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Two spheres each of mass ‘m’, each moving with velocity u moving in directions at $30^{0}$ S of W and $30^{0}$ N of W respectively collide at point O and stick to each other. The velocity of the combination later becomes

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a

$\frac{\sqrt{3} u}{2}$ due East

b

$\sqrt{3} u$ due East

c

$\frac{2 u}{\sqrt{3}}$ due North

d

$\frac{\sqrt{3} u}{2}$ due West

answer is D.

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Detailed Solution

$\begin{array}{l} {\bar{P}}_{1} = - P \cos 60 \hat{j} - P \sin 60 \hat{i} = - \frac{P}{2} \hat{j} - \frac{P \sqrt{3}}{2} \hat{i}; \\ {\bar{P}}_{2} = P \cos 60 \hat{j} - P \sin 60 \hat{i} = \frac{P}{2} \hat{j} - \frac{P}{2} \sqrt{3} \hat{i} \\ \bar{V} = \frac{{\bar{P}}_{1} + {\bar{P}}_{2}}{m_{1} + m_{2}} = - \frac{\sqrt{3}}{2} u \hat{i} \Rightarrow V = \frac{\sqrt{3} u}{2} i n W e s t \end{array}$

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