When a shell was following a parabolic path in the air, it explodes somewhere in its flight. The centre of mass of fragments will continue to move ina)any directionb)horizontal directionc)same parabolic pathd)vertical directionCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

The ball will continue moving in same parabolic path

Answer

Exploding of shell is due to internal forces and the center of mass of an object changes due to action of any external force. So as here no external force is applied thus center of mass will not change and hence continues to follow the same parabolic path which it was following earlier.

Answer

Why the Centre of Mass of Fragments Continues to Move in the Same Parabolic Path?

Introduction:

When a shell follows a parabolic path in the air and explodes, it breaks into several fragments. These fragments will have their own individual velocities and directions of motion. However, the center of mass of the fragments will continue to move in a specific manner.

Explanation:

When an explosive shell is in motion, it possesses both translational and rotational kinetic energy. The explosion disrupts the shell's motion, causing it to break into multiple fragments. Each fragment now becomes an individual projectile moving under the influence of gravity.

Conservation of Linear Momentum:

The linear momentum of the system before and after the explosion remains conserved. This means that the total momentum of all the fragments combined is equal to the initial momentum of the shell. Since linear momentum is a vector quantity, it has both magnitude and direction.

Conservation of Angular Momentum:

The angular momentum of the system is also conserved. The shell's explosion does not exert any external torque on the fragments, so their total angular momentum remains constant. This implies that the fragments will continue to move in the same plane as the original shell's motion.

Center of Mass Motion:

The center of mass of a system of particles moves as if all the mass of the system is concentrated at that point. Since the fragments have different masses and velocities, the center of mass will be closer to the heavier fragments and move along a parabolic path.

Conclusion:

When a shell explodes while following a parabolic path, the center of mass of the fragments will continue to move in the same parabolic path. This is because the linear momentum and angular momentum of the fragments are conserved. The center of mass behaves as if all the mass of the system is concentrated at that point.

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