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 each speed v. The energy released during the process is

Step-by-step solution

The particle of mass 5 ~m breaks in three fragments of mass m, m and 3 ~m respectively. Two fragments of mass meach, move in perpendicular direction 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, aligned 5 ~m 0 & = mv i + mv j +3 mv ^ v ^ & =- v 3 i - v 3 j | v ^ | & = (- v 3 )^2+ (- v 3 )^2 = v 2 3 aligned Energy released aligned E & = 1 2 m v^2+ 1 2 m v^2+ 1 2 3 ~m ( v 2 3 )^2 & =