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 directions each with speed v. The energy released during the process is [NEET (Odisha) 2019]

The particle of mass 5m breaks into three fragments of masses m, m and 3m, respectively. Two fragments of mass m each move in perpendicular directions with velocity v and the left fragment will move in a direction with velocity v' such that the total momentum of the system must remain conserved.By law of conservation of momentum,                    5m×0=mvi^+mvj^+3mv'⇒                           v'=-v3i^-v3j^∴                  v'=-v32+-v32=v23∴  Energy released,                       E=12mv2+12mv2+12×3mv232                         =mv2+mv23=43mv2