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 . The speed of each particle is :

Question

$(a)\;\sqrt{\large\frac{GM}{R}} \qquad(b)\; \sqrt{2 \sqrt{2}\large\frac{GM}{R}} \qquad(c)\; \sqrt{\large\frac{GM}{R}(1+2 \sqrt{2})}\qquad(d)\;\large\frac{1}{2} \sqrt{\large\frac{GM}{R}(1+2 \sqrt{2})}$