Question

3 identical point particles of mass M move in such a way that distance between particles is 'd' which remain constant. Only force is the gravitational force between particles. Then magnitude of relative velocity (in $m/s$ ) of one particle with respect to other particle will be : [Take $\sqrt{\frac{GM}{d}}=\sqrt{3}m/s$ ]

Answer 1

Particle will move in circle.

$2\frac{GM^{2}}{ d^{2}}cos30^\circ =\frac{MV^{2}}{R}$
$v=\sqrt{\frac{GM}{d}}=\sqrt{3}m/s\left[\right.R\sqrt{3}=d\left]\right.$
Relative velocity $=2vcos30^\circ =3m/s$