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Kinetic Energy and Momentum

Practice Questions:

Question 1: easy

A 1 kg mass has a kinetic energy of 1 joule when its speed is :

1. 0.45 m/s

2. 1 m/s

3. 1.4 m/s

4. 4.4 m/s

View Answer

Kinetic Energy K = ½mv²

So, 1J = ½(1)v² so, v= √2 m/s= 1.414 m/s

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Question 2: easy

When the velocity of a body is doubled :

1. its kinetic energy is doubled

2. its potential energy is doubled

3. its acceleration is doubled

4. its momentum is doubled

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Momentum of an object is P = m.v

So, when velocity is doubled momentum also doubles

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Question 3: 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 4: 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 5: 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 6: moderate

The graph between √E and 1/p is (E = kinetic energy and p = momentum):

View Answer

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Question 7: easy

If the kinetic energy of a body increases by 800%, its momentum increases by

1. 400%

2. 200%

3. 141%

4. 121%

View Answer

The momentum \(P\) is related to kinetic energy \(K\) by \(P = \sqrt{2mK}\). An 800% increase means the new kinetic energy is \(K' = 9K\). Thus, the new momentum is \(P' = \sqrt{9} P = 3P\), representing an increase of 200%.

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Question 8: easy

Two masses \( 4m \) and \( 9m \) move with equal kinetic energy. The ratio of the magnitude of their momenta is:

1. \( 4 : 9 \)

2. \( 2 : 3 \)

3. \( 9 : 4 \)

4. \( 3 : 2 \)

View Answer

Since kinetic energy \( K \) is the same for both masses, the momentum is proportional to the square root of the mass, \( p = \sqrt{2mK} \). Thus, the ratio of their momenta is \( \frac{p_1}{p_2} = \sqrt{\frac{4m}{9m}} = \frac{2}{3} \).

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