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Question

Two bodies A and B are moving with velocities 6v and 32v respectively. If their kinetic energies are identical, find the ratio of mass of body A to that of body B.

A
1:8
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B
1:16
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C
1:2
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D
1:32
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Solution

The correct option is B 1:16
Given: velocity of body A, va=6v, velocity of body B, vb=32v.
Let the masses of bodies A and B be ma and mb respectively.

Kinetic energy of A = Kinetic energy of B
12mav2a=12mbv2b
mamb=v2bv2a=(32v)2(6v)2
94×36=116
Thus. the ratio of masses of body A and B is 116

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