Question

A body of mass explodes at rest break up into three parts. If two parts having equal masses fly off perpendicularly to each other with a velocity of $18m/s$, then calculate the velocity of the third part which has a mass $3$ times the mass of each part.

Answer 1

Initially the body is at rest. Initially linear momentum of the body is zero. Let due to explosion the body break up into three parts. There is no external force acting on the body. hence, linear momentum just after collision also be zero.

Let total mass of the body by $5m$, hence the masses of the broken parts will be $m$, $m$ and $3m$ respectively.

Linear momentum just after explosion

${\overline{P}}_{final}={\overrightarrow{P}}_1+{\overrightarrow{P}}_2+{\overrightarrow{P}}_3=m{\nu }_1\hat{j}+{\overline{P}}_3$

A ${\overline{P}}_{initial}={\overrightarrow{P}}_{final}⟹l{\overline{P}}_{3}i=\sqrt{2}m{\nu }_1⟹3m\nu =\sqrt{2}m{\nu }_1$

$\nu =\frac{\sqrt{2}{\nu }_1}{3}=\frac{\sqrt{2}\times 18}{3}=6\sqrt{2}m{s}^{-1}$

$⟹6\sqrt{2}m{s}^{-1}$ at an angle ${135}^o$ from the either ball.

Note: During explosion there will not be any change in gravitational potential energy of the body. But kinetic energy of the broken parts of the body will increase due to internal provided during explosion. This increase in kinetic energy will be equal to energy released during explosion.