Option (b) – Same parabolic path
The internal forces do not affect the trajectory of the centre of mass, and the forces due to explosion are the internal forces. So the centre of mass will follow the same parabolic path even after the explosion.
The concept of centre of mass (COM) is useful in analysing the complicated motion of objects, particularly When two and more objects collide or an object explodes into fragments. When an explosive shell travelling in a parabolic path under the effect of gravity explodes, the centre of mass of the fragments will move along the original parabolic path.