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 inversely proportional to $R^{5/2}$ then the time period of revolution is proportional to $R^{k/4}$ . Find the value of k.

• A. 5
• B. 3
• C. 7
• D. 9

Answer 1

Answer: (C)

7

$\frac{{mv}^2}{R}=\frac{GMm}{R^{5/2}}$

${R\omega }^2=\frac{GM}{R^{5/2}}$

$\omega =\sqrt{\frac{GM}{R^{7/2}}}$..........(i)

$T=\frac{2\pi }{\omega }$..........(ii)

from (i) and (ii)

$T\propto R^{7/4}$