A box kept in a closed box moves in the box making collisions with the walls. The box is kept on the smooth surface. The velocity of the centre of the mass:
A) of the box remains constant.
B) of the (box+ball) system remains constant.
C) of the ball remains constant.
D) of the ball relative to the box remains constant.

Hint: Newton’s Second law says that the rate of change of velocity with respect to time is known as force which is equal to net external force acting on the body. Newton's second law gives us acceleration for anybody.

Formula used:
 The acceleration of the body is given by $a = \dfrac{F}{m}$, where a is the acceleration F is the force and m is the mass of the body.

Complete step by step solution:
It is given that the box contains a moving ball in it and we need to tell if the centre of the mass of the box, ball or system is constant. As we can observe that in the problem it is given that the ball is moving inside a box kept on the surface but here the external force on the whole system is zero as there is no force mentioned in problem which is acting on the system i.e. (Box+Ball). So as the net external force on the system is zero which means that the net acceleration of the system is also zero. The acceleration is change in velocity with respect to time that means there is no change in velocity. Therefore the centre of mass of the box+ball i.e. the centre of mass of the system does not change.

Hence, The correct answer for this problem is option B.

Note: Newton's second law gives us force on the body but it should be remembered that the external force on the body will be equal to the force produced on the body. The acceleration of the whole system depends upon the net external force on the system.