Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.

Explanation

Here the two particles always remain diametrically opposite so that the force on each particle will be directed along the radius. If we consider one particle of mass .m., force on each particle is `F = (Gm^2)/(4R^2)`
This force must provide required centripetal force
`rArr (Gm^2)/(4R^2) = (mv^2)/(R)` and ` v = sqrt((Gm)/(R))`