A body falling vertically downward under gravity breaks in two parts under gravity.The centre of mass of two are taken together:
A. shift horizontally towards heavier piece
B. shifts horizontally towards lighter piece
C. Doesn’t shift horizontally
D. shift horizontally if initial speed is zero

Hint:To answer this question, we must first understand the concept of the centre of mass. Any motion of a body in which gravity is the only force acting on it is defined as free fall in Newtonian physics. In general relativity, gravity is reduced to a space-time curvature, so a body in free fall has no force acting on it.

Complete answer:
A point at which the entire mass of a body or all the masses of a system of particles appeared to be concentrated is known as the centre of mass of a body or system of particles.The centre of mass of the system of particles is this location.

For the above given question ,Since the velocity is in the downward direction, the centre of mass would also move in that direction and no force acts in the horizontal direction.Centre of mass cannot shift horizontally because the horizontal portion of force is zero.

So, the correct answer is option C.

Note:Only when external forces act on the system does the system's centre of mass accelerate. If the particles that make up the structure are only subjected to internal forces, the centre of mass does not accelerate and its velocity remains constant. The system's cumulative linear momentum is conserved.