A fire cracker following a parabolic path explodes in mid air. The centre of mass of all the fragments will follow a path

Options

A. along horizontal
B. along vertical
C. along same parabola
D. along circulae

Answer

To solve the question regarding the path followed by the center of mass of a firecracker that explodes mid-air while following a parabolic trajectory, we can break down the solution into the following steps:

### Step-by-Step Solution:

1. **Understanding the Initial Motion**:
- The firecracker is initially moving along a parabolic path due to the influence of gravity. This path is defined by the projectile motion equations, where the horizontal motion is uniform and the vertical motion is uniformly accelerated due to gravity.

**Hint**: Recall the equations of motion for projectile motion to understand the parabolic path.

2. **Explosion of the Firecracker**:
- When the firecracker explodes, it breaks into several fragments. However, the explosion generates only internal forces among the fragments. These internal forces do not affect the overall motion of the center of mass of the system.

**Hint**: Consider the principle of conservation of momentum and how internal forces operate within a system.

3. **Center of Mass Motion**:
- The center of mass of the firecracker and its fragments continues to move in the same manner as it was before the explosion. This is because the external forces acting on the system (in this case, gravity) remain unchanged. The center of mass will maintain its velocity and trajectory.

**Hint**: Remember that the center of mass moves as if all mass were concentrated at that point and is influenced only by external forces.

4. **Effect of Gravity**:
- The only external force acting on the system is the gravitational force (mg) acting downwards. This force causes the center of mass to continue accelerating downwards, maintaining the parabolic trajectory.

**Hint**: Think about how gravity affects the vertical motion of the center of mass.

5. **Conclusion**:
- Since there are no external forces acting in the horizontal direction and the vertical motion is still influenced by gravity, the center of mass will continue to follow a parabolic path even after the explosion. Therefore, the path of the center of mass remains parabolic.

**Hint**: Visualize the trajectory of the center of mass and how it relates to the motion of the individual fragments.

### Final Answer:
The center of mass of all the fragments will follow a parabolic path.