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A particle of mass 3m with an initial velocity $u \hat{i}$ collides perfectly elastically with a mass m at rest. It moves with a velocity $v \hat{i}$ after collision, then, v is given by:

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$v = \frac{3}{2} u$

$v = \frac{2}{3} u$

$v = \frac{u}{\sqrt{2}}$

$v = \frac{u}{2}$

answer is D.

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Detailed Solution

$v_{1} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} u_{1} + \frac{2 m_{2}}{m_{1} + m_{2}} u_{2}$

$v_{2} = \frac{2 m_{1}}{m_{1} + m_{2}} u_{1} - \frac{m_{1} - m_{2}}{m_{1} + m_{2}} u_{2}$

$v_{1} = \frac{u}{2}$

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