A body A of mass M while falling vertically downwards under gravity breaks into two parts, a body B of mass \[\dfrac{1}{3}M\] and a body C of mass \[\dfrac{2}{3}M\]. Then, what happens to the centre of mass of bodies B and C that have taken together shifts compared to that of body A?
A. Depends on height of the breaking
B. Does not shift
C. Body C
D. Body B

Hint: Before we start addressing the problem, we need to know about gravity and the centre of mass. Gravity is defined as the force between an object and the earth’s surface. Centre of one in which the whole mass of the body is concentrated at the centre and it depends on mass and distance from the centre to any point in the body.

Complete step by step solution:
The forces responsible for the breaking of the body A into two parts are internal forces, and in horizontal direction that is \[{F_{ext}} = 0\] on the mass M. So gravity is the only force acting on system A in a vertically downwards direction both before and after the breaking.

Therefore, the centre of mass will continue moving vertically downward with the acceleration g and there will not be any relative shift of the centre of mass of the system towards B or C.

Hence, option B is the correct answer.

Note:Don’t get confused with the centre of mass and centre of gravity. The Centre of mass is the point at which the distribution of mass of a body is equal in all directions and does not depend on the gravitational field. But the centre of gravity is the point at which the distribution of the weight of a body is equal in all directions and it is also not dependent on the gravitational field.