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Q.

A bomb of mass in at rest explodes into three pieces, two of which of mass $\frac{M}{4}$ each are thrown off in perpendicular directions with velocities $3 m s^{- 1}$ and $4 m s^{- 1}$ . What is the velocity of the third piece after the explosion?

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a

$2 {ms}^{- 1}$

b

$1.5 {ms}^{- 1}$

c

$3 {ms}^{- 1}$

d

$2.5 {ms}^{- 1}$

answer is C.

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Detailed Solution

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$\begin{array}{l} P_{1} = \frac{M}{4} \times 3, P_{2} = \frac{M}{4} \times 4 = M \\ P_{3} = \sqrt{{P_{1}}^{2} + {P_{2}}^{2}} \Rightarrow \frac{M}{2} V_{3} = \sqrt{\frac{9}{16} M^{2} + M^{2}} = \frac{5}{4} M \\ V_{3} = \frac{5}{4} \frac{M}{\frac{M}{2}} = \frac{10}{4} = 2.5 m s^{- 1} \end{array}$

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