Collisions

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Question

A particle experiences a perfectly elastic collision with a stationary particle. Then the ratio of their masses , if after this head on collision the particles by apart in opposite directions with equal velocities is 1 : X, then X =

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Solution

Given $u_{2} = 0$ and $V_{1} = - V_{2}$
$(\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} = \frac{- 2 m_{1} u_{1}}{m_{1} + m_{2}} \Rightarrow 3 m_{1} = m_{2}$
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{1}{3}$

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