Two bodies of masses $m_{1}$ and $m_{2}$ have same kinetic energy. The ratio of their momentum is

\sqrt{\frac{m_{2}}{m_{1}}}

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\sqrt{\frac{m_{1}}{m_{2}}}

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\frac{m_{1}^{2}}{m_{2}^{2}}

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\frac{m_{2}^{2}}{m_{1}^{2}}

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Solution

The correct option is B $\sqrt{\frac{m_{1}}{m_{2}}}$
Let $p_{1}$ be the momentum of body of mass $m_{1}$
and $p_{2}$ be the momentum of body of mass $m_{2}$

Given that both masses have same kinetic energy

$⟹ \frac{p_{1}^{2}}{2 m_{1}} = \frac{p_{2}^{2}}{2 m_{2}}$

$⟹ (\frac{p_{1}}{p_{2}})^{2} = \frac{m_{1}}{m_{2}}$

$⟹ \frac{p_{1}}{p_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$ ........... Required Answer

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