ball rolling on a surface because it can set another ball into motion by striking it.
2. A bullet fired from a gun as it is able to penetrate some distance into a target which it strikes.
3. A tarpedo in motion as it can do work by penetrating into the side' of a ship.
4. Water in motion as it can turn a wheel or a turbine.
5. A fast wind as it can set a boat in motion when striking against its sail.
6. A moving hammer as it drives a nail into a wall against the resistance offered to it by the wall.
7. A falling body as it can break something on which it falls.
Consider an object of mass m which is moving with an initial velocity u on a perfectly frictionless surface. Let a constant external force F act on it and produce an acceleration a in it. If v is the final velocity of the object after having undergone a displacement s, then from
This work done (W) in making the object acquire a velocity v after starting from rest has not gone waste and is, in fact, stored in the object.
Work stored up in a moving object is called the kinetic energy of the object.
If kinetic energy of an object is denoted by Ek then
Ek = mv2 ...(6)
Kinetic energy of a moving object is defined as half the product of the mass of the object and the square of the speed of the object.
(i) The more the mass of a body, the greater its kinetic energy.
(ii) The more the velocity of a body, the more its kinetic energy.
(iii) Kinetic energy of a body depends both on its mass and velocity.
Work Energy Theorem: This theorem states that the work done by the forces acting on a body is equal to the change in the kinetic energy of the body.
Consider a body of mass m moving with a velocity u. Let a force F be applied on the body, so that it is accelerated with an acceleration ‘a’.
Then, F = ma
If a be the distance travelled by the body during its accelerated motion, then the work done by the force F is given by W = Fs = mas,
Since (F = ma) ...(i)
Let the body acquires velocity v after travelling a distance s, the from v2 – u2 = 2as, we have
Equation (iv) gives us the relationship between force & energy.
The difference between the final and initial kinetic energies is the change in K.E. of the body D(K.E.)
\ W = change in K.E. = D(K.E.)
The energy possessed by an object by virtue of its position or configuration is called its potential energy. It is measured by the work that the object can do in passing from its present position or configuration to some standard position or configuration (known as zero position or zero configuration)
The kinetic energy of mass m converts into elastic potential energy of spring.
Let us take an example :- Let a small mass m be released from a smooth inclined plane. Another mass M is kept at a rough horizontal plane at rest. The mass m will move along the inclined plane and strike the mass M. Both the masses will move along the horizontal surface for some distance and come to rest. The mass M moves a distance s by the force applied by m. Thus, m does work for which it requires energy. This energy is possessed by m at A as it was at a height h from the horizontal surface. This energy due to position is called potential energy. Precisely speaking this energy is called gravitational potential energy.
Thus potential energy is defined as follows :
The energy possessed by a body due to its position or change in shape is called potential energy.
Note : The energy possessed by a body due to its height from the surface of earth is called gravitational potential energy and that due to change in shape is called elastic potential energy.
Other examples where elastic potential energy is stored are :
(i) a stretched bow
(ii) a stretched rubber band
(iii) a wound spring
All above examples are because of change in shape.
Let us consider a block of mass m kept on the surface of earth. Let the block be lifted to a height h. For that a force F is required which is equal to mg.
This force lifts the block through a distance h. The work done by this force,
W = F × h 
\ W = mg × h [Q F = mg]
This work is converted into potential energy (P.E.) of the block.
P.E = mgh
The expression shows that potential energy depends on
(a) mass m
(b) height h from ground
(c) acceleration due to gravity g
We have discussed various forms of energy available to us. We convert energy from one form to another. Given by following examples.
1. CONVERSION OF MECHANICAL ENERGY INTO ELECTRICAL ENERGY. The potential energy of water stored in a dam is changed to kinetic energy when it falls from a height. This kinetic energy rotates a turbine to produce electric energy.
2. CONVERSION OF ELECTRICAL ENERGY INTO MECHANICAL ENERGY. An electric motor uses electrical eneIrgy to run various electrical appliances, e.g., a train, a fan, washing machine, mixer, grinder etc.
3. CONVERSION OF ELECTRICAL ENERGY INTO HEAT ENERGY. In an electric heater, a geyser, a toaster, an oven etc., electric energy is changed to heat energy.
4. CONVERSION OF HEAT ENERGY INTO MECHANICAL ENERGY In heat engines (e.g., a steam engine), heat energy changes to mechanical energy.
5. CONVERSION OF ELECTRICAL ENERGY INTO LIGHT ENERGY. In an electric bulb, a fluorescent tube, a flood light etc., electrical energy is changed to light energy.
6. CONVERSION OF ELECTRIC ENERGY INTO SOUND ENERGY. An electric bell, a stereo, a loudspeaker etc., change electric energy into sound energy.
7. CONVERSION OF CHEMICAL ENERGY INTO HEAT ENERGY. When fuels are burnt, chemical energy gets converted into heat energy.
8. CONVERSION OF ELECTRICAL ENERGY INTO CHEMICAL ENERGY. When a battery is charged, electrical energy changes into chemical energy. An inverter in our home does the same thing.
9. CONVERSION OF SOUND ENERGY INTO ELECTRICAL ENERGY. A microphone converts sound energy into electrical energy.
10. CONVERSION OF CHEMICAL ENERGY TO ELECTRICAL ENERGY. An electric cell converts chemical energy into electrical energy.
11. CONVERSION OF LIGHT ENERGY INTO ELECTRIC ENERGY. A solar cell converts light energy into electrical energy.
12. CONVERSION OF CHEMICAL ENERGY INTO MECHANICAL ENERGY. In automobiles, chemical energy of petrol, diesel or CNG (compressed natural gas) is converted into mechanical energy.
13. CONVERSION OF LIGHT ENERGY INTO CHEMICAL ENERGY. In photosynthesis, light energy .from the Sun is absorbed by green plants and is converted to chemical energy.
14. CONVERSION OF NUCLEAR ENERGY INTO ELECTRICAL ENERGY. Nuclear power. plants are used to generate electrical energy from nuclear energy.
Some man made devices which convert one form of energy into another are is given as follows.
DEVICE INPUT ENERGY OUTPUT ENERGY
1. Fan Electrical energy Kinetic energy
2. Electric lamp Electrical energy Light energy
3. Electrical heaters Electrical energy Heat energy
4. Radio Electrical energy Sound energy
5. Water pump Electrical energy to kinetic energy of impeller
to potential energy of water
6. Cell Chemical energy Electrical energy
7. Microphone Sound energy Electrical energy
8. Rechargeable cell (a) During discharging (a) Electrical energy
Chemical energy
(b) During charging (b) Chemical energy
Electrical energy
9. Loudspeaker Electrical energy Sound energy
10. Elevator moving up Electrical energy Potential energy
11. Television Electrical energy Sound energy, light energy
12. Thermal power plant Chemical energy of coal Electrical energy
13. Car Chemical energy of petrol/diesel Mechanical energy
14. Nuclear power plant Nuclear energy Electrical energy
15. Solar cell Solar energy Electrical energy
16. Watch Potential energy of wound spring K.E. of hands of watch
17. Generator Kinetic energy Electrical energy
According to law of conservation of energy, energy can neither be created nor destroyed, it can be converted from one form to another.
Let us consider two cases where mechanical energy is conserved. 
CASE: A ball is dropped from some height.
At point A: Let a ball of mass m is dropped from a height h. Here the total
energy (T.E.) of the ball is the sum of kinetic energy (K.E.) and potential
energy (P.E.).
Potential energy = mgh
Kinetic energy = m (0)2 = 0 (u = 0)
\ [T.E.]A = mgh + 0 = mgh ... (A)
At point B: Let the ball travel a distance of h1 in time t during its fall.
