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 =(Gmm)/((2r)^2)" " i.e V = sqrt((Gm)/r)`