A body of mass M at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^-1 and 40 ms^-1 respectively. The velocity of the third piece will be :

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25 ms^-1

35 ms^-1

15 ms^-1

50 ms^-1

answer is B.

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Detailed Solution

Mass of pieces by $\frac{M}{4}, \frac{M}{4}, \frac{M}{2}$
conserving momentum
$\begin{aligned} {\vec{P}}_{1} + {\vec{P}}_{2} + {\vec{P}}_{3} = 0 \\ {\bar{P}}_{3} = - ({\bar{P}}_{1} + {\bar{P}}_{2}) \end{aligned}$
As ${\bar{P}}_{1} & {\bar{P}}_{2}$ are perpendicular
so $P_{3} = \sqrt{P_{1}^{2} + P_{2}^{2}}$
$P_{3} = (50) \frac{M}{4}$
& $P_{3} = \frac{M}{2} v$
so v = 25