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Question

# If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

A
100 %
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B
200 %
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C
300 %
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D
400 %
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Solution

## The correct option is A 100 %The K.E of a moving body has relation with momentum as K.E, K=P22m ⇒ P∝√K Given, the Kinetic energy of a moving body becomes four times its initial Kinetic energy. Let initial K.E of the body be K ⇒ final K.E of the body will be 4K ∴ P2P1=√4KK, where, P2 and P1 are the final momentum and initial momentum of the body respectively. ⇒P2P1=2 Percentage change in momentum is given by, (P2−P1P1) %=(P2P1−1)×100=(2−1)×100=100 % ⇒ (ΔPP1) %=100 % Hence, option (a) is correct.

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