A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is

Question

A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2}$. Both of them have the same momentum but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1}>m_{2}$ then\

Professor PC Thomas Classes · Answer

(a) : Kinetic energy $=\frac{p^{2}}{2 m}$\ $\therefore \quad \frac{E_{1}}{E_{2}}=\frac{p_{1}^{2} / 2 m_{1}}{p_{2}^{2} / 2 m_{2}} \Rightarrow \frac{E_{1}}{E_{2}}=\frac{m_{2}}{m_{1}}$\ or $E_{1}<E_{2}$\[0pt] [as $m_{1}>m_{2}$ ]\