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

Question

Aicharya · Accepted Answer

The total momentum of the system will be conserved before and after explosion.

Then, $p_{i} = p_{f}$
$O = m v \hat{i} + m v \hat{j} + 2 m \vec{v}$
$\vec{v} = - \frac{v}{2} \hat{i} - \frac{v}{2} \hat{j}$
$|\vec{v}| = \frac{v}{\sqrt{2}}$
Total kinetic energy generated due to explosion is $K E = \frac{v}{2} m v^{2} + \frac{v}{2} m v^{2} + \frac{v}{2} 2 m {(\frac{v}{\sqrt{2}})}^{2} = m v^{2} + \frac{m v^{2}}{2} = \frac{3}{2} m v^{2}$

A body of mass 4 m is lying in x - y plane at rest. It suddenly explodes into three pieces. Two pieces, each…

Solution