Question

If gravitational force between two objects where proportional to $1/r$ where r is the separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to ______.

Answer 1

Let $F=\frac{k}{r}$

$\therefore F=\frac{m{v}^2}{r}$

$\therefore \frac{k}{r}=\frac{m{v}^2}{r}$

$\Rightarrow v=\sqrt{km}$

$\Rightarrow v\propto \sqrt{m}$

orbital speed $v$ is directly proportional to the square root of mass of the particle $m$