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Defining Kinetic Energy

Two bodies of...

Question

Two bodies of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. If $p_{1}$ and $p_{2}$ are their respective momentum, then ratio $p_{1} : p_{2}$ is equal to

A

$m_{1} : m_{2}$

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B

$m_{2} : m_{1}$

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C

$\sqrt{m_{1}} : \sqrt{m_{2}}$

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D

$m_{1}^{2} : m_{2}^{2}$

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Solution

The correct option is C
$\sqrt{m_{1}} : \sqrt{m_{2}}$

$P = \sqrt{2 m E} (i f E = c o n s t .) ∴ \frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$

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