During uniform circular motion ,which of the following relationships is necessarily true?

Explanation

In uniform circular motion, the object moves in a circle at a constant speed. The centripetal force, which is required to keep the object moving in a circular path, acts towards the center of the circle and is perpendicular to the object's velocity. Since work is defined as the force along the direction of motion times the distance traveled, no work is done by the centripetal force because it does not contribute to the displacement in the direction of the force. Therefore, Option A is correct. Option B is incorrect because the centripetal force does not do work. Option C is incorrect because velocity does not perform work. Option D is incorrect as potential energy in a vertical circle would depend on height, not horizontal position, but this is irrelevant to the work done by the centripetal force.