Two bodies of masses $m_{1} a n d m_{2}$ have equal kinetic energies. Find the ratio of their momentum.

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

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

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

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

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Solution

The correct option is A $\sqrt{\frac{m_{1}}{m_{2}}}$
Given $K . E_{1} = K {. E}_{2} \frac{1}{2} M_{1} V_{2}^{1} = \frac{1}{2} M_{2} V_{2}^{2} {(\frac{V_{1}}{V_{2}})}^{2} = \frac{M_{2}}{M_{1}} \frac{M_{1}}{M_{2}} \frac{V_{1}}{V_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} \frac{M_{1}}{M_{2}} \frac{P_{1}}{P_{2}} = \sqrt{\frac{M_{1}}{M_{2}}}$

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