When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be

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Solution

Q.
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be [2024]

1 600%

2 500%

3 60%

4 6%

Ans.
(2)

Kinetic energy $(K) = \frac{P^{2}}{2 m} \Rightarrow P = \sqrt{2 m K}$

If $K_{f} = 36$ $K_{i} .$ So $P_{f} = 6$ $P_{i}$

% increase in momentum

$= \frac{P_{f} - P_{i}}{P_{i}} \times 100 % = \frac{6 P_{i} - P_{i}}{P_{i}} \times 100 % = 500 % \Rightarrow ∆ P % = 500 %$

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