A small sphere of mass \(M\) is attached to a light string of length \(L\) and is swung in a vertical circle. At the top of the path, the sphere has a speed of \(v_T\) and the tension in the string is \(T_T\). At the bottom of the path, the sphere has a speed of \(v_B\) and the tension in the string is \(T_B\). If the speed of the sphere at the bottom is exactly twice the speed of the sphere at the top (\(v_B = 2v_T\)), which of the following expressions correctly relates the tension at the bottom to the tension at the top?