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Question

Two bodies of masses ′m′ and ′4m′ are having linear momentum in the ratio of 2:1, respectively. The ratio of their kinetic energy is

A
4:1
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B
1:4
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C
1:8
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D
16:1
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Solution

The correct option is D 16:1
Lets assume that
P1= Linear momentum of mass m
KE1= Kinetic energy of mass m
P2= Linear momentum of mass 4m
KE2= Kinetic energy of mass 4m

We also know that, the relation between kinetic energy and linear momentum is given by,
KE=P22m
KE1KE2=P212mP222×4m

P1P2=(21) (given)

KE1KE2=(21)2×4=(16:1)

Hence option D is the correct answer.

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