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 .

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