When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid air, the centre of mass of the fragments will move.

Options

A. vertically downwards
B. along the original parabolic path
C. vertically upwards and then vertically downwards
D. horizontally followed by parabolic path

Explanation

To solve the problem of the explosive shell traveling in a parabolic path and exploding in mid-air, we need to analyze the motion of the center of mass of the fragments after the explosion. Here’s a step-by-step breakdown of the reasoning:

### Step 1: Understand the Motion of the Shell
The shell is initially moving along a parabolic trajectory under the influence of gravity. This means that it has both horizontal and vertical components of motion.

**Hint:** Remember that the path of a projectile under gravity is parabolic.

### Step 2: Identify Forces Acting on the Shell
When the shell explodes, the explosion generates internal forces among the fragments. However, there are no external forces acting on the system apart from gravity, which is constant and acts downwards.

**Hint:** Internal forces do not affect the overall motion of the center of mass.

### Step 3: Apply the Principle of Conservation of Momentum
Since there are no external forces acting on the system in the horizontal direction, the horizontal momentum of the system is conserved. The center of mass of the system (the shell and its fragments) will continue to move in the same manner as before the explosion.

**Hint:** The center of mass moves in a straight line unless acted upon by an external force.

### Step 4: Analyze the Effect of Gravity
Gravity is the only external force acting on the shell, and it continues to act even after the explosion. Therefore, the vertical motion of the center of mass will still be influenced by gravity, causing it to follow a downward path.

**Hint:** Gravity affects the vertical motion of the center of mass, but not the horizontal motion due to the explosion.

### Step 5: Conclusion on the Path of the Center of Mass
Since the center of mass of the fragments is not affected by the internal forces of the explosion and is only influenced by gravity, it will continue to follow the same parabolic path it was on before the explosion.

**Final Answer:** The center of mass of the fragments will move along the original parabolic path.