Question

If the gravitational force between two bodies is directly proportional to $\frac{1}{r}\left(not\frac{1}{R^2}\right)$, where ${}^{\prime }{R}^{\prime }$ is the distance between the bodies. Then the orbital speed for this force in circular orbit is proportional to

• A. $\frac{1}{R^2}$
• B. $R^o$
• C. $R$
• D. $\frac{1}{R}$

Answer 1

The correct option is B $R^o$

According to question, gravitational force $F_G=\frac{GMm}{R}$

Now $F_{centrfugal}=F_G$

$\frac{m{v}^2}{R}=\frac{GMm}{R}⟹v=\sqrt{GM}$

Thus $v\propto R^o$