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A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular direction with speed v each. The energy released during the process is:
Detailed Solution
Momentum conservation: $mv\hat{i}+mv\hat{j}+3m\vec{v}'=0 \Rightarrow |\vec{v}'|=\frac{\sqrt{2}v}{3}$. Energy released $=\frac{1}{2}mv^2+\frac{1}{2}mv^2+\frac{1}{2}(3m)\frac{2v^2}{9}=\frac{4}{3}mv^2$.