Question

A body of mass $\left(4m\right)$ is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(m\right)$ move perpendicular to each other with equal speeds $\left(v\right)$. The total kinetic energy generated due to explosion is

• A. $\frac{3}{2}m{v}^2$
• B. $2m{v}^2$
• C. $4m{v}^2$
• D. $m{v}^2$

Answer 1

The correct option is A $\frac{3}{2}m{v}^2$

Let the direction of motion and velocity of particles after a collision are as shown,

Total momentum before explosion $=0$
Total momentum after explosion $=\sqrt{2}mv-2m{v}_1$

By conservation of linear momentum
$\sqrt{2}mv-2m{v}_1=0$
$2m{v}_1=\sqrt{2}mv\Rightarrow v_1=\frac{v}{\sqrt{2}}$

Total KE generated $=2\times \frac{1}{2}m{v}^2+\frac{1}{2}\left(2m\right)v_1^2$
$=m{v}^2+\frac{m{v}^2}{2}=\frac{3}{2}m{v}^2$

Hence, option $\left(\text{B}\right)$ is correct.