11th Class Physics Unit 4 Work, Energy and Power Short Questions and Answers

1.Why is electrical power required at all when the elevator is descending? Why should there be a limit on the number of passengers in this case?

When an elevator is descending, electrical power might still be required for:
1. Controlled descent: To ensure a smooth, controlled descent, and prevent free fall.
2. Braking: To slow down or stop the elevator safely.
A limit on the number of passengers is necessary for:
1. Safety: Overloading can cause mechanical stress, increasing the risk of accidents.
2. Controlled movement: Too many passengers can affect the elevator's ability to descend smoothly and safely.
These limits ensure safe operation and prevent potential hazards.

2.A body is being raised to a height H from surface of the Earth. What is the sign of work done by both (body and Earth? justify.

The expression for work done is dot product of force and displacement
W = F̄·d̄
W = Fd cosθ
The work done by Earth's gravity is negative, since force and displacement are in opposite direction (θ = 180°)
w = − Fd
The work done by person is positive, since, the force and displacement are in the same direction so, θ = 0°
W = FHcosθ = FH
Justification: (gravity pulls downward, opposite to displacement) So, it does negative work. The applied force does positive work to raise the body.

Initial potential energy = 0
Final potential energy = mgH

3.A body falls towards the Earth in air. Will its total mechanical energy be conserved during fall? Justify.

when an object falls towards Earth, then according to law of conservation of energy for non-resistance medium, it can be written as,
Mathematically:
loss in P.E = gain in K.E
This shows total mechanical energy remains conserved.
The law of conservation for resistive medium can be written as
Mathematically:
loss in P.E = given in K.E + work done against friction.
It is clear that a part of energy is converted into heat energy to perform work against friction so total mechanical energy does not remain conserved.

4.Calculate power of a crane in kilowatt which lifts a mass of 1000 kg to a height of 100 min 20 second.

m = 1000 kg
h = 100 m
t = 20 s
P = ?
Work = w = m × g × h
= 1000 kg × 9.8 m/s² × 100 m
= 980,000 J
Power = Work / time
= 980,000 J / 20 s
= 49,000 W
= 49 kW
So, the power of crane is 49 kW.

5.A trolley of mass 1500 kg carrying sand bags of 500 kg is moving uniformly with a speed of 40km h⁻¹ on a frictionless track. After some time, sand starts leaking out of whole sand bags on the road at a rate of 0.05 kg s⁻¹. What is the speed of the trolley after entire sand bags are empty?

Total mass = M₁ = initial mass of trolley + sandbags
= 1500 kg + 500 kg
= 2000 kg
M_f = 1500 kg
v_i = 40 km/h = 40×1000/3600 = 11.11 m/s
v_f = ?
Using principle of conservation of momentum:
Initial momentum = Final momentum
M₁v_i = M_f v_f
2000 × 11.11 = 1500 × v_f
v_f = (2000 × 11.11) / 1500
v_f = 14.81 m / s

6.Give absolute and gravitational units of work in M.K.S and C.G.S systems.

Here are the units MKS System:
1. Absolute unit: Joule (J)
2. Gravitational unit: kilogram-meter (kg-m)
CGS System:
1. Absolute unit: erg
2. Gravitational unit: gram-centimeter (g-cm)
Note that:
1 Joule = 10⁷ ergs

7.A body dropped from a height of H reaches the ground with a speed of 1.2√gH. Calculate work done by air friction.

Height = H, speed = V = 1.2√gh
Initial potential energy = mgH
Final kinetic energy
= 1/2 m v² = 1/2 m(1.2√(gH))² = 0.72mgH
Work done by gravity = mgh
Work done by air friction = change in mechanical energy
= final KE – initial PE
= 0.72mgH – mgH
= – 0.28mgH
So, work done by air friction is -0.28mgH.
The negative sign indicates energy loss due to friction.

8.A bicycle has a K.E. of 150 J. What K.E. would the bicycle have if it had: (i) same mass but has speed double? (ii) three times mass and was moving with one half of the speed?

Initial KE = 150 J = 1/2 m v²
(i) Double speed:
New KE = 1/2 m(2v)²
= 4 × 1/2 m v² (Putting value of initial K.E)
= 4 × 150 J
= 600 J
(ii) Three times mass, half speed:
New KE = 1/2 (3 m) (v / 2)²
= 1/2 × 3m × v²/4
= (3/4) × 1/2 m v² (Again putting value of K.E)
= (3/4) × 150 J
= 112.5 J
So, the new kinetic energies would be 600 J and 112.5 J, respectively.

9.What will be the effect on K.E. of the body having mass m, moving with velocity v when its momentum becomes double? Justify.

∴K.E = p²/2m --------- (1)
If p' = 2p
K.E' = (2p)²/2m
K.E' = 4p²/2m
Using Eq. (1)
K.E' = 4K.E
Hence, when momentum is doubled then K.E becomes four times.

10.Does the international space station have gravitation P.E, or Kinetic energy or both? Explain.

The International Space Station (ISS) has:
Gravitational Potential Energy (PE):
due to its height above Earth's surface. It is in orbit, but still within Earth's gravitational field. (P.E = −GMm/r)
Kinetic Energy: due to it is orbital velocity. K.E allows it to continuously fall around the Earth, maintaining orbit. (K.E = 1/2 m v²)
Both PE and KE are essential for the ISS's orbital motion.

1.How work is calculated graphically?

When a force F acts through a certain distance the event can be plotted by taking the distance along x-axis and the force along y-axis. The area under a force-displacement curve represent the work done by the force.

