Four particles of equal mass M move along a circle of radius .R under the action of their mutual gravitational attraction [Fig.]. The speed of each particle is

The gravitational force on each particle due to other three particles provides the necessary centripetal force.GM2(2R)2cos⁡45∘+GM2(2R)2cos⁡45∘+GM2(2R)2=Mv2R2GM22R2×12+GM24R2=Mv2R2GM2R+GM4R=v2 ∴ v=GMR22+14