Two particles of equal mass m go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

Explanation

The particles will always remain diametrically oposite so that the force on each particle wil be directed along the radius. Consider the motion of one of the particle.The force on the particle is `F=(Gm^2)/(4R^2)`. If the speed is v its acceleration is `v^2/R.`
Thus, by Newton's law
`(Gm^2)/(4R^2)=(mv^2)/R`
or `v=(sqrt((Gm)/(4R)))`