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

The particle will always remain diametrically opposite, so that the force on each particle will be directed along the radius.
When each particle is describing a circular orbit, the gravitational force on one of the particles must be equal to the necessary centripetal force.
`(mV^(2))/(r) = (Gm m)/((2r)^(2)) " "` i.e, `V = sqrt((Gm)/(4r))`