Question

Suppose the gravitational force varies inversely as the $n$th power of distance, then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to.

• A. $R^{\frac{n+1}{2}}$
• B. $R^{\frac{n-2}{2}}$
• C. $R^n$
• D. $R^{\frac{n-1}{2}}$

Answer 1

The correct option is A $R^{\frac{n+1}{2}}$

F=$\frac{GmM}{R^n}=m{\omega }^{2}R\to \omega =\sqrt{\frac{GM}{R^{n+1}}}$ hence time period is proportional to $R^{\frac{n+1}{2}}$