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Q.

The object at rest suddenly explodes into three parts with the mass ratio 2:1:1. The parts of equal masses move at right angles to each other with equal speed V. Then the speed of the third part just after explosion will be ___

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a

V

b

$\sqrt{2} V$

c

$\frac{V}{2}$

d

$\frac{V}{\sqrt{2}}$

answer is D.

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Detailed Solution

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Let $m_{1} = 2 m, m_{2} = m, m_{3} = m$ By conservation of linear momentum___
$\begin{array}{l} O = \vec{P_{1}} + \vec{P_{2}} + \vec{P_{3}} \\ ∴ \vec{P_{1}} = - (\vec{P_{2}} + \vec{P_{3}}) \\ P_{1} = \sqrt{P_{2}^{2} + P_{3}^{2} + P_{2} P_{3} \cos 90^{\circ}} \\ (2 m) V_{1} = m \sqrt{V^{2} + V^{2}} \\ V_{1} = \frac{V}{\sqrt{2}} \end{array}$

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