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:

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 t h power of R. If the period of rotation of the particle is T, then:, T ∝ R n / 2, T ∝ R 3 / 2 for any n, T ∝ R n 2 + 1, T ∝ R n + 1 2

MARKS App · Accepted Answer

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

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