Then the velocity of the ball after time t can be found by using equation of
motion. u = 0, a = g, S = h1, v = v
Using v2 – u2 = 2as
v2 – u2 = 2gh1
Þ v2 = 2gh1
Now K.E. at B = mv2 = m × 2gh1 = mgh1
P.E. at B = mg (h – h1)
Total energy at B = K.E. + P.E. = mgh1 + mg(h – h1) = mgh ... (B)
At point C : Suppose the ball cover a distance h when it moves from A to C. Let V be the velocity of the ball at point C just before it touches the ground, then
v2 – u2 = 2gh
v2 – 0 = 2gh or v2 = 2gh therefore
Kinetic energy (K.E.) = 1/2 mv2 = 1/2 m (2gh) = mgh
and potential energy at C \ P.E. = 0
Hence total energy at point C.
E = K.E. + P.E. = mgh + 0 = mgh ... (C)
Thus it is clear from equations A, B and C, that the total mechanical energy of a freely falling ball remain constant. There is, simply, a transformation of mechanical energy. This transformation is depicted in the graph of figure.
1. Power of a machine is defined as the rate of work done by the machine.
2. Power is defined as the rate of doing work.
3. Power of a machine is defined as work done by the machine per second.
If you lift a block of mass 1 kg through a distance of 1 m in 2 seconds, what is the work done?
W = F × s = = mg × h = 1 × 9.8 × 1 = 9.8 J
If you lift the same block through the same height in 1 minute, what is the work done? The answer comes out to be the same 9.8 J.
What is the work done if the time taken is 5 minutes? The work done is again 9.8 J.
But we are generally interested in time oriented work, i.e., work should be completed in a particular amount of time. The physical quantity which takes care of 'how fast is the work done' is power.
Note: If we want to find rate of work done by a man then the word 'machine' can be replaced by 'man'.
or 
Power is scalar quantity
Unit of power
SI unit of power is watt (W)
1 kW = 1000 W
1 MW (Mega watt) = 106 W
1GW(giga watt) = 109 W
Another unit of power is horse power (HP).
1 HP = 746W
Definition of Watt
When t = 1 s, W = 1J, then P = 1 W
One watt is the power of a man or a machine capable of doing work at the rate of one joule per second
Power in terms of energy :
Since work and energy are interconvertible, therefore,
Power = or P = E = P × t
Also, W = F × s When displacement is applied in the direction of force
then P = = F ×
Þ P = F × v This is power in terms of force and velocity.
Average power : Average power of an agent is defined as the ratio of total work done to the total time taken.
Average Power = total work done/total time taken
² Commercial Unit of Energy : Kilowatt-hour (kwh)
One kilowatt hour is the amount of energy consumed (or work done) by an agent in one hour working at a constant rate of one kilowatt.
Is kWh a unit of power or energy? The answer is energy.
We can write 1 kWh as 1 kW × 1h.
Now, since P = \ E = P × t
If power is in kW (kilowatt) and time in hour, then the unit of energy is kWh.
The unit kWh is important because this is a commercial unit of energy used by electricity boards. If you enquire from your parents what was the last electricity bill? If the answer is 600 units, it means that you have used 600 kWh of energy during the duration of bill. Thus, you pay for the electrical energy that you use.
Relation between kWh and Joule
1 kWh = 1000 Wh [Q 1 kW = 1000 W]
Now, 1 W = 1 Js–1 and 1 h = 60 × 60 s = 3600 s
\ 1kWh = 1000 Js–1 × 3600 s = 3600000 J = 3.6 × 106 J
\ 1 kWh = 3.6 × 106 J = 3.6 MJ
Note : An energy of 1 kWh is equivalent to using a bulb of 1 kW for 1 hour.
Relationship between kinetic energy and linear momentum:
What can you conclude from the relationship, K.E. = mv2
we can conclude as follows :
When the velocity of a body is kept constant, the kinetic energy is directly proportional to the mass of the body, K.E. µ m
Thus,
If the mass of a body is doubled (v remaining constant), the kinetic energy of the body also gets doubled.
If the mass of the body is reduced to half (v remaining constant), the kinetic energy of the body also gets halved.
The kinetic energy of a body is directly proportional to the square of its velocity (or speed) i.e., K.E. µ v2
So, (Q m is constant)
If the velocity of a body is doubled, then its kinetic energy increases four times.
If the velocity of a body is reduced to half, then its kinetic energy gets to one-fourth.
How is the kinetic energy of a body related to its momentum:
Ex.1 A boy pushes a book by applying a force of 40N. Find the work done by this force as the book is displaced through 25 cm along the path.
Sol. Here, force acting on the book, F = 40N
distance through which book is displaced, s = 25 cm = 0·25 m
Work done by the force, i.e., W = F × s = (40 N) (0·25 m) = 10J
Ex.2 A ball of mass 1 kg thrown upwards, reaches a maximum height of 4 m. Calculate the work done by the force of gravity during the vertical displacement. (g = 10 m/s2).
Sol. Here, force of gravity on the ball, F = mg = (1 kg) (l0 m/s2) = 10N
vertical displacement of the ball, s = 4m
Since the force and the displacement of the ball are in opposite directions, work done by the force of gravity, i.e., W= –F × s = – (10N) (4m) = – 40J
Obviously, work done against the force of gravity = 40J
Ex.3 Find the amount of work done by a labourer who carries n bricks of m kilogram each to the roof of a house h metre high by climbing a ladder.
Sol. Here, force exerted by the labourer in carrying n bricks (each of mass m kg),
F = (mn) g = (mng) newton
displacement of the bricks, s = h metre
Work done by the labourer, W = F × s = (mng newton) × (h metre) = mngh joule
Ex.4 An engine pulls a train 1 km over a level track. Calculate the work done by the train given that the frictional resistance is 5 × 105 N.
Sol. Here, frictional resistance, F = 5 × 105 N
distance through which the train moves, s = 1 km = 1000 m
Work done by the frictional force, i.e., W = – Fs = – (5 × 105 N) (1000 m) = - 5 × 108 J
(F and s are in opposite directions)
Obviously, work done by the train is 5 × 108 J
Ex.5 A man weighing 70 kg carries a weight of 10 kg on the top of a tower 100 m high. Calculate the work done by the man. (g = 10 m/s2).
Sol. Here, force exerted by the man, F = (70 + 10) kg wt = 80 kg wt
= 80 × 10 N = 800 N (1 kg wt = 10 N)
vertical displacement, s = 100 m
Work done by the man, i.e., W = F × s = (800N) (100m) = 80000 J
Ex.6 How fast should a man of mass 60 kg run so that his kinetic energy is 750 J ?
Sol. Here, mass of the man, m = 60 kg
kinetic energy of the man, Ek = 750J
Ex.7 Find the mass of the body which has 5J of kinetic energy while moving at a speed of 2 m/s. 
Ex.8 A player kicks a ball of mass 250 g at the centre of a field. The ball leaves his foot with a speed of
10 m/s, Find the work done by the player on the ball.
Sol. The ball, which is initially at rest, gains kinetic energy due to work done on it by the player.
Thus, the work done by the player on the ball, W = kinetic energy (Ek) of the ball as it leaves his foot, i.e.,
W = Ek = mv2
Here, m = 250 g = 0·25 kg, v = 10 m/s
W = 1/2(0·25kg) (10 m/s)2 = 12·5 J
Ex.9 A body of mass 5 kg, initially at rest, is subjected to a force of 20N. What is the kinetic energy acquired by the body at the end of 10s ?
Ex.10 A bullet of mass 20 g moving with a velocity of 500 m/s, strikes a tree and goes out from the other side with a velocity of 400 m/s. Calculate the work done by the bullet in joule in passing through the tree.
