Question

A particle of mass $3m$ is projected from point-A with speed $3v_0$ as shown in figure. When the particle is at point P, it explodes into three identical pieces. The direction of motion of two pieces are as shown.
Choose the incorrect statement regarding the physical quantities just before and just after the explosion.

• A. The linear momentum of the system can be conserved just before and just after explosion.
• B. The centre of mass of the system will trace the same path as it will follow without the explosion.
• C. The mechanical energy of the system remains conserved just before and just after explosion.
• D. The impulse given by the weight of particle during explosion is negligible as compared to that given by the explosive forces.

Answer 1

The correct option is C The mechanical energy of the system remains conserved just before and just after explosion.

In any explosion, linear momentum is conserved as there is no external force acting on the exploding body. As a result, the centre of mass will trace the same path as it will follow without the explosion.

Also, during the collision, the impulse due to weight can be neglected as the time period of explosion is very small and gravity is a finite force, hence $F\Delta t\to 0$

Mechanical energy is not conserved in the explosion because in the explosion, energy is released.

Therefore, only option (c) is incorrect.