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 :
For circular motion \[\frac{m{{v}^{2}}}{R}=\frac{c}{{{R}^{n}}}\] \[\therefore v=\sqrt{\frac{c}{m{{R}^{n-1}}}}\] \[\therefore Time\,\,period\,\,T=\left( \frac{2\pi R}{v} \right)\] \[T\propto {{R}^{\left( \frac{n+1}{2} \right)}}\]
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