Physics - Gravitation Question with Solution | TestHub

Gravitational force provides the necessary centripetal force required by the given planet for circular motion. So

$\frac{{\text{mv}}^2}{\text{r}}\propto {\text{r}}^{-5/2}$

$\Rightarrow \frac{{\text{mv}}^2}{\text{r}}={\text{kr}}^{-5/2}$,$\mathrm{k}$= constant

$\therefore \text{v}=\sqrt{\frac{{\text{kr}}^{-3/2}}{\text{m}}}$

$\text{T}=\frac{2\pi \text{r}}{\text{v}}=2\pi \text{r}\times \frac{\sqrt{\text{m}}}{\sqrt{\text{k}{\text{r}}^{-3/2}}}$

i.e.,$\text{T}\propto {\text{r}}^{7/4}$.