NEETPhysicsWork, Power and Energy
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The instantaneous power delivered by the centripetal force to a particle in uniform circular motion is always zero. Reason (R): The magnitude of centripetal force acting on a particle of mass m moving with speed v in a circle of radius r is mv^2 r . In the light of the above statements, choose the
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are 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
Correct answer
B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
Step-by-step solution
The instantaneous power is given by the dot product of force and velocity vectors: P = F v = Fv . In uniform circular motion, the centripetal force is directed radially inward towards the centre, while the velocity vector is tangential to the circular path. Thus, the angle between them is 90^ . Therefore, P = Fv 90^ = 0 . Hence, Assertion (A) is true. The magnitude of centripetal force is indeed given by the formula mv^2 r . Hence, Reason (R) is also true. However, the formula for the magnitude of the force does no