A stationary particle explodes into two particles of masses $m_{1}$ and $m_{2}$ which move in opposi

Question

A stationary particle explodes into two particles of masses $m_{1}$ and $m_{2}$ which move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies $E_{1} / E_{2}$ is\

Professor PC Thomas Classes · Answer

(a): $m_{1} v_{1}=m_{2} v_{2}$\ (conservation of linear momentum) $$ \frac{E_{1}}{E_{2}}=\frac{(1 / 2) m_{1} v_{1}^{2}}{(1 / 2) m_{2} v_{2}^{2}}=\frac{m_{1}^{2} v_{1}^{2}}{m_{2}^{2} v_{2}^{2}} \cdot \frac{m_{2}}{m_{1}}=\frac{m_{2}}{m_{1}} $$