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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

View Answer

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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Question 9: easy

Two masses \(1\text{ g}\) and \(9\text{ g}\) are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is

1. \(1 : 9\)

2. \(9 : 1\)

3. \(1 : 3\)

4. \(3 : 1\)

View Answer

Since linear momentum \(p = \sqrt{2mK}\) and kinetic energy \(K\) is constant, \(p \propto \sqrt{m}\). Therefore, the ratio of momenta is \(\frac{p_1}{p_2} = \sqrt{\frac{1}{9}} = 1:3\).

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Question 10: easy

Assertion (A): A body cannot have kinetic energy without having linear momentum but it can have momentum without having mechanical energy.

Reason (R): Linear momentum and energy have same dimensions.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is false:

If a body has linear momentum (\(p \neq 0\)), it must have velocity (\(v \neq 0\)), which implies it must also have kinetic energy (\(KE = \frac{1}{2}mv^2 \neq 0\)). Since kinetic energy is a component of mechanical energy, it cannot have momentum without mechanical energy.

Reason (R) is false: Linear momentum has dimensions \(MLT^{-1}\) while energy has dimensions \(ML^2T^{-2}\), which are different.

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