Fan Out !!!

The rotatory fan out

In free space an assembly of two identical particles each of mass m=2 kg connected by two identical uniform ropes is rotating at a constant angular velocity $\omega=2\frac{rad}{s}$

about the axis passing through the centre of the line segment joining them. Since the ropes have mass they fan out. and assume a constant unchanged curved shape as shown in the figure. If the distance between the midpoints of the rope is d=1.1547m tension at the midpoint of the rope is T=9N and the included angle between the ropes at the particles is $\theta=60^{o}$ . Find the distance between the particles in metres .