Question

A body of mass $8m$ is kept in $X-Y$ plane at rest. If it suddenly explodes into three pieces with two of them moving perpendicular to each other at equal speeds, the kinetic energy generated during explosion is (refer figure)

• A. $\frac{m{v}^2}{2}$
• B. $m{v}^2$
• C. $\frac{5m{v}^2}{6}$
• D. $\frac{7m{v}^2}{6}$

Answer 1

The correct option is D $\frac{7m{v}^2}{6}$


Conservation of linear momentum gives us,
$\sqrt{(mv{)}^2+(mv{)}^2}=6m{v}^{\prime }\Rightarrow 6m{v}^{\prime }=\sqrt{2}\left(mv\right)\Rightarrow v^{\prime }=\frac{\sqrt{2}v}{6}$
$\Rightarrow$ Kinetic energy generated during explosion is,
$(K.E{)}_{net}=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2+\frac{1}{2}(6m\left)\right(v^{\prime }{)}^2=m{v}^2+3m\left[\frac{2v^2}{36}\right]=m{v}^2+\frac{m{v}^2}{6}=\frac{7m{v}^2}{6}$