A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which more in opposite direction…
A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which more in opposite direction with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1 / E_2$ is:
$m_2 / m_1$
$m_1 / m_2$
1
$m_1 m_2 / m_2 m_1$
Solution
According to law of conservation of linear momentum
$\begin{aligned}
& m_1 v_1=m_2 v_2 \quad \ldots \text { (i) } \\
& E_1=\frac{1}{2} m_1 v_1^2, E_2=\frac{1}{2} m_2 v_2^2 \\
& \therefore \frac{E_1}{E_2}=\frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_1^2}=\frac{\left(m_1 v_1\right)^2}{\left(m_2 v_2\right)^2} \times \frac{m_2}{m_1} \\
& \therefore \frac{E_1}{E_2}=\frac{m_2}{m_1}
\end{aligned}$