A body A of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3M$ and a body C of mass $2/3M$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards:

The explosion or breaking of the body is caused by internal forces. Internal forces do not change the motion of the centre of mass of a system.As long as no external horizontal force acts on the system, the horizontal position of the centre of mass remains unchanged. Since the body was falling vertically, its centre of mass continues to follow the original vertical path of body A.