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