Two bodies of masses $m_{1}$ and $m_{2}$ have equal kinetic energy. What is the ratio of their momentum?

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Solution

Given,
Two bodies $m_{1}$ and $m_{2}$
Let the velocity of 1st body be = $v_{1}$
Then its Kinetic energy = $\frac{p^{2}}{{2 m}_{1}}$ = $\frac{{(m_{1} v_{1})}^{2}}{{2 m}_{1}}$
Let the velocity of 2nd body be = $v_{2}$
Then its Kinetic energy = $\frac{p^{2}}{{2 m}_{2}}$ = $\frac{{(m_{2} v_{2})}^{2}}{{2 m}_{2}}$
Now, $\frac{{(m_{1} v_{1})}^{2}}{{2 m}_{1}}$ = $\frac{{(m_{2} v_{2})}^{2}}{{2 m}_{2}}$
∴ $\frac{m_{1} v_{1}}{m_{2} v_{2}}$ = $\frac{\sqrt{{2 m}_{2}}}{\sqrt{{2 m}_{1}}}$
Then Ratio = $\sqrt{({2 m}_{2})}$ : $\sqrt{({2 m}_{1})}$

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