Question

A satellite is revolving around a planet in a circular orbit of radius r. If the gravitational force between the planet and satellite is inversely proportional to r, then orbital speed of satellite is proportional to
(1)r ^1/2
(2)r ^-1/2
(3)r^–1
(4) r⁰

Answer 1

$$\begin{gathered} \mathrm{Centripetal}\mathrm{force}=\frac{{\mathrm{mv}}^2}{\mathrm{r}} \\ \mathrm{Gravitational}\mathrm{force}\mathrm{\alpha }\frac{1}{\mathrm{r}} \\ \mathrm{Hence}, \\ \frac{{\mathrm{mv}}^2}{\mathrm{r}}\mathrm{\alpha }\frac{1}{\mathrm{r}} \\ {\mathrm{mv}}^2\mathrm{\alpha }1 \\ {\mathrm{mv}}^2\mathrm{\alpha }{\mathrm{r}}^{\mathrm{o}} \\ \mathrm{v}\mathrm{\alpha }{\mathrm{r}}^{\mathrm{o}} \\ \mathrm{Ans}:\mathrm{option}-4 \end{gathered}$$