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Kinetic Energy

Two bodies of...

Question

Two bodies of mass $m_{A}$ and $m_{B}$ have equal kinetic energy. The ratio of their momenta is

A

\sqrt{m_{A}} : \sqrt{m_{B}}

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B

m_{A}^{2} : m_{B}^{2}

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C

m_{A} : m_{B}

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D

m_{B} : m_{A}

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Solution

The correct option is A $\sqrt{m_{A}} : \sqrt{m_{B}}$
Given that two bodies of mass $m_{A}$ and $m_{B}$ have equal kinetic energy hence,

$\frac{1}{2} m_{A} (v_{A})^{2} = \frac{1}{2} m_{B} (v_{B})^{2}$

$\frac{1}{2} \frac{(m_{A})^{2} (v_{A})^{2}}{m_{A}} = \frac{1}{2} \frac{(m_{B})^{2} (v_{B})^{2}}{m_{B}}$

$\frac{(p_{A})^{2}}{m_{A}} = \frac{(p_{B})^{2}}{m_{B}}$

$\frac{(p_{A})^{2}}{(p_{B})^{2}} = \frac{m_{A}}{m_{B}}$

$\frac{(p_{A})^{2}}{(p_{B})^{2}} = \frac{\sqrt{m_{A}}}{\sqrt{m_{B}}}$

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