2.Give the characteristics of work.

(i) Work is a scalar quantity.
(ii) If θ < 90°, work is done is said to the positive work.
(iii) If θ = 90°, no work is done.
(iv) If θ > 90°, the work done is said to be negative.

3.Give the examples of work done under variable force.

(i) A rocket moves away from the earth, work is done against the force of gravity, which varies as the square of distance from the earth's centre.
(ii) The force exerted by a spring increases with the amount of stretch.

4.What is gravitational field?

The space around the earth in which it's gravitational force acts on a body, is called the gravitational field.

5.What is a conservative field?

The field in which the work done is independent of the path followed or work done in a closed path is zero, is called conservative field.

6.Discuss the frictional force as a non-conservative force.

The frictional force is a non-conservative force, because if an object is moved over a rough surface between two points along different paths the work done against the frictional force is certainly different. Hence it is a non-conservative force.

7.What is the commercial unit of electrical energy? Define it

Kilowatt hour is the commercial unit of electrical energy.
One Kilowatt-hour is the work done in one hour by an agency whose power is one kilowatt.
Therefore,
1kWh = 1000w × 3600s
= 3.6 × 10⁶ J = 3.6MJ

8.Absolute potential energy = U_g = −GmM/R what does negative sign signify?

The negative sign shows that the earth's gravitational force for mass m is attraction.

9.A car is moving along a circle of radius 'r'. Its complete four revolutions and terminate its journey at starting point. How much work is done by the car? Explain.

The work by a body is written as:
W = F̄.d̄ = Fd cos θ
In a circular path the centripetal force acting on the body is perpendicular to the direction of motion i.e. θ = 90°
w = F.d cos 90° = 0
w = 0

10.State work-energy principle also write its relation.

Work energy principle states that work done in accelerating the body is always equal to the change in its K.E. i.e.
Fd = 1/2 m v_f² − 1/2 m v_i²

If this body is raised against gravitational field with constant velocity. then according to work-energy principle.
Work done = Δ(P.E)
Or W_A→B = (P.E)_B − (P.E)_A

1.When will you say that a force is conservative? Give two conditions.

A force is considered conservative if:
1. Work done is path-independent: The work done by the force on an object depends only on the initial and final positions, not on the path taken.
2. Work done in a closed loop is zero: When an object moves in a closed loop (returns to its initial position), the total work done by the conservative force is zero.
Examples: gravitational force, elastic force, electrostatic force.

2.A light and heavy body have same linear momentum, which one has greater K.E.?

∴ K.E = p²/2m ⟹ K.E ∝ 1/m When p = constant
This expression shows that light mass has greater K.E for same momentum.

3.A motorcycle is running with constant speed on a horizontal track. Is any work being done on the motorcycle, if no net force is acting on it?

Since motorcycle is moving with a constant speed, so there is no acceleration which clearly shows no net force acts and hence no work done i.e. w = Fd ⟹ (0) (d) = 0

4.A force acts on a ball moving with 14 ms⁻¹ speed and brings its speed to 6 ms⁻¹. Has the force done positive or negative work? Explain your answer.

Reason The force is opposing the motion, causing the ball's speed to decrease from 14 m/s to 6 m/s. This means the force is acting opposite to the direction of motion, resulting in a decrease in kinetic energy, using work – energy principle,
w = 1/2 m v_f² − 1/2 m v_i²
As v_f < v_i, so work done will be negative.

5.A slow moving truck can have more kinetic energy than a fast moving car. How is this possible?

The expression for K.E is expressed as:
Kinetic Energy (K.E) = ½mv²
A slow-moving truck can have more K.E than a fast-moving car if the truck's mass (m) is significantly larger than the mass of the car.
K.E depends on both mass and velocity, so a larger mass can compensate for lower velocity.

6.Why work done against friction is non-conservative in nature? Explain briefly.

Actually, work done against friction is non-conservative in nature.
Reason: Frictional force opposes motion and converts mechanical energy into heat energy, which is dissipated and cannot be recovered. This energy loss makes friction a non-conservative force in nature. Secondly, work done by friction depends on path followed by the object.

7.Does wind contain kinetic energy? Explain.

Yes, wind contains kinetic energy (K.E).
Reason: Wind is moving air, and its motion gives it kinetic energy. The faster the wind blows; the more kinetic energy it possesses.
(K.E = 1/2 m v²)

1.Define K.E. Derive an expression for the same.

See Q.7 of theory.

2.How work is done by a: (i) constant force (ii) variable force?

See Q.1 and 2 of theory.

3.Define conservative field. Show that gravitational field is conservative in nature.

See Q.3 and 4 of theory. (both proof will be shown).

4.What is meant by absolute P.E.? Derive an expression for absolute P.E.

See Q.8 of theory.

5.State and explain work-energy theorem in a resistive medium.

See Q.10 of theory.

6.Define escape velocity. Show that an expression for escape velocity can be expressed as √2Rg where R and g denote radius of the Earth and acceleration due to gravity, respectively. Also find its numerical value.

See Q.9 of theory.

Unit 4: Work, Energy and Power — Short Questions

Exercise Short Questions

SLO Based Additional Short Questions + Past papers Short Questions of Punjab Boards

Graphical representation of work

Characteristic of work

Work done by variable force

Gravitational field

Conservative field

Non-conservative force

Commercial unit of electric energy

Absolute P.E.

Work done

Work-energy principle

Constructed Response Questions

Comprehensive Questions