Two objects of masses m_1 and m_2 possess equ | vedclass

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(C) The kinetic energy $K$ of an object of mass $m$ and momentum $p$ is given by the relation $K = \frac{p^2}{2m}$.Given that the kinetic energies are

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

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(C) The kinetic energy $K$ of an object of mass $m$ and momentum $p$ is given by the relation $K = \frac{p^2}{2m}$.Given that the kinetic energies are equal,we have $K_1 = K_2$.Therefore,$\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$.Rearranging the terms to find the ratio of momenta,we get $\frac{p_1^2}{p_2^2} = \frac{m_1}{m_2}$.Taking the square root on both sides,we obtain $\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}} = \frac{\sqrt{m_1}}{\sqrt{m_2}}$.Thus,the ratio $p_1: p_2$ is $\sqrt{m_1}: \sqrt{m_2}$.

Two objects of masses $m_1$ and $m_2$ possess equal kinetic energies. If $p_1$ and $p_2$ are their respective momentum,then $p_1: p_2$ is

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