If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions then the centre of mass
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When a bomb explodes in a parabolic path, different fragment goes in different path with different trajectories, but COM continues to travel in the same parabolic path because force generated during explosions is internal force and an internal force cannot change path of COM.
Path of COM can only be decided with the help of external force only(in this case gravity) therefore parabolic path.
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