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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 fly apart in opposite directions with equal velocities.

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1 : 3

3 : 1

3 : 2

2 : 3

answer is A.

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Detailed Solution

$m_{1} u_{1} + 0 = - m_{1} v_{1} + m_{1} v_{2}$ = $(- m_{1} + m_{2}) V_{2}$

$m_{1} u = (- m_{1} + m_{2}) \frac{u_{1}}{2}$

$2 m_{1} + m_{1} = m_{2}$ $∴ \frac{m_{1}}{m_{2}} = \frac{1}{3}$

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