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 $R^{\frac{-5}{2}}$ then:

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{M{v}^2}{R}\propto R^{\frac{-5}{2}}$ $\therefore v\propto R^{\frac{-3}{4}}$

Now, $T=\frac{2\pi R}{v}$ or $T^2\propto {\left(\frac{R}{v}\right)}^2$ or $T^2\propto {\left(\frac{R}{R^{\frac{-3}{4}}}\right)}^2$ or $T^2\propto R^{\frac{7}{2}}$