Uniform Circular Motion and Power – Rankers Physics

Uniform Circular Motion: Practice Problem & Solution

Assertion (A): In uniform circular motion of a particle, sum of power delivered to it by all the forces acting on the particle is zero. Reason (R): In uniform circular motion dot product of two perpendicular vectors, force and velocity is always zero.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Uniform Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

In UCM, net force is perpendicular to velocity, so power \(P = \vec{F} \cdot \vec{v} = Fv \cos{90^{\circ}}\) is zero. Thus, (A) is true. Reason (R) correctly states that the dot product of perpendicular vectors is zero, which explains (A).

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