Sol. Here, mass of the bullet, m = 20 g = 0·02 kg
initial velocity of the bullet, u = 500 m/s
final velocity of the bullet, v = 400 m/s
If W is the work done by the bullet in passing through the tree, then according to work-energy theorem
W = 1/2mu2 – 1/2mv2 = 1/2m(u2 – v2)
or W = 1/2(0·02 kg) [(500 m/s)2 – (400m/s)2] = 900J
Ex.11 A body of mass 4 kg is taken from a height of 5 m to a height 10 m. Find the increase in potential energy.
Sol. Here, mass of the body, m = 4 kg
increase in height of the body, h = (10m – 5m) = 5m
Increase in potential energy, Ep = mgh = (4 kg) (10 m/s2) (5m) = 200J
Aliter. Initial potential energy of the body, Epi = mgh = (4 kg) (10 m/s2) (5m) = 200J
Final potential energy of the body, Epf = mghf = (4 kg) (10 m/s2) (10 m) = 400J
Increase in potential energy, Ep = Epf – Epi = 400J – 200J = 200J
Ex.12 An object of mass 1 kg is raised through a height h. Its potential energy increases by 1 J. Find the height h.
Sol. Here, mass of the object, m = 1 kg increase in potential energy, Ep = 1J
Ex.13 A 5 kg ball is thrown upwards with a speed of 10 m/s.
(a) Find the potential energy when it reaches the highest point.
(b) Calculate the maximum height attained by it.
Sol. (a) Here, mass of the ball, m = 5 kg,
speed of the ball, v = 10 m/s
Ex.14 A 5 kg ball is dropped from a height of 10m.
(a) Find the initial potential energy of the ball.
(b) Find the kinetic energy just before it reaches the ground and
(c) Calculate the velocity before it reaches the ground.
Sol. Here, mass of the ball, m = 5 kg
height of the ball, h = 10m
(a) Initial potential energy of the ball,
Ex.15 A body is thrown up with a kinetic energy of 10 J. If it attains a maximum height of 5 m, find the mass of the body.
Ex.16 A rocket of mass 3 × 106 kg takes off from a launching pad and acquires a vertical velocity of 1 km/s and an altitude of 25 km. Calculate its (a) potential energy (b) kinetic energy.
Sol. Here, mass of the rocket, m = 3 × 106 kg
velocity acquired by the rocket, v = 1 km/s = 1000 m/s
height attained by the rocket, h = 25 km = 25000 m
(a) Potential energy of the rocket, Ep = mgh = (3 × 106 kg) (10 m/s2) (25000 m) = 7·5 × 1011 J
(b) Kinetic energy of the rocket,
Ek = 1/2mv2 = (3 × 106 kg) (1000m/s)2 = 1·5 × 1012 J
Ex.17 A boy of mass 40 kg runs up a flight of 50 steps, each of 10 cm high, in 5 s. Find the power developed by the boy.
Sol. Here, mass of the boy, m = 40 kg
total height gained, h = 50 × 10 cm = 500 cm = 5m
time taken to climb, t = 5s
Work done by the boy, W = mgh = (40 kg) (10 m/s2) (5m) = 2000J
Power developed, P = W/t = 2000J/5s= 400W
Ex.18 What should be the power of an engine required to lift 90 metric tonnes of coal per hour from a mine whose depth is 200 m ?
Ex.20 Calculate the units of energy consumed by 100 W electric bulb in 5 hours.
Sol. Here, power of the electric bulb, P = 100 W = 0·1 kW
time for which bulb is used, t = 5h
As P = W/t , W = Pt
Energy consumed by the bulb, W = Pt = 0·1 kW (5 h) = 0·5 kWh = 0·5 units
Ex.21 A lift is designed to carry a load of 4000 kg through 10 floors of a building, averaging 6 m per floor, in
10 s. Calculate the power of the lift.
Sol. Total distance covered by the lift, s = 10 × 6 m = 60 m
time in which this distance is covered, t = 10 s
force exerted by the lift, F = 4000 kg wt = 4000 × 10 N
= 4 × 104 N (1 kg wt = 10 N)
velocity of the lift, V = s/t = 60/10s = 6 m/ s
Power of the lift, P = F v = (4 × 104 N) (6 m/s) = 24 × 104 W = 240 kW
Ex.22 What kind of energy transformation takes place in the following cases ?
(a) When water flowing down a dam runs a turbine to generate electricity.
(b) A running steam engine.
(c) Power generation in a thermal power station.
Ans. ± The scheme of energy transformation when water stored in a dam is used to produce electricity is,
Potential energy of water ® Kinetic energy of flowing water ® Kinetic energy turbine ® Electrical energy
Thus, in a hydropower station, the potential energy of water stored in a dam is converted into kinetic energy of the turbine which finally gets converted into electrical energy.
± The scheme of energy transformation in a running steam engine is,
Chemical energy of coal ® Heat energy of steam ® Kinetic energy of moving parts of the engine ® Kinetic energy of the engine and boggies.
So, in a running steam engine the scheme of energy transformation is,
Chemical energy ® Heat energy ® Kinetic energy
± The scheme of energy transformation in a thermal power stations is,
Chemical energy of fuel (coal / diesel) ® Heat energy of steam ® Kinetic energy of turbine ® Electrical energy.
Ex.23 A force of 7N acts on an object. The displacement is 8m in the direction of force. The force acts on the object throughout the displacement. What is the work done by the force ?
Sol. F = 7N s = 8 m
W = F × s = 7 × 8 = 56 J
Ex.24 A pair of bullocks exert a force of 140 N on a plough. The field being ploughed is 15m long. How much work is done in ploughing the length of the field ?
Sol. W = F × s
= 140 × 15 [The displacement of the plough is along the direction of force exerted by the bullocks]
= 2100 J
Ex.25 A boy pulls a toy with force of 50N through a string which makes an angle of 30° with the horizontal so as to move the boy by a distance of 1m horizontally. What is the amount of work done ?
Q.1 Define the term 'work done'.
Ans. Work done = force × displacement.
Q.2 How much work is done by a man who tries to push the wall of a house but fails to do so.
Ans. W = FS = 0 (Q S = 0)
Q.3 What is the work done by a student who is reading a book while sitting on a bench ?
Ans. Zero.
Q.4 What is SI unit of work ?
Ans. S.I. unit of work is joule (J).
Q.5 Write the expression for a work done by a force F acting on an object at an angle q with the displacement S of the object.
Ans. W = FS cos q.
Q.6 Is work a scalar or a vector quantity ?
Ans. Work is a scalar quantity.
Q.7 Work done by a force is equal to the product of ................... and ...................
Ans. The magnitude of force, distance.
Q.8 How is the kinetic energy of a body related to its momentum ?:
Q.9 What is energy ?
Ans. The capacity of doing work by an object is known as the energy of the object.
Q.10 What is SI unit of energy ?
Ans. S.I. unit of energy is joule (J).
Q.11 What type of energy is possessed by a cricket ball just before being caught by a fielder ?
Ans. Kinetic energy.
Q.12 Give an example of an object having elastic potential energy
Ans. A stretched spring or a compressed spring has elastic potential energy.
Q.13 What do you mean by transformation of energy
Ans. The process of converting one form of energy into another form of energy is called transformation of energy.
Q.14 State the energy transformation taking place when a body falls from a certain height.
Ans. Potential energy of a falling body converts into its kinetic energy.
Q.15 A log of wood cut by a saw becomes hot. From where this heat energy comes ?
Ans. Mechanic energy is converted into heat energy.
Q.16 State the law of conservation of energy.
Ans. Energy can neither be created nor be destroyed but can be changed from one form into another form.
Q.17 What is SI unit of power ?
