Two particles of masses m_{1} and m_{2} have | vedclass

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(C) Given,the kinetic energy $(K)$ of two particles of masses $m_{1}$ and $m_{2}$ is equal.We know that kinetic energy is related to momentum $(p)$ by

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$\sqrt{m_{1}}: \sqrt{m_{2}}$

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(C) Given,the kinetic energy $(K)$ of two particles of masses $m_{1}$ and $m_{2}$ is equal.We know that kinetic energy is related to momentum $(p)$ by the formula $K = \frac{p^{2}}{2m}$.Since $K_{1} = K_{2}$,we have $\frac{p_{1}^{2}}{2m_{1}} = \frac{p_{2}^{2}}{2m_{2}}$.Rearranging the terms to find the ratio of momenta $\frac{p_{1}}{p_{2}}$,we get $\frac{p_{1}^{2}}{p_{2}^{2}} = \frac{m_{1}}{m_{2}}$.Taking the square root on both sides,we obtain $\frac{p_{1}}{p_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \frac{\sqrt{m_{1}}}{\sqrt{m_{2}}}$.Therefore,the ratio of their momenta is $\sqrt{m_{1}}: \sqrt{m_{2}}$.

Two particles of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. The ratio of their momentum is

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