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A particle of mass 5 m 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

1. 4/3 mv²
2. 3/5 mv²
3. 5/3 mv²
4. 2/3 mv²

Correct answer: 5/3 mv²

Solution

The initial momentum of the system is zero since the particle is at rest. After the break, the two fragments of mass m each move perpendicularly with speed v, so their momenta are m*v and are perpendicular. The third fragment must balance the momentum to conserve it. Using energy conservation, the total kinetic energy of the fragments is calculated as 5/3 mv².

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