For particles of equal masses M that move along a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.

Explanation

The two particles will move on a circular path if they always remain diametrically opposite so that the gravitational force on one particle due to other is directed along the radius. Taking into consideration the circulation of one particle, we have,
`(m upsilon^(2))/(r ) = (Gmm)/((2r)^(2))` or `upsilon = sqrt((Gm)/(4r))`