Two bodies of different masses $m_1$ and $m_2$ have equal momenta. Their kinetic energies $E_1$ and $E_2$ are in the ratio

Given - Momentum of two bodies are same i.e. $p_1=p_2$ and mass of two bodies $m_1$ and $m_2$ The relationship between the kinetic energy (KE) and Linear momentum ( p ) is - Momentum of first body whose mass is $\mathrm{m}_1$. $p=\sqrt{2 m_1 K E_1}$ $\qquad ...\mathrm{(1)}$ Momentum of second body whose mass is $\mathrm{m}_2$ $p=\sqrt{2 m_2 K E_2}$ $\qquad ...\mathrm{(2)}$ Divide equation (1) and (2). $\begin{aligned} & \frac{p}{p}=\frac{\sqrt{2 m_1 K E_1}}{\sqrt{2 m_2 K E_2}} \\ & \sqrt{2 m_2 K E_2}=\sqrt{2 m_1 K E_1} \end{aligned}$ By squaring both side, we get $\begin{aligned} & 2 m_2 K E_2=2 m_1 K E_1 \\ & \frac{K E_1}{K E_2}=\frac{m_2}{m_1} \end{aligned}$