A light rope passes over a light frictionless pulley attached to the ceiling. An

Question

A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest, the heavier object moves downward, and the lighter object moves upward with an acceleration of the same magnitude. Which of the following statements is true for the system consisting of the two objects?

a. The center of mass remains at rest.

b. The velocity of the center of mass is a constant.

c. The acceleration of the center of mass is g, downward.

d. Choices a, b, and c are all false.

Explanation / Answer

As the whole system is moving under effect of gravity, the center of mass cannot be at rest.

Both the masses are of different mass, so there will be unbalanced force which will result in accelaration of bodies.So, velocity of COM cannot be constant.

The masses are not freeing moving under gravity. Pulley will exert upward force with the help of string. So, accelaration of masses will be less than g.

SO, a, b, c are false.

Correct option : d

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