# A particle of mass m with an initial velocity ui^ collides perfectly elastically with a mass 3 m at rest.

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

(1) $v=\sqrt{2\over3}u$

(2) $v={u\over\sqrt{3}}$

(3) $v={u\over\sqrt{6}}$

(4) $v={u\over\sqrt{2}}$
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Finally I've got good question on collision topic

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verified

Ans: (4) $v={u\over\sqrt{2}}$

Sol: From momentum conservation

$mu\hat{i}+0=mv\hat{j}+3m\hat{v'}$

$\hat{v'}={u\over3}\hat{i}-{v\over3}\hat{j}$

From kinetic energy conservation

${1\over2}mu^2={1\over2}mv^2+{1\over2}(3m)\Big(\big({u\over3}\big)^2+\big({v\over3}\big)^2\Big)$

Solving $v={u\over\sqrt{2}}$

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