Ans. S.I. unit of power is watt.
Q.18 What is the practical unit of power ?
Ans. Practical unit of power is horse power (H.P.)
Q.19 State the relationship between watt and horse power.
Ans. 1 h.p. = 746 W.
Q.20 A man buys an electric motor of 1 H.P. What is its power in watts ?
Ans. 1 H.P. = 746 W
Q.21 What is the relationship between ‘watt’ and 'kilowatt' ?
Ans. 1 kilowatt = 1000 watt.
Q.22 Define 1 kWh.
Ans. 1 kWh is the amount of electric energy used by 1000 W electrical appliances in 1 hour.
Q.23 A bus and a car have same kinetic energy. Which of the two is moving fast ? Explain.
Q.24 If the speed of a particle is increased four times, how will its kinetic energy be affected ?
Ans. K.E. = 1/2mv2. When v1 = 4v \ New (K.E.) = 1/2mv2 = 1/2m × 16 v2 = 16 K.E.
Q.25 The kinetic energy of a body is 10 J. What will be its new kinetic energy when its speed becomes double?
Ans. K.E. = 1/2mv2 = 10 J
When v1 = 2 v
\ New K.E. = 1/2mv'2 = 1/2m × 4v2 =4 × 1/2mv2 = 4 × 10 J = 40 J
Q.1 A force of 7N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case ?
Q.2 When do we say that work is done ?
Ans. Work is said to be done when a force causes displacement of an object in the direction of applied force.
Q.3 Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Ans. Work Done = Force × Displacement i.e., W = F × S
Q.4 Define 1 J of work.
Ans. When a force of 1N causes a displacement of 1 m, in its own direction then work done is said to be one joule.
Q.5 A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field ?
Ans. Work done= Force × Displacement = 140 × 15 = 2100 J
Q.6 What is the kinetic energy of an object ?
Ans. The energy possessed by a body by virtue of its motion is called kinetic energy.
Q.7 Write an expression for the kinetic energy of an object.
Ans. KE = mv2 where KE ® kinetic energy of an object.
'm' – mass of an object.
'v'– velocity.
Q.8 The kinetic energy of an object of mass m, moving with a velocity of 5 ms–1 is 25 J. What will be its kinetic energy when its velocity is doubled ? What will be its kinetic energy when its velocity is increased three times?
Q.9 What is power ?
Ans. Power is defined as the rate of doing work. It is measured in watt and also in horsepower.
Q.10 Define 1 watt of power.
Ans. When a work of 1 joule is done in 1 s, the power is said to be one watt.
Q.11 A lamp consumes 1000 J of electrical energy in 10 s. What is its power ?
Ans. Power =Energy/Time = 1000/10 = 100 W
Q.12 Define average power.
Ans. When a machine or person does different amounts of work or uses energy in different interval of time, the ratio between the total work or energy consumed to the total time is average power.
Average Power = Total work done or energy consumed/Total Time
Q.13 Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term 'work'.
Ans. (a) Work is done because the displacement of swimmer takes place in the direction of applied force.
(b) If the donkey is not moving, no work is done as the displacement of load does not take place in the direction of applied force.
(c) Work is done, as the displacement takes place in the direction of force.
(d) No work is done, because no displacement takes place.
(e) Work is done, because displacement takes place in the direction of applied force.
(f) No work is done, because displacement does not takes place.
(g) Work is done because displacement takes place in the direction of force.
Q.14 An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object ?
Ans. Since the object returns to its level of projection, therefore there is no change in its PE. Hence work done by the force of gravity is zero.
Q.15 A battery lights a bulb. Describe the energy changes involved in the process.
Ans. Within the electric cell of the battery the chemical energy changes into electric energy.
The electric energy on flowing through the filament of the bulb, first changes into heat energy and then into the light energy.
Q.16 Certain force acting on a 20 kg mass changes its velocity from 5 ms–1 to 2ms–1. Calculate the work done by the force.
Ans. W.D. by the force when velocity is
5 ms–1 = /2 mv2 = 1/2× 20 × (5)2 = 250 J
W.D. by the force when velocity is
2 ms–1 = 1/2mv2 = × 20 × (2)2 = 40 J
Resultant W.D. by the force = Change in KE = 40 – 250 = –210 J
Q.17 A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal. What is the work done on the object by the gravitational force ? Explain your answer.
Ans. The work done is zero. This is because the gravitational force and displacement are perpendicular to each other.
Q.18 The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy ? Why ?
Ans. It does not violate the law of conservation of energy. Whatsoever, is decrease in PE due to loss of height, same is the increase in the KE due to gain in velocity.
Q.19 What are the various energy transformations that occur when you are riding a bicycle ?
Ans. The chemical energy of the food changes into heat and then to muscular energy. On paddling, the muscular energy changes to mechanical energy.
Q.20 Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going ?
Ans. Energy transfer does not take place as no displacement takes place in the direction of applied force. The energy spent is used to overcome inertia of rest of the rock.
Q.21 A certain household has consumed 250 units of energy during a month. How much energy is this in joule?
Ans. Energy consumed in a month = 250 units = 250 kWh
= 250 kW × lhr = 250 × 1000W × 3600s = 900,000,000J = 9 × 108 J
Q.22 An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.
Ans. Mass of object (m) = 40 kg
Height (h) = 5 m
Acc. due to gravity (g) = 10 ms–2
\ PE at a height of 5 m (PE) = mgh = 40 × 10 × 5 = 2000J
PE at a half-way height, i.e., : 2.5 m (PE) = mgh = 40 × 10 × 2.5= 1000 J
Decrease in PE = Increase in KE = 2000 – 1000 = 1000 J.
Q.23 What is the work done by the force of gravity on a satellite moving around the earth ? Justify your answer.
Ans. The W.D. by the force of gravity on the satellite is zero because the force of gravity acts at right angles to the direction of motion of the satellite. Therefore, no displacement is caused in the direction of applied force. The force of gravity only changes the direction of motion of the satellite.
Q.24 Can there be displacement of an object in the absence of any force acting on it ? Think, Discuss this question with your friends and teacher.
Ans. The answer is both Yes or No. Yes because when an object moves in deep space from one point to another point in a straight line, the displacement takes place, without the application of force. No, because force cannot be zero for displacement on the surface of earth i.e., some force is essential.
Q.25 A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not ? Justify your answer.
Ans. The person does no work because, no displacement takes place in the direction of applied force as the force acts in the vertically upward direction.
Q.26 An electric heater is rated 1500 W. How much energy does it use in 10 hours ?
Ans. Energy used by heater = Power × Time = 1500 W × 10 h = = 15 kWh.
Q.27 Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest ? What happens to its energy eventually ? Is it a violation of the law of conservation of energy ?
Ans. When the pendulum bob is pulled (say towards left), the energy supplied is stored in it is in the form of PE on account of its higher position. When the pendulum is released so that it starts moving towards right, then its PE changes into KE, such that in mean position, it has maximum KE, and zero PE. As the pendulum moves towards extreme right, its KE changes into PE; such that at the extreme position, it has maximum PE and zero KE. When it moves from this extreme position to mean position, its PE again changes to KE. This illustrates the law of conservation of energy. Eventually, the bob comes to rest, because during each oscillation a part of the, energy possessed by it transferred to air and in overcoming friction at the point of suspension. Thus, the energy of the pendulum is dissipated in air.
The law of conservation of energy is not violated because the energy merely changes its form and is not destroyed.
Q.28 An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest ?
Ans. W.D. to bring the object to rest = change in KE of the object
0 – 1/2mv2 = 1/2mv2
Q.29 Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of
60 kmh–1.
Q.30 In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.
Q.31 Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her ? Why ?
