Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their…

The kinetic energy $\left(K\right)$ of an object is given by

$\begin{array}{rcl}K& =& \frac{1}{2}m{v}^2\\ & =& \frac{p^2}{2m} ...\left(1\right)\end{array}$

Following equation (1), for the two given bodies, it can be written that

$$\begin{gathered} \frac{p_1^2}{2 {\mathrm{m}}_1}=\frac{p_2^2}{2 {\mathrm{m}}_2} \\ \Rightarrow \frac{p_1}{p_2}=\sqrt{\frac{{\mathrm{m}}_1}{ {\mathrm{m}}_2}} \\ =\sqrt{\frac{4}{25}} \\ =\frac{2}{5} \end{gathered}$$