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. $R^{\frac{7}{2}}$
• C. $R^{\frac{5}{2}}$
• D. $R^{\frac{3}{2}}$

Answer 1

The correct option is B

$R^{\frac{7}{2}}$

For revolution of planet centripetal force is provided by gravitational force of attraction
$m{\omega }^{2}R\propto R^{\frac{-5}{2}}\Rightarrow \frac{1}{T^2}\propto R^{\frac{-7}{2}}\Rightarrow T^2\propto R^{\frac{7}{2}}$