Ans. Yes, we do agree when the number of forces act on a body, such that they constitute balanced forces, then net force acting on the body is zero. In such a situation no acceleration acts on the object.
Q.32 Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.
Ans. Total power of 4 devices = 4 × 500 = 2000 W = 2000/1000 = 2 kW
Time = 10h
\ Energy consumed = Power × time = 2 kW × 10 h = 20 kWh
Q.33 A freely failing object eventually stops on reaching the ground. What happens to its kinetic
energy ?
Ans. The KE on reaching the ground changes into heat energy, sound energy etc. and therefore gets dissipated in air.
Q.1 A player kicks a ball of mass 250 g placed at the centre of a field. The ball leaves his foot with a speed of 8 m/s. Find the work done by the player on the ball.
Q.2 A 10 kg ball is thrown upwards with a speed of 5 m/s. (a) Find its potential energy when it reaches the highest point. (b) Calculate the maximum height it reaches.
Q.3 A body A of mass 3.0 kg and a body B of mass 10 kg are dropped simultaneously from a height of 14.9 m. Calculate (a) their momentum, (b) their potential energies, and (c) their kinetic energies when they are 10 m above the ground.
Q.4 Calculate the work done by a person in lifting a load of 20 kg from the ground and placing it on a 1 m high table.
Q.5 Find the mass of a body which has 5J of kinetic energy while moving at a speed of 2 m/s.
Q.6 The mass of a ball A is double the mass of another ball B. The ball A moves at half the speed of the ball B. Calculate the ratio of the kinetic energy of A to the kinetic energy of B.
Q.7 Calculate the increase in potential energy as a block of 2kg is lifted up through 2m.
Q.8 A ball of mass 200g falls from a height of
5 metres. What is its kinetic energy when it just reaches the ground? (g = 9.8 m/s2).
Q.9 Find the momentum of a body of mass 100g having a kinetic energy of 20J.
Q.10 How fast should a man of mass 50kg run so that his kinetic energy be 625J ?
Q.11 A horse and a dog are running with the same speed. If the weight of the horse is ten times that of the dog, what is the ratio of their kinetic energies?
Q.12 A ball of mass 0.5 kg slows down from a speed of 5 m/s to that of 3 m/s. Calculate the change in kinetic energy of the ball. State your answer giving proper units.
Q.13 Two bodies having equal masses are moving with uniform speeds of v and 2v respectively. Find the ratio of their kinetic energies.
Q.14 What is the kinetic energy of a body of mass 1 kg moving with a speed of 2 m/s ?
Q.15 A body of 2 kg falls from rest. What will be its kinetic energy during the fall at the end of 2 s ? (Assume g = 10 m/s2)
Q.16 A man drops a 10 kg rock from the top of a 5 m ladder. What is its speed just before it hits the ground ? What is its kinetic energy when it reaches the ground ?
( g = 10 m/s2)
Q.17 A boy weighing 40 kg makes a high jump of 1.5 m.
(i) What is his kinetic energy at the highest point?
(ii) What is his potential energy at the highest point? (g = 10 m/s2).
Q.18 To what height should a box of mass 150 kg be lifted, so that its potential energy may become 7350 joules? (g = 9.8 m/s2).
Q.19 A body of mass 2kg is thrown vertically upwards with an initial velocity of 20 m/s. What will be its potential energy at the end of 2s ?
(Assume g = 10 m/s2).
Q.20 A man is instructed to carry a package from the base camp at B to summit A of a hill at a height of 1200 metres. The man weighs 800N and the package weighs 200N.
(i) How much work does man do against gravity?
(ii) What is the potential energy of the package at A if it is assumed to be zero at B ?
Q.21 Calculate the work done by a student in lifting 0·5 kg book from the ground and keeping it on a shelf 1·5m high.
Q.22 A coolie carries a load of 50kg on his head and walks on a level road upto 100m. What is the work done by him?
Q.23 A crane pulls up a car of mass 500kg to a vertical height of 4m. Calculate the work done by the crane.
Q.24 A boy of mass 55kg runs up a flight of 40 stairs, each measuring 0·15m. Calculate the work done by the boy.
Q.25 A bullet of mass 0·03kg moving with a speed of 400m/s penetrates 12cm into fixed block of wood. Calculate the average force exerted by the wood on the bullet.
Q.26 A bullet of mass 5g travels with a speed of 500m/s. If it penetrates a fixed target which offers a constant resistive force of 1000N to the motion of the bullet, find (a) the initial kinetic energy of the bullet (b) the distance through which the bullet has penetrated.
Q.27 Two bodies of equal masses move with uniform velocities v and 3v respectively. Find the ratio of their kinetic energies.
Q.28 A truck weighing 5000 kg f and a cart weighing 500 kg f are moving with the same speed. Compare their kinetic energies.
Q.29 A bullet of mass 20g is found to pass two points 30m apart in 4s ? Assuming the speed to be constant, find its kinetic energy.
Q.30 A 60kg person climbs stairs of total height 20m in 2min. Calculate the power delivered.
Q.31 The work done by the heart is 1J per beat. Calculate the power of the heart if it beats 72 times/min.
Q.32 A man exerts a force of 200N in pulling a cart at a constant speed of 16m/s. Calculate the power spent by the man.
Q.33 Calculate the power of an engine required to lift 105kg of coal per hour from a mine 360m deep.
Q.34 A man does 200J of work in 10s and a boy does 100J of work in 4s. (a) Who is delivering more power? (b) Find the ratio of the power delivered by the man to that delivered by the boy.
Q.1 Search for different forms of energy for daily use.
Q.2 Using different methods for enhancing the use of energy.
Q.1 Conserving energy.
Q.2 Alternative sources of energy.
Q.3 "Energy saved is energy produced".
Q.1 Describe an activity to show that positive work and negative work and done simultaneously when an object is lifted upwards.
Q.2 Answer to a question based on activity : when an object falls from a certain height, then the gravity and the displacement of the object are in the same direction. Hence, work done by the gravity on the object is positive work done.
Q.3 Think of the situations when an applied force does not produce any displacement in the objects.
Q.4 Wind up a toy car once and place it on the floor.
(a) Did the car move ?
(b) Measure the distance it moved.
(c) Give two, three, four etc., winding and study the distances the car has moved.
Explain your findings.
Q.5 Make a catapult. Now hold a small stone n the rubber band, pull it and release.
(a) What do you observe
(b) Now observe the effect of stretching pull on the distance moved by the stone.
Q.1 The SI unit of energy is .......................
Q.2 Kilowatt hour is a unit of .......................
Q.3 The kinetic energy of a body is by virtue of its .......................
Q.4 The potential energy of a body is by virtue of its .......................
Q.5 Work is said to be done if a force ....................... a body through a certain distance in the direction of force.
Q.6 Work done is said to be positive if the applied force has a ....................... in the direction of displacement.
Q.7 Work done is said to be negative if the applied force has a ....................... in the direction opposite to displacement.
Q.8 Work done is said to be zero if the applied force is ....................... to the direction of displacement.
Q.9 ....................... is the SI unit of work.
Q.10 Work done is said to be one joule if a force of one ....................... displaces a body through a distance of one ....................... in the direction of force.
Q.11 The ....................... of a body to do work is called energy.
Q.12 Kinetic energy depends upon the ....................... and the square of ....................... of a body.
Q.13 The rate of doing work is called .......................
Q.14 Instantaneous power is the product of force and .......................
Q.1 When energy changes from one form to another, the energy that disappears from one form, reappears in exactly equivalents amount in the other form.
Q.2 A force does not work, if it produces no motion.
Q.3 Kilowatt hour is the unit of power.
Q.4 Work and Energy have different units.
Q.5 In order to get minimum work, the angle between force and displacement should be 90°.
