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. $T^2$ is proportional to $R^2$
• B. $T^2$ is proportional to $R^{\frac{7}{2}}$
• C. $T^2$ is proportional to $R^{\frac{3}{2}}$
• D. $T^2$ is proportional to $R^{\frac{5}{2}}$

Answer 1

Answer: (B)

Given, $F=K{R}^{-\frac{5}{2}}$
We know, $F=m{\omega }^{2}R$
$\Rightarrow {\omega }^2\propto {\text{R}}^{-\frac{7}{2}}$
$\Rightarrow {\text{T}}^2\propto {\text{R}}^{\frac{7}{2}}$ ( since $T\propto \frac{1}{\omega }$ )