question_answer

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the \[{{\text{n}}^{\text{th}}}\] power of R. If the period of rotation of the particle is T, then: [JEE Main Online 08-04-2018]

A)  \[\text{T}\propto {{\text{R}}^{(n+1)/2}}\]

B)                   \[\text{T}\propto {{\text{R}}^{n/2}}\] C)  \[\text{T}\propto {{\text{R}}^{3/2}}\] for any \[n\] D)       \[T\propto {{R}^{\frac{n}{2}+1}}\] Correct Answer: A Solution : [a] For circular motion