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

Answer 1

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

Let direction of motion and velocity if particles after collision be 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 $=2\times \frac{1}{2}m{v}^2+\frac{1}{2}\left(2m\right)v_1^2$
$=m{v}^2+\frac{m{v}^2}{2}=\frac{3}{2}m{v}^2$