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(C) The kinetic energy $K$ of a body with mass $m$ and momentum $p$ is given by the relation $K = \frac{p^2}{2m}$.Rearranging this for momentum,we get

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$\sqrt{m_1} : \sqrt{m_2}$

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(C) The kinetic energy $K$ of a body with mass $m$ and momentum $p$ is given by the relation $K = \frac{p^2}{2m}$.Rearranging this for momentum,we get $p = \sqrt{2mK}$.Since the kinetic energy $K$ is the same for both bodies,we have $p \propto \sqrt{m}$.Therefore,the ratio of their momenta is $\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}}$.Thus,$p_1 : p_2 = \sqrt{m_1} : \sqrt{m_2}$.

Two bodies of different masses $m_1$ and $m_2$ have the same kinetic energy. If $p_1$ and $p_2$ are their respective momenta,find the ratio $p_1 : p_2$.

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