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A body moves in a circular orbit of radius $\mathrm{R}$ under the action of a central force. Potential due to the central force is given by $V(r)=\operatorname{kr}(k$ is a positive constant). period of revolution of the body is proportional to :
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The correct answer is:
$R^{1 / 2}$
$V(r)=k r$
$U(r)=m k r \quad \omega^{2}=\frac{k}{r}$
$\begin{aligned} F=-\frac{d u}{d r}=-m k \quad \omega=\sqrt{\frac{k}{r}} \\ & T=\frac{2 \pi \sqrt{r}}{\sqrt{k}} \end{aligned}$
$U(r)=m k r \quad \omega^{2}=\frac{k}{r}$
$\begin{aligned} F=-\frac{d u}{d r}=-m k \quad \omega=\sqrt{\frac{k}{r}} \\ & T=\frac{2 \pi \sqrt{r}}{\sqrt{k}} \end{aligned}$
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