Question

Assertion (A): If a body moving in a circular path has constant speed, then there is no force acting on it.
Reason (R): The direction of the velocity vector of a body moving in a circular path is changing.

• A. both A and R are true and R is the correct explanation of A
• B. both A and R ane true but R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

Answer: (D)

We know that if a body moves with constant speed on a circular path, it is a uniform circular motion, an acceleration along radius towards centre and has magnitude. $ a={{a}_{r}}=\frac{{{v}^{2}}}{r}=r{{\omega }^{2}} $ This is called central acceleration. So, speed and magnitude of acceleration are constant but their direction are always changing to provide centripetal acceleration by Newtons second law of force, $ F=ma=\frac{m{{v}^{2}}}{r}=mr{{\omega }^{2}} $ This force is called centripetal force and is of constant magnitude but changing direction. Hence assertion is wrong and reason which is, that the direction of velocity vector of a body moving in a circular path is changing is true.