Two bodies A and B are moving with velocities $6 v$ and $\frac{3}{2} v$ respectively. If their kinetic energies are identical, find the ratio of mass of body A to that of body B.

1:8

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1:16

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1:2

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1:32

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Solution

The correct option is B 1:16
Given: velocity of body A, $v_{a} = 6 v$ , velocity of body B, $v_{b} = \frac{3}{2} v$ .
Let the masses of bodies A and B be $m_{a}$ and $m_{b}$ respectively.

Kinetic energy of A = Kinetic energy of B
$∴ \frac{1}{2} m_{a} v_{a}^{2} = \frac{1}{2} m_{b} v_{b}^{2}$
$\Rightarrow \frac{m_{a}}{m_{b}} = \frac{v_{b}^{2}}{v_{a}^{2}} = \frac{(\frac{3}{2} v)^{2}}{(6 v)^{2}}$
$\Rightarrow \frac{9}{4 \times 36} = \frac{1}{16}$
Thus. the ratio of masses of body A and B is $\frac{1}{16}$

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