Question

A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant:
A. Acceleration
B. Velocity
C. Momentum
D. Kinetic energy

Answer 1

Hint:As the body has uniform angular velocity which means that the body is moving in uniform circular motion i.e. it will have constant speed.

Complete step by step solution:
In uniform circular motion speed of the body is constant but velocity changes continuously therefore velocity is not constant and hence option (B) is not correct. Also by the formula:
\[\overset{\to }{\mathop{P}}\,=m\overset{\to }{\mathop{v}}\,\]
Momentum is directly proportional to velocity therefore it is also not constant and hence option (C) is also not correct.

As centripetal force continuously acts on the body that is why it is moving in circular motion so if force is present then acceleration must be present and hence option (A) is also not correct. Also, there is one more reason for option (A) to be incorrect is that velocity is not constant which clearly means some acceleration must be present which is responsible for changing direction of velocity. Acceleration here is present in the form of centripetal acceleration. Kinetic energy depends on speed and not on velocity, so if speed is constant then kinetic energy is also constant.

Hence option D is the correct answer.

Note: Make it very clear that in uniform circular motion the body moves with constant speed and constant angular velocity but velocity changes at every point (direction of velocity is changed by centripetal acceleration).