A) \[{{r}^{1/2}}\]
B) r
C) \[{{r}^{3/2}}\]
D) \[{{r}^{2/3}}\]
Correct Answer: B
Solution :
Central attractive force \[F=-\frac{k}{r}\] \[mr{{\omega }^{2}}=-\frac{k}{r}\] \[mr\,{{\left( \frac{2\pi }{T} \right)}^{2}}=-\frac{k}{T}\] \[\frac{mr4{{\pi }^{2}}}{{{T}^{2}}}=-\frac{k}{T}\] \[{{T}^{2}}=\frac{m{{r}^{2}}4{{\pi }^{2}}}{k}\] \[{{T}^{2}}\propto {{r}^{2}}\] or \[T\propto r\]
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