Work Energy and Power

Practice Questions:

Question 11: moderate

Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

1. 1:2

2. √2:1

3. 4:1

4. 1:16

View Answer

Kinetic Energy is given by K = ½mv² and Momentum is P=m.v, relation between kinetic energy and momentum is

K= P²/2m so P=√(2mK)

So P1/P2= √(m1)/√(m2)= √1/√4 = 1:2

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Question 12: moderate

If the kinetic energy of a body is increased by 300%, its momentum will increase by :

1. 100%

2. 150%

3. 200%

4. 400%

View Answer

Relation between Kinetic Energy and Momentum is

P = √(2mK)

When kinetic energy is increased by 300 % it becomes 4K so new momentum is

P1= √(2m.4K) =2P

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Question 13: moderate

If the kinetic energy of a body is increased by 3%, its momentum will increase by :

1. 1 %

2. 1.5 %

3. 3 %

4. 4.5 %

View Answer

K = P²/2m so,

∇K/K=2∇P/P

Solving We get , ∇P/P = 1.5%

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Question 14: easy

A cubical vessel of height 1 m is full of water. The minimum work done in taking water-out from vessel will be

1. 5000 J

2. 10000 J

3. 5 J

4. 10 J

View Answer

As side length of cubical tank is 1 m. Volume is 1 m³. Volume of water in 1 m³ is 1000 lit and mass will be 1000 kg.

Height of center of mass of the tank will be 1/2 m.

Potential Energy = 1000 ×10 × 1/2 = 5000 J

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Question 15: moderate

A man pulls a bucket full of water from h metre deep well. If the mass of rope is m and mass of bucket full of water is M, then work done by the man is

1. ( m + M/2) gh

2. ( m + M) gh

3. ( m/2 + M) gh

4. ( 2m + M) gh

View Answer

Bucket of mass M will rise by a distance of h.

While center of mass of the rope rises by height of h/2.

So, Work Done = (M+m/2).g.h

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Question 16: moderate

Potential energy of a particle at position x is given by U = x² – 5x. Which of the following is equilibrium position of the particle?

1. x = 0

2. x = 2.5 m

3. x = 5 m

4. x = 7.5 m

View Answer

For Equilibrium,

dU/dx = 0

⇒ d(x²-5x)/dx=0

⇒ 2x-5 = 0

⇒ x =2.5 m

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Question 17: moderate

In a conservative field, the potential energy U as a function of position x is given by U = x². Then the corresponding conservative force is given by

1. x

2. 2x

3. -x

4. -2x

View Answer

By definition Force F = -dU/dx, so

F = - d(x²)/dx= -2x

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Question 18: easy

Select correct statement regarding stable equilibrium

1. Potential energy of body is minimum in stable equilibrium

2. Slope of potential energy versus position graph is zero at stable equilibrium

3. A restoring force acts on the body when it is slightly displaced from its stable equilibrium position

4. All of these

View Answer

All the statements are true regarding stable equilibrium

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Question 19: moderate

In a certain field, the potential energy is U = ax² – bx³, where a and b constants. The particle is in stable equilibrium at x equal to

1. zero

2. a/3b

3. 2a/3b

4. 2a/b

View Answer

Potential Energy is U = ax² – bx³. For Equilibrium F = -dU/dx

⇒ dU/dx= 2ax- 3bx²=0

⇒ x = 2a/3b

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Question 20: easy

An engine pumps 400 kg of water through height of 10 m in 40 s. Find the power of the pump (g = 10 m/s²).

1. 500 W

2. 750 W

3. 1000 W

4. 1250 W

View Answer

Power = Work Done / Time Taken

Here , Work Done = 400 ×10 ×10 J = 40000 J

Time Taken = 40 sec , So,

Power = 40000/40 = 1000 W= 1 KW

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