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Q.

Three identical particle with velocities $v_{0} \hat{i}, - 3 v_{0} \hat{j}$ and $5 v_{0} \hat{k}$ collide successively with each other in such a way that they form a single particle. The velocity vector of resultant particle is

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a

$\frac{v_{0}}{3} (\hat{i} + \hat{j} + \hat{k})$

b

$\frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + \hat{k})$

c

$\frac{v_{0}}{3} (\hat{i} - \hat{j} + \hat{k})$

d

$\frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + 5 \hat{k})$

answer is D.

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Detailed Solution

$\begin{array}{l} From principle of conservation of linear momentum : \\ {\vec{P}}_{initial} = {\vec{P}}_{final} \\ ∴ m (v_{0} \hat{i}) + m (- 3 v_{0} \hat{j}) + m (5 v_{0} \hat{k}) = 3 m \vec{v} \\ ∴ \vec{v} = \frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + 5 \hat{k}) \end{array}$

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