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COM of Center of Masses

Particle 1 of...

Question

Particle 1 of mass $m_{1}$ collides with a stationary particle 2 of mass $m_{2}$ elastically. Find the ratio of $\frac{m_{2}}{m_{1}}$ , if after collision they move in opposite direction with equal velocities.
Assume Head on collision

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Solution

Ratio of velocities after collision is $\frac{v_{1}}{v_{2}} = \frac{(m_{1} - m_{2}) u_{1} + 2 m_{2} u_{2}}{(m_{2} - m_{1}) u_{2} + 2 m_{1} u_{1}}$
Here $u_{2} = 0, v_{1} = - v_{2}$
$- 1 = \frac{(m_{1} - m_{2}) u}{2 m_{1} u}$
$\frac{m_{2}}{m_{1}} = 3$

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