Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle

Explanation

Force acting on a particle
`=(GM^2)/((2R)^(2))+(GM^2)/((R//sqrt(2))^(2))cos45^(@)+(GM^2)/((Rsqrt(2))^(2))cos45^(@)`
`F=(GM^2)/(R^2)[(1)/(4)+(1)/(sqrt2)]`
Since particle moving circular path experience centripetal force,
`F=(MV^2)/(R)`
`(MV^2)/(R)=(GM^2)/(R^2)[(1)/(4)+(1)/(sqrt2)]`
`thereforeV=(1)/(2)sqrt((GM)/(R)(1+2sqrt(2)))`