A small block of mass \(m\) on a frictionless horizontal tabletop is connected to an ideal string that passes through a small hole at the center of the table. The block initially revolves in a circle of radius \(R_0\) with constant speed \(v_0\), having angular momentum \(L_0\), kinetic energy \(K_0\), and string tension \(T_