Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to $R^{-\frac{5}{2}}$, then $T^2$ is proportional to

• A. $R^3$
• B. $R^{7/2}$
• C. $R^{5/2}$
• D. $R^{3/2}$

Answer 1

The correct option is B $R^{7/2}$

For revolution of planet centripetal force is provided by gravitational force of attraction
$m{\omega }^{2}R\propto R^{-5/2}$

$\frac{1}{T^2}\propto R^{-7/2}$
$\Rightarrow T^2\propto R^{7/2}$