Q.6 When a body falls on the ground and stops, the principle of conservation of energy is violated.
Q.7 When velocity is halved, its kinetic energy becomes 1/4th.
Q.8 When an arrow is released from a bow,
potential energy changes into kinetic energy.
Q.9 Work done by a force depends upon how fast work is done.
Q.10 The rate of doing work is called power.
Q.11 Work done by centripetal force is zero.
Q.12 The unit of work is watt.
Q.13 If we know the speed and mass of an object we can find out its kinetic energy.
Match the Single column (matrix) :
Q.1 Column-I Column-II
(A) Total work done by (p) Non-zero and conservative force. negative.
(B) Total work done by (q) Change in total non-conservative force. energy.
(C) Work done by gravity (r) Negative.
on a freely falling body.
(D) Work done by friction (s) Positive.
on a sliding body.
Q.2 Column-I Column-II
(A) Motor. (p) Light into electrical energy.
(B) Inverter (q) Electrical into mechanical
energy.
(C) Loudspeaker. (r) Electrical into chemical energy.
(D) Photocell. (s) Electrical into sound energy.
Double column (matrix) :-
Q.3 Column-I Column-II
(A) Work done by a force (p) Zero.
during climbing.
(B) Total work done. (q) Change in kinetic energy.
(C) Total work done in a (r) Positive.
closed loop.
(D) Total work done by (s) Negative.
a force.
Q.4 Column-I Column-II
(A) Net force. (p) Energy / distance.
(B) Conservative force. (q) Energy / Time.
(C) Total power. (r) Mass x acceleration.
(D) Force × velocity (s) Power / velocity.
1. 8 J 2. (a) 125 J (b) 1.25 m
3. (a) 29.4 kg m/s, 98 kg m/s (b) 300 J, 1000 J (c) 144 J, 480 J
4. 196 J 5. m = 2.5 kg 6. 1 : 2
7. 40 J 8. 9.8 J 9. 2 kg m/s
10. 5 m/s 11. 10 : 1 12. 4 J
13. 1 : 4 14. 2 J 15. 400 J
16. 500 J and 10m/s
17. (i) zero (ii) 600 J 18. h = 5m
19. 20 m, 400 J
20. (i) 1200000 J (ii) 24 × 104 J 21. 7·5 J
22. zero 23. 20000J 24. 3300J
25. 2 × 104 N
26. (a) 625 J (b) 0·625 m 27. 1 : 9
28. 10 : 1 29. 0·5625J 30. 100 W
31. 1·2 W 32. 3·2 kW 33. 100 kW
34. (a) The boy delivers more power (b) 4/5
1. Joule 2. Energy
3. Motion 4. Position
5. Displaces 6. Component
7. Component 8. Perpendicular
9. Joule 10. Newton, metre
11. Capactiy 12. Mass, Velocity
13. Power 14. Velocity
1. T 2. T 3. F 4. F
5. T 6. F 7. T 8. T
9. F 10. T 11. T 12. F
13. T
1. (A – q), (B – p), (C – s), (D – r)
2. (A – q), (B – r), (C – s), (D – p)
3. (A – p, r, s), (B – p, q, r, s), (C – p),
(D – p, q, r, s)
4. (A – p, r, s), (B – p), (C – q), (D – q)
Q.1 No work is done when an object moves:
(A) along the direction of force
(B) opposite to the direction of force
(C) at any angle to the direction of force (D) at 90° to the direction of force.
Q.2 Capacity of doing work is called:
(A) power (B) momentum (C) energy (D) force.
Q.3 Energy possessed by a body on account of position or configuration is called
(A) kinetic energy
(B) potential energy
(C) mechanical energy
(D) magnetic energy.
Q.4 Energy possessed by a body on account of its motion is called:
(A) mechanical energy
(B) potential energy
(C) kinetic energy
(D) magnetic energy.
Q.5 A stone rolls down an inclined plane. Midway during the motion, the stone has:
(A) only kinetic energy
(B) only potential energy
(C) both kinetic and potential energy (D) neither potential nor kinetic energy.
Q.6 An aeroplane flying at a height of 20,000 m at a speed of 300 kmh–1 has:
(A) only potential energy
(B) only kinetic energy
(C) both, potential and kinetic energy (D) none of the above.
Q.7 A stone is placed on the top of a building of height 'h'. Its potential energy is directly proportional to its:
(A) mass
(B) height
(C) acceleration due to gravity
(D) all the above.
Q.8 If a body is raised through height 'h' on the surface of earth and the energy spent is E, then for the same amount of energy the body on the surface of moon will rise through the height of:
(A) 2h (B) 6h
(C) 4h (D) 12h
Q.9 The kinetic energy of a body is directly proportional to its:
(A) mass (B) velocity
(C) (velocity)2 (D) both (A) and (C)
Q.10 A ball is thrown upward from a point P, reaches to the highest point Q :
(A) kinetic energy at P is equal to kinetic energy at Q
(B) potential energy at P is equal to kinetic energy at Q
(C) kinetic energy at P equal to potential energy at Q
(D) potential energy at P is equal to potential energy at Q
Q.11 Two stones of masses I kg and 2 kg are dropped simultaneously from the same height. Both the stones during free fall have:
(A) momentum
(B) same potential energy
(C) same kinetic energy
(D) same acceleration.
Q.12 When the speed of a particle is increased 3 times, its kinetic energy:
(A) increases 3 times
(B) remains same
(C) increases 9 times
(D) decreases to 1/3.
Q.13 A force of 7N acts on an object through a distance of 8m in its own direction. The work done is :
(A) 7J (B) 8J
(C) 56J (D) 65J
Q.14 A pair of bullocks exert a force of 140N on a plough through distance of 15 m. The work done by the bullocks is:
(A) 280J (B) 1400J
(C) 2100J (D) 21000J
Q.15 The kinetic energy of an object of mass 'm', moving with a velocity of 5 ms–1 is 25 J. If the velocity is increased by three times, the kinetic energy is :
(A) 100J (B) 225J
(C) 400J (D) 180J
Q.16 An electric lamp consumes 1000 J of electric energy in 10 second. The power of lamp is :
(A) 10 W (B) 50 W
(C) 100 W (D) 1000 W.
Q.17 A body of mass 20 kg, slows down from
5 ms–1 to 2 ms–1 by a retarding force. The work done by the force is:
(A) –50J (B) –200J
(C) –300J (D) –210J
Q.18 A mass of 10 kg at point A on a table is moved to point B. If the line joining the A and B is horizontal, the work done by the body is :
[a = 10 ms–2]
(A) 10 kg × AB (B) 10N × AB (C) 100N × AB (D) 50N × AB.
Q.19 A certain household consumes 250 units of electric energy in a House. The energy consumed in mega joule is:
(A) 900 MJ (B) 750 MJ
(C) 2250 MJ (D) 1750 MJ.
Q.20 An object of mass 40 kg (g = 10 ms–2) is raised to a height of 8 m above the ground. The gain potential energy by the object:
(A) 200J (B) 3200J
(C) 1500J (D) 1000J.
Q.21 An electric heater is rated 1500 W. The energy used by it in 10 hours is :
(A) 5 kWh (B) 10 kWh
(C) 15 kWh (D) 20 kWh.
Q.22 An object of mass m is moving with a constant velocity 'u'. The work done on the object to bring it to rest is :
(A) mv2 (B) ½ mv2
(C) mv (D) m2v/2
Q.23 A car of mass 1500 kg is moving with a velocity of 60 kmh–1. The work done by its brakes to bring it to rest is:
(A) 208.42 kJ (B) 198.52 kJ
(C) 112.42 kJ (D) 212.52 kJ
Q.24 The energy consumed (in kWh) by four devices of 500W each in 10 hours is :
(A) 4 kWh (B) 5 kWh
(C) 10 kWh (D) 20 kWh.
