A body of mass (4m) 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 (v), The total kinetic energy generated due to explosion is : 

\(\frac{3}{2}\)mv²

p_i = 0 ; p_f = \(\sqrt{2}mv + 2 mv'\)

By conservation of liner momentum

\(\sqrt{2}mv + 2 mv'\) = 0

⇒ v' = -\(\frac{v}{\sqrt{2}}\)

\(KE = 2 \text{ x } \frac{1}{2} mv^2 + \frac{1}{2}(2m) \frac{v}{\sqrt{2}}^2 \)

\(KE = \frac{3}{2} mv^2\)