Two particles of equal mass `'m'` go around a circle of radius `R` under the action of their mutual gravitaitonal attraction. The speed of each particle with respect to their centre of a mass is -

Explanation

The force on each particle is acting radially inwards. The two particles will always lie at the ends of a diameter so that the distance between them is 2R.
`:. F = (G M M)/((2R)^(2)) = (GM^(2))/(4R^(2))`
This force provides the necessary centripetal force for the particles to go round the circle.
`:. (M v^(2))/(R ) = F = (GM^(2))/(4R^(2))`
`rArr v = sqrt((GM)/(4R))`