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 $R^{-5/2}$ 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 $R^{5/2}$

Answer 1

Answer: (B)

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

Given, $\frac{m{v}^2}{R}\propto R^{-5/2}$
$V\propto R^{-3/4}$
Now, $T=\frac{2\pi R}{v}$
$T^2\propto {\left(\frac{R}{v}\right)}^2$
$\Rightarrow T^2\propto {\left(\frac{R}{v}\right)}^2\Rightarrow T^2\propto R^{\frac{7}{2}}$