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{\frac{GM}{R} }$
( B ) $\frac{1}{2} \sqrt{\frac{GM}{R} (1+ 2 \sqrt{2})}$
( C ) $ \sqrt{2 \sqrt{2}\frac{GM}{R} }$
( D ) $ \sqrt{\frac{GM}{R} (1+ 2 \sqrt{2})}$