A projectile of total mass 3m is moving horizontally with speed 20 m/s at its highest point. It suddenly explodes into two fragments of masses m and 2m. Immediately after the explosion, the fragment of mass m comes to rest. If the speed of the 2m fragment is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
JEE Mains NEET JEE Advanced

Question

A projectile of total mass 3m is moving horizontally with speed 20 m/s at its highest point. It suddenly explodes into two fragments of masses m and 2m. Immediately after the explosion, the fragment of mass m comes to rest. If the speed of the 2m fragment is N m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

During the very short explosion interval, the external impulse due to gravity is negligible, so total linear momentum is conserved. Just before explosion, p(initial) = 3m×20 = 60m in the horizontal direction. The fragment of mass m is at rest immediately after explosion, so its momentum is zero. Therefore 2m×V = 60m. Hence V = 30 m/s and N = 30.