Satellites - Orbital Velocity & Period question from JEE Main 2014

Answer: (d)

1. Adjacent masses $\sqrt{2}R$ apart, opposite one $2R$ away.
2. Net pull: $\frac{GM^2}{2R^2}\cdot 2\cos 45^\circ + \frac{GM^2}{4R^2} = \frac{GM^2}{4R^2}(1+2\sqrt{2})$.
3. $\frac{Mv^2}{R} = \frac{GM^2}{4R^2}(1+2\sqrt{2}) \Rightarrow v = \frac{1}{2}\sqrt{\frac{GM}{R}(1+2\sqrt{2})}$.
4. So the answer is (d).