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

• A. $1$
• B. $ m_{1}v_{2}/m_{2}v_{1} $
• C. $ m_{2}/m_{1} $
• D. $ m_{1}/m_{2} $

Answer 1

Answer: (C)

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