Q.25 A locomotive exerts a force of 7500N and pulls a train by 1.5 km. The work done by the locomotive in mega joules is :
(A) 12.25 MJ (B) 11.25 MJ
(C) 10.75 MJ (D) 11.50 MJ
Q.26 A horse does a work of 6250J while applying a force of 250N in pulling a tonga. The displacement produce in tonga is :
(A) 12.5m (B) 15m
(C) 25m (D) 20m.
Q.27 A work of 60 J done by a force F, which causes a displacement of 2 m. The magnitude of force F is :
(A) 120N (B) 60N
(C) 30N (D) 45N.
Q.28 The work done by an electric drill rated 50 W in 30s is :
(A) 1200J (B) 600J
(C) 900J (D) 1500J.
Q.29 Find the work done by a force of 5N to displace a book through 20 cm along the direction of the push.
(A) 3.0 J (B)5.0J (C) 1.0 J (D)4.0J
Q.30 A ball of mass 1 kg thrown upwards reaches a maximum height of 5.0 m. Calculate the work done by the force of gravity during this vertical displacement.
(A) – 59J (B) – 49J (C) – 30J (D) – 48J
Q.31 A person pulls a body on a horizontal surface by applying a force of 5.0 N at an angle of 30° with the horizontal. Find the work done by this force in displacing the body through 2.0 m.
(A) 5 J (B) 6 J (C) 7 J (D) 4J
Q.32 An object of mass 1 kg is raised through a height 'h'. Its potential energy is increased by 1 J. Find the height 'h'.
(A) 0.102 m (B) 0.105 m (C)0.130m (D) 0.110m
Q.33 The kinetic energy of a ball of mass 200 g moving at a speed of 20 cm/s is:
(A) 0.005 J (B) 0.004 J (C) 0.001 J (D) 0.007 J
Q.34 The work done by a student in lifting a 0.5 kg book from the ground and keeping it on a shelf of height 1.5 m is :
(A) 8.30 J (B)7.35J (C) 5.40 J (D) 6.45 J
Q.35 A block of mass 1 kg slides down on an inclined plane of inclination 30°. Find the work done by the weight of the block as it slides through 50 cm.
(A) 3.45 J (B) 5.30 J (C) 2.45 J (D) 3.50 J
Q.36 A force of 10 N displaces an object through 20 cm and does work of 1 J in the process. Find the angle between the force and displacement.
Q.37 A body of mass 0.5 kg is taken to a height Re. above the earth’s surface, where Re is the radius of the earth. If the body is now raised through a height of 2 m, what is the increase in its potential energy?
(A) 2.45 J (B) 5.45 J (C) 6.35 J (D) 8.30 J
Q.38 A ball is dropped from a height H. When it reaches the ground, its velocity is 40 m/s. Find the height?
(A) 71.6 m (B) 32.5 m (C) 81.6 m (D) 51.6 m
Q.39 How much time will it take to perform 440 J of work at a rate of 11 W?
(A) 50 s (B) 40 s (C) 30 s (D) 20 s
Q.40 When the speed of a particle is doubled, its kinetic energy
(A) remains the same (B) gets doubled
(C) becomes half (D) becomes four times
Q.41 When the speed of a particle is doubled, the ratio of its kinetic energy to its momentum
(A) remains the same (B) gets doubled
(C) becomes half (D) becomes four times
Q.42 A person A does 500 J work in 10 minutes and another person B does 600 J of work in 20 minutes. Let the power delivered by A and B be P1 and P2 respectively, then
(A) P1 = P2
(B) P1 > P2
(C) P1 < P2
(D) P1 and P2 are undefined
Q.43 By what factor does the kinetic energy of a particle increase if the velocity is increased by a factor of three?
(A) 6 (B) 7 (C) 8 (D) 9
Q.44 A block is thrown upwards with a kinetic energy 1 J. If it goes up to a maximum height of 1 m, then the mass of the block is :
(A) 110 g (B) 100 g (C) 105 g (D) 104 g
Q.45 Two persons do the same amount of work, one in 10 s and the other in 20 s. Find the ratio of the power used by the first person to that by the second person.
(A) 6 (B) 2 (C) 5 (D) 4
Q.46 Calculate the velocity of the bob of a simple pendulum at its mean position if it is able to rise to a vertical height of 10 cm. (Given : g = 980 cms–2)
(A) 1.40 ms–1 (B) 2.54 ms–1 (C) 3.43 ms–1 (D) 5.35 ms–1
Q.47 A one kilowatt motor pumps out water from a well 10 metres deep. Calculate the quantity of water pumped out per second.
(A) 10.204 g (B) 15.302 g (C) 11.201 g (D) 16.204 g
Q.48 Which of the following equations show the correct relationship between mass, momentum and kinetic energy?
Q.49 A light body and a heavy body have the same kinetic energy. Which one will have a greater momentum?
(A) Lighter body
(B) Heavier body
(C) Both bodies have same momentum (D) None of the above
Q.50 The momentum of a body is numerically equal to the kinetic energy of the body. What is the velocity of the body?
Q.51 A car is accelerated from 10 ms–1 to 15 ms–1. The increase in kinetic energy is Ek1 . Again, the car is accelerated from 15 ms–1 to 20 ms–1. The increase in kinetic energy is now Ek2. What is the ratio of ?
(A) 0.5. (B) 0.7 (C) 0.1 (D) 0.4
Q.52 If a graph between P.E. of the body in relation to the height through which it falls freely is plotted, it may be noted that the total energy remains the same. Which of the following graphs shows this relation correctly?
Q.53 A graph of the total energy, (P.E + K.E.) of a freely falling body from a height is plotted. Which of the following is the best approximation?
Q.54 A girl of mass 40 kg climbs 50 stairs of average height 20 cm each in 50 s. The power of the girl is : (g = 10ms–2)
(A) 50 W (B) 50 × 20 W (C) 80 W (D) 50 × 20 × 2W
Q.55 When a light and a heavy body have equal K.E, then which one has a greater momentum?
(A) light body
(B) heavy body
(C) both have equal momentum
(D) uncertain
Q.56 In SI system, the unit of P.E. is
(A) erg (B) dyne-cm
(C) J (D) none of these
Q.57 Kilowatt hour (kWh) represents the unit of
(A) power (B) impulse
(C) momentum (D) none of these
Q.58 When speed of a motor car increases six times, then kinetic energy increases by
(A) 6 times (B) 36 times
(C) 12 times (D) 24 times
Q.59 1 kWh equals
(A) 36 × 102 Joules (B) 36 × 104 Joules (C) 3.6 × 106 Joules (D) none of these
Q.60 When speed of the moving object is doubled its
(A) acceleration is doubled
(B) momentum becomes four times more
(C) K E. is increased to four times
(D) potential energy is increased
Q.61 When time taken to complete a given amount of work increases, then
(A) power increases (B) power decreases (C) energy increases (D) energy decreases
Q.62 When the force applied and the displacement of the body are inclined at 90° with each other, then work done is
(A) infinite (B) maximum
(C) zero (D) unity
Q.63 The KE. of a body in increased most by doubling its
(A) mass (B) weight
(C) speed (D) density
Q.64 If a force F is applied on a body and it move with velocity v, then power will be :-
(A) F x v (B) F/v2
(C) F/v (D) F × v2
Q.65 Work done by a centripetal force
(A) increases by decreasing the radius of the circle
(B) decreases by increasing the radius of the circle
(C) increases by increasing the mass of the body
(D) is always zero
Q.66 A 1 kg mass falls from a height of 10 m into a sand box. What is the speed of the mass just before hitting the sand box? If it travels a distance of 2 cm into the sand before coming to rest, what is the average retarding force?
