Question:
A particle of mass $m$ moves in a circular orbit under the central potential
field, $U(r)=\frac{-C}{r}$, where $C$ is a positive constant. The correct radius -
velocity graph of the particle's motion is :
Correct Option: 1
Solution:
(1)
$\mathrm{U}=-\frac{\mathrm{C}}{\mathrm{r}}$
$\mathrm{F}=-\frac{\mathrm{dU}}{\mathrm{dr}}=-\frac{\mathrm{C}}{\mathrm{r}^{2}}$
$|\mathrm{F}|=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$
$\frac{\mathrm{C}}{\mathrm{r}^{2}}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$
$\mathrm{v}^{2} \propto \frac{1}{\mathrm{r}}$
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