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.