Question

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

• A. $T^2$ is proportional to $R^2$
• B. $T^2$ is proportional to $R^{7/2}$
• C. $T^2$ is proportional to $R^{3/2}$
• D. $T^2$ is proportional to $R^{3.75}$

Answer 1

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

Gravitational force $\alpha$ $R^{-5/2}$

Centripetal force $\alpha$ $R^{-5/2}$

$mR{w}^2$ $\alpha$ $R^{-5/2}$

$w^2$ $\alpha$ $R^{-5/2-1}$

$w^2$ $\alpha$ $R^{-7/2}$

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

$T^2$ $\alpha$ $R^{7/2}$

$T^2$ is proportional to $R^{7/2}$.