Young's modulus for steel is $200\cdot 10^{9}\, Pa.$ Guy-wires are needed to support a radio tower. The wires will be anchored such that they make a $60^\circ$ angle with the ground and attach to the tower $20\, m$ above the ground. With typical winds, the horizontal force in any one direction on the tower are about $2000\, N$. Assume that one wire must resist a force $5$ times the typical horizontal force from winds. Further assume that the wind force, the wire and the tower all lie in the same plane as shown in the figure below.

What should the minimum diameter of the wire (with circular cross section) be if the horizontal motion of the tower is to be $2.00\, cm$ maximum at the point where the guy wire is attached? Final answer is rounded to two significant figures.