Question

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n^th power of R. If the period of rotation of the particle is T, then:

(A) T ∝ R^(n+1)/2

(B) T ∝ R^n/2

(C) T ∝ R^3/2 for any n

(D) T ∝ R\(\frac{n}{2}+1\)

Answer 1

(A) T ∝ R^(n+1)/2

The centripetal force acting on the particle is provided by the central force,