Rotational Mechanics

Hate to bother your guys but I cant make heads or tails of this problem, it says:Two wires are tied to the 2.0 kg sphere shown in the figure  < a href = "http://session.masteringphysics.com/problemAsset/1073611/3/knight_Figure_07_60.jpg">Figure</a>  . The sphere revolves in a horizontal circle at constant speed.  Can anyone help me out here

OP here sorry I forgot the question silly me:For what speed is the tension the same in both wires?

All of them.

The set of all real speeds

y direction
T₁sin + T₂cos = mg

x direction
T₁cos + T₂sin = mr omega²

solve, set the 2 tensions equal

If you were smart, you'd set the tensions equal (before solving) and realize the above force equations are equal.  Thus,
g = r omega²