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COM in Collision and Explosion

A stationary ...

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

m_{2} / m_{1}

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B

m_{1} / m_{2}

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C

1

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D

m_{1} v_{2} / m_{2} v_{1}

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Solution

The correct option is A $m_{2} / m_{1}$
$m_{1} v_{1} = m_{2} v_{2} (P_{1} = P_{2});$
$\frac{E_{1}}{E_{2}} = \frac{\frac{1}{2} m_{1} v_{1}^{2}}{\frac{1}{2} m_{2} v_{2}^{2}} = \frac{\frac{P_{1}^{2}}{2 m_{1}}}{\frac{P_{2}^{2}}{\frac{P_{2}^{2}}{2 m_{2}}}} = \frac{m_{2}}{m_{1}}$

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