Two spheres, each of mass m and radius r are tied with a spring of spring constant k. The spring is stretched by a certain amount and the system is kept on a rough surface where friction is sufficient to prevent sliding. If one sphere is solid and the other is hollow, then for the spring-sphere system-
(A) Conservation of momentum is valid
(B) Conservation of energy is valid
(C) Displacement of centre of mass is not zero
(D) Velocity of centre of mass is zero
Multiple answers can be correct.
The Attempt at a Solution
Since this is a rough surface with no sliding, friction will not act on the system because there will be pure rolling. Since net external force is zero, I think (A), (B) should hold.
Since net ext. force is zero, acceleration of centre of mass is also zero. Since velocity of COM before the system was released from rest was zero, and acc. of COM is zero, (D) should hold. And if velocity of COM is zero, (C) should also be true. But my answer is incorrect.