A small sphere of mass \(m\) is attached to an ideal string of length \(R\) and whirled in a vertical circle. When the sphere is at the highest point of its path, it has a speed \(v_0\) and the tension in the string has a magnitude \(T\). The speed of the sphere is then increased such that the new speed at the highest point is \(2v_0\). What is the new magnitude of the tension in the string when the sphere is at the highest point with this new speed?