(A) 12 m/sec and 3600N
(B) 14 m/sec and 4900N
(C) 16 m/sec and 6400N
(D) 18 m/sec and 8100N
Q.67 Work done in moving a 50 kg block through a horizontal distance of 10 m by applying a force of 100N which makes an angle of 60° with the horizontal is
(A) 200 joule (B) 425 joule
(C) 500 joule (D) 575 joule
Q.68 kWh is the unit of
(A) force (B) power
(C) time (D) energy
Q.69 An elevator is designed to lift a load of 1000 kg through 6 floors of a building averaging 3·5 m per floor in 6 sec. Power of the elevator, neglecting other losses, will be
(A) 3·43 × 104 watt (B) 4·33 × 104 watt
(C) 2·21 × 104 watt (D) 5·65 × 104 watt
Q.70 The work done by a body is directly proportional to :
(A) force acting on the body
(B) displacement produced in the body
(C) mass of the body
(D) both (A) and (B)
Q.71 Work done is said to be positive when a force causes displacement:
(A) in its own direction
(B) in the direction opposite to the applied force
(C) in the direction at right angles to the direction of applied force
(D) none of the above.
Q.72 Work done is said to be negative, when a force causes displacement:
(A) in the direction opposite to the direction of applied force
(B) in the direction of applied force
(C) in the direction opposite to the direction of applied force
(D) none of the above.
Q.73 In which case work is not done:
(A) a girl swimming in a pond
(B) a windmill lifting water from a well
(C) a standing man holding a suit case in his hand
(D) a sail boat moving in the direction of wind.
Q.74 In which case work is done:
(A) a green plant carrying out photosynthesis
(B) a porter standing at a place and carry heavy load on his head
(C) drying of food grains in sun
(D) a trolley rolling down a slope
Q.75 A stone is tied to a string and whirled in a circular path. The work done by the stone is :
(A) negative (B) zero
(C) positive (D) none of the above.
Q.76 A man carries a suitcase in his hand climbs up the stairs. The work done by the man is :
(A) positive (B) negative
(C) zero (D) none of the above.
Q.77 A rocket rises up in the air due to the force generated by the fuel. The work done by the:
(A) fuel is negative work and that of force of gravity is positive work
(B) fuel is positive work and that of force of gravity is negative work
(C) both fuel and force of gravity do positive work
(D) both fuel and force of gravity do negative work.
Q.78 One joule work is said to be done when a force of one newton acts through a distance of:
(A) 1 cm (B) 1 mm
(C) 1 m (D) 1 km
Q.79 Work is the product of time and:
(A) power (B) energy
(C) force (D) acceleration.
Q.80 In angle in between the direction of applied force and displacement, for maximum work should be :
(A) 90° (B) 45°
(C) zero (D) 30°
Q.81 Work done upon a body is: [NTSE]
(A) a vector quantity (B) a scalar quantity
(C) always positive (D) always negative
Q.82 In the SI system the unit of P.E. is: [NTSE]
(A) erg (B) dyne-cm
(C) J (D) none of these
Q.83 Kilowatt hour (kWh) represents the unit of:
(A) power (B) impulse [NTSE]
(C) momentum (D) none of these
Q.84 Two unequal masses possess the same K.E. Then, the heavier mass has: [NTSE]
(A) grater momentum
(B) smaller momentum
(C) the same momentum as the lighter mass (D) greater speed
Q.85 Two unequal masses possess the same momentum, then the kinetic energy of the heavier mass is _________ the kinetic energy of the lighter mass. [NTSE]
(A) same as (B) greater than
(C) smaller than (D) much greater than
Q.86 The speed of a motor car becomes six times, then the kinetic energy becomes: [NTSE]
(A) 6 times (B) 36 times
(C) 12 times (D) 24 times
Q.87 The number of joules contained in 1 kWh is:
(A) 36 × 102 (B) 36 × 103 [NTSE]
(C) 36 × 104 (D) 3.6 × 106
Q.88 A body moves through a distance of 3 m in the following different ways. In which case is the maximum work done? [NTSE]
(A) when pushed over an inclined plane (B) when lifted vertically upward
(C) when pushed over smooth rollers (D) when pushed on a plane horizontal surface
Q.89 In the above example, the work done is minimum when the body is: [NTSE]
(A) pushed over an inclined plane
(B) lifted vertically upward
(C) pushed over the smooth rollers
(D) pushed on a plane horizontal surface
Q.90 A truck and a car are moving on a smooth, level road such that the K.E. associated with them is same. Brakes are applied to both of them simultaneously. Which one will cover a greater distance before it stops? [NTSE]
(A) car
(B) truck
(C) both will cover the same distance (D) nothing can be decided
Q.91 A wound watch spring has ___ energy. [NTSE]
(A) mechanical (B) kinetic
(C) potential (D) kinetic and potential
Q.92 Two bullets P and Q masses 10 and 20g, are moving in the same direction towards a target with velocities of 20 and 10 m/s respectively. Which one of the bullets will pierce a greater distance through the target? [NTSE]
(A) P
(B) Q
(C) both will cover the same distance (D) nothing can be decided
Q.93 When the time taken to complete a given amount of work increases, then, [NTSE]
(A) power increases (B) power decreases
(C) energy increases (D) energy decreases
Q.94 When the force applied and the displacement of the body are inclined at 90° with each other, the work done is: [NTSE]
(A) infinite (B) maximum
(C) zero (D) unity
Q.95 A car is moving along a straight level road with constant speed. Then [NTSE]
(A) the work done on the car is infinite (B) the work done on the car is zero
(C) the work done on the car is a measure of the gravitational potential energy
(D) the work done on the car cannot be found
Q.96 Kg m2 s–2 represents the unit of: [NTSE]
(A) kinetic energy only
(B) work done only
(C) potential energy only
(D) all the above
Q.97 The moon revolves around the earth because the earth exerts a radial force on the moon. Does the earth perform work on the moon? [NTSE]
(A) no (B) yes, sometimes
(C) yes, always (D) cannot be decided
Q.98 The K.E. of a body is increased most by doubling its: [NTSE]
(A) mass (B) weight
(C) speed (D) density
Q.99 A body is dropped from a certain height from the ground. When it is halfway down, it possesses, [NTSE]
(A) only K.E. (B) both K.E. and P.E.
(C) only P.E. (D) zero energy
Q.100 A body of mass 20 kg is dropped from a height of 2m. If g is taken to be equal to 10 m/s2, the kinetic energy of the body, just before striking the ground, will be: [NTSE]
(A) 400 J (B) 4 J
(C) 40 J (D) none of these
ANSWER KEY
1. D 2. C 3. B 4. C
5. C 6. C 7. D 8. B
9. D 10. C 11. D 12. C
13. C 14. C 15. B 16. C
17. D 18. C 19. A 20. B
21. C 22. B 23. A 24. D
25. B 26. C 27. C 28. D
29. C 30. B 31. A 32. A
33. B 34. B 35. C 36. A
37. A 38. C 39. B 40. D
41. B 42. B 43. D 44. B
45. B 46. A 47. A 48. A
49. B 50. B 51. B 52. B
53. D 54. C 55. B 56. C
57. D 58. B 59. C 60. C
61. B 62. C 63. C 64. A
65. D 66. B 67. C 68. D
69. A 70. D 71. A 72. A
73. C 74. D 75. B 76. A
77. B 78. C 79. A 80. C
81. B 82. C 83. D 84. A
85. C 86. B 87. D 88. B
89. C 90. C 91. C 92. A
93. B 94. C 95. B 96. D
97. A 98. C 99. B 100. A