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 stars is proportion to $R_1/2$ , there $T^2$ is proportional to.

• A. $R^2$
• B. $R^{1/2}$
• C. $R^{-1/2}$
• D. $R^1/3$

Answer 1

The correct option is B $R^{1/2}$

When planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T then centripetal force is balanced by gravitational force as

$mR{\omega }^2=\frac{GmM}{R^{\frac{-1}{2}}}$

${\omega }^2=\frac{1}{R^{\frac{1}{2}}}$

$\because \omega =\frac{2\pi }{T}$

${\left(\frac{2\pi }{T}\right)}^2=\frac{1}{R^{\frac{1}{2}}}$

$\frac{1}{T^2}\propto \frac{1}{R^{\frac{1}{2}}}$

$T^2\propto R^{\frac{1}{2}}$