Firstly, note that T=mg.

Then, draw the forces acting on the ball outside the cone(Reaction force, gravity, tension and the centripetal force).

If the system is in equilibrium, R sin 30 + T cos 30 = mg

0.5 R + mg (root3 /2)= mg

R= (2- root(3)) mg

For horizontal components, T sin 30 - R cos 30 = mrw^2

Substitute T=mg and R.