Physics - Gravitation Question with Solution | TestHub

Two particles of mass $m$ are moving in a circle of radius $r$.

The distance between the two particles is the diameter of the circle, which is $2r$.

The gravitational force of attraction between them provides the necessary centripetal force for circular motion.

Gravitational force $F=\frac{Gmm}{(2r{)}^2}=\frac{G{m}^2}{4r^2}$

Centripetal force $F_c=\frac{m{v}^2}{r}$

Equating the two forces:

$\frac{m{v}^2}{r}=\frac{G{m}^2}{4r^2}$

$v^2=\frac{Gm}{4r}$

$v=\sqrt{\frac{Gm}{4r}}$

Answer: $\sqrt{\frac{Gm}{4r}}$