D

Step 1: Understand the concept of the centre of mass (COM). The centre of mass of a system of particles is the point where the total mass of the system may be considered to be concentrated for the purposes of analyzing translational motion.
Step 2: When the bomb explodes, the individual fragments that make up the bomb will move in various directions due to the explosion. However, the total momentum of the system (the bomb before the explosion) must be conserved.
Step 3: According to the principle of conservation of momentum, the centre of mass of the fragments will continue to move in the same path it was following before the explosion, provided no external forces act on it other than gravity.
Step 4: Since gravity acts on all fragments equally and there are no other forces acting on the system's horizontal motion, the centre of mass will continue to follow the original parabolic trajectory of the bomb as if it had not exploded.
Conclusion: Therefore, the correct answer is option D: the centre of mass of the fragments will move in the parabolic path which the unexploded bomb would have travelled.