The principle which lie in the problem is "conservation of momentum".Blasting and fragmentation is something in which no external force is needed. It occur due to some chemical reaction (not in all cases) going on inside the bomb. Since no external force is there, so net change in momentum for the bomb will be zero. so all fragments will move in such a way that their net momentum (Don't forget that momentum is a vector) should remain same.In this question, since bomb is at rest before explosion so even after explosion its center of mass must be at rest to conserve the momentum. 
Hope it help.

**Explanation:**

When a shell at rest explodes, it breaks into multiple fragments. Each fragment will have its own velocity and direction of motion. However, the total momentum of the system before and after the explosion must be conserved.

**Conservation of Momentum:**

The law of conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it. In other words, the total momentum before the explosion is equal to the total momentum after the explosion.

Mathematically, we can write this as:

**Total Initial Momentum = Total Final Momentum**

Since the shell is at rest initially, its momentum is zero. Therefore, the total initial momentum is zero.

After the explosion, the fragments will have individual momenta. However, the sum of their momenta will still be zero in order to conserve momentum.

**Center of Mass:**

The center of mass of a system is the point at which the system's total mass can be considered to be concentrated. It is the point at which the system's motion can be analyzed as if all the mass was concentrated at that point.

The center of mass of a system does not change its position if no external forces are acting on the system. This is known as the law of conservation of center of mass.

**Analysis:**

In the case of the exploding shell, the fragments will move in different directions with different velocities. However, the center of mass of the system will remain at rest. This is because the individual momenta of the fragments will cancel each other out, resulting in a total momentum of zero for the system.

Since the center of mass remains at rest, it does not move along any path. It stays at the same position before and after the explosion.

Therefore, the correct answer is option 'A': the center of mass of the fragments remains at rest.