A bomb traveling in a parabolic path under the effect of gravity, explodes in mid air. The center of mass of fragments will :

Options

A. Move vertically upwards and then downwards
B. Move vertically downwards
C. Move in irregular path
D. Move in the parabolic path which the unexploded bomb would have travelled.

Answer

To solve the problem regarding the trajectory of the center of mass of a bomb that explodes in mid-air while traveling in a parabolic path under the influence of gravity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion of the Bomb**:
- The bomb is initially projected and travels along a parabolic path due to the influence of gravity. This motion is described as projectile motion.

2. **Explosion of the Bomb**:
- At some point in its trajectory, the bomb explodes into fragments. This explosion is an internal event.

3. **Identifying Forces Acting on the Bomb**:
- Before the explosion, the only external force acting on the bomb is its weight (mg), where m is the mass of the bomb and g is the acceleration due to gravity.
- After the explosion, the fragments experience internal forces due to the explosion, but no external forces are acting on the system as a whole.

4. **Center of Mass Concept**:
- The center of mass of a system of particles (or fragments, in this case) moves according to the net external force acting on the system.
- Since there are no external forces acting on the bomb (other than gravity, which acts uniformly on all fragments), the center of mass of the fragments will continue to follow the same trajectory.

5. **Conclusion**:
- Therefore, the center of mass of the fragments will continue to move along the same parabolic path that the bomb was following before the explosion.

### Final Answer:
The center of mass of the fragments will continue to follow the same parabolic path.

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