Question

When a body moves with constant speed in a circular path which of the following is true?
A. Work done is zero
B. Acceleration is zero
C. Force acting on the body is zero
D. Its velocity remains constant.

Answer 1

When a body moves with constant speed in a circular path, the motion of body is said to be uniform circular motion. Force acting on the body in circular motion is centripetal force which results in centripetal acceleration. Work done can be calculated by determining the dot product of force and displacement vectors of the body.

Complete step by step answer:
Although speed of the body is constant, in circular motion, the direction of motion of the particle changes constantly, which means velocity of the particle is not constant. Since, the velocity of a particle changes continuously, acceleration of the particle is non-zero. The force responsible for the change in the direction is known as centripetal force which always acts perpendicular to the velocity of the particle. Centripetal force must be non-zero in order to produce acceleration.
Work done by any force acting on any object is given by dot product of force and displacement of the object. Centripetal force and displacement vector in uniform circular motion are perpendicular to each other. Dot product of perpendicular vectors is always zero. Therefore, work done by the centripetal force in uniform circular motion, which is the dot product of centripetal force and displacement of the particle, is zero.

Hence, option A is correct.

Note:
Work done by centripetal force in uniform circular motion is always zero. Centripetal force in uniform circular motion always acts perpendicular to the direction of motion of the particle and is directed towards the centre of the circle. Uniform circular motion is the particular kind of circular motion in which a particle moves with constant speed.