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A shell following a parabolic path explo...

A shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragements will move in

A

Vertical direction

B

Any direction

C

Horizontal direction

D

Same parabolic path

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The correct Answer is:
To solve the question regarding the motion of the center of mass of fragments after a shell explodes while following a parabolic path, we can break down the solution into clear steps: ### Step-by-Step Solution: 1. **Understanding the Initial Motion**: - A shell is fired at an initial speed \( u \) at an angle \( \theta \) to the horizontal. This creates a parabolic trajectory due to the influence of gravity. 2. **Explosion of the Shell**: - At some point during its flight, the shell explodes into two fragments with masses \( M_1 \) and \( M_2 \). The total mass before the explosion was \( M = M_1 + M_2 \). 3. **Analyzing Forces on the System**: - Before the explosion, the only force acting on the shell is gravity, which acts downward. After the explosion, if we consider the system of the two fragments, there are no external horizontal forces acting on them. 4. **Conservation of Momentum**: - Since no external forces are acting on the system, the momentum of the center of mass of the system must be conserved. This means that the center of mass of the fragments will continue to move as if the explosion had not occurred. 5. **Center of Mass Motion**: - The center of mass of the system will continue to follow the same parabolic path that the shell was on before the explosion. This is because the explosion does not impart any net external force to the system. 6. **Conclusion**: - Therefore, the center of mass of the fragments will continue to move in the same parabolic path as the shell would have if it had not exploded. It will land at the same point it would have if the explosion had not taken place. ### Final Answer: The center of mass of the fragments will move in the same parabolic path. ---
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