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

Step-by-step solution

F = K R n ⇒ m V 2 r = K R n ⇒ V 2 ∝ K R n - 1 ⇒ V ∝ 1 R n - 1 2 ⇒ T = 2 π R V ∝ R V ⇒ T ∝ R 1 R n - 1 2 ⇒ T ∝ R n + 1 2