Question

A stationary object explodes into masses $m_1$ and $m_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of kinetic energy $E_1$ to kinetic energy $E_2$ is

• A. $\frac{m_{2}}{m_{1}}$
• B. $\frac{m_{1}}{m_{2}}$
• C. $\frac{2m_{2}}{m_{1}}$
• D. $\frac{2m_{1}}{m_{2}}$

Answer 1

Answer: (A)

As stationary object explodes into mases $m_{1}$ and $m_{2}$ and move in opposite direction According to conservation of momentum
$m_{1} v_{1}=-m_{2} v_{2} \Rightarrow \frac{v_{1}}{v_{2}}=\frac{-m_{2}}{m_{1}}$
Now, ratio of $KE$
$\frac{ KE _{1}}{ KE _{2}}=\frac{1 / 2\, m_{1} v_{1}^{2}}{1 / 2 \,m_{2} v_{2}^{2}}=\frac{m_{1}}{m_{2}}\left[\frac{m_{2}}{m_{1}}\right]^{2}=\frac{m_{2}}{m_{1}}$