A small block of mass \(m\) is attached to an ideal string and undergoes uniform circular motion on a horizontal, frictionless surface. The string is anchored to the center of the surface, and the block moves with a constant speed \(v\) in a circle of radius \(R\). The tension in the string has a magnitude \(F\). The experiment is repeated with the same block, but the speed is increased to \(2v\) and the radius is decreased to \(R/2\). What is the new magnitude of the tension in the string?