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

Four particles, each of mass M and equidistant from each other, move a

1.	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
Answer» SOLUTION :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)))`