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Kinetic Energy

Two bodies of...

Question

Two bodies of masses $m_{1} a n d m_{2}$ are moving with equal kinetic energies. What is the ratio of their momenta?

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Solution

Kinetic energy, $K = \frac{p^{2}}{2 m}$ where $p =$ momentum and $m =$ mass
So, $p = \sqrt{2 m K}$
Thus, $= \frac{p_{1}}{p_{2}} = \sqrt{\frac{2 m_{1} K}{2 m_{2} K}} = \sqrt{m_{1} / m_{2}}$

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