Question

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 $30m{s}^{-1}$ and $40m{s}^{-1}$ respectively. The velocity of the third piece will be :

• A. $15m{s}^{-1}$
• B. $25m{s}^{-1}$
• C. $35m{s}^{-1}$
• D. $50m{s}^{-1}$

Answer 1

Answer: (B)

Mass of pieces by $\frac{M}{4},\frac{M}{4},\frac{M}{2}$
conserving momentum
${\overrightarrow{P}}_1+{\overrightarrow{P}}_2+{\overrightarrow{P}}_3=0$
${\overline{P}}_3=-\left({\overline{P}}_1+{\overline{P}}_2\right)$
As ${\overline{P}}_1\&{\overline{P}}_2$ 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 $v=25$