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 the planet and the star is proportional to $R^{\frac{-5}{2}}$, and $T^2$ is proportional to

• A. $R^3$
• B. $R^{\frac{7}{2}}$
• C. $R^{\frac{3}{2}}$
• D. $R^{\frac{9}{2}}$

Answer 1

The correct option is B

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

Centripetal force $\propto R^{\frac{-5}{2}}$

or $mR{\omega }^2\propto R^{\frac{-5}{2}}$

or ${\omega }^2\propto R^{\frac{-5}{2-1}}$

or $\omega \propto R^{\frac{-7}{2}}$

or ${\left(\frac{2\pi }{T}\right)}^2\propto R^{\frac{-7}{2}}$

or $T^2\propto R^{\frac{7}{2}}$