Two bodies with kinetic energies in the ratio $4 : 1$ ` are moving with equal linear momentum. The ratio of their masses is:

1 : 2

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1 : 1

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4 : 1

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1 : 4

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Solution

The correct option is D $1 : 4$
$K E = \frac{p^{2}}{2 m}$

$K E \propto \frac{1}{m}$

$\frac{K E_{1}}{K E_{2}} = \frac{m_{2}}{m_{1}} = 4 : 1$

So $\frac{m_{1}}{m_{2}} = 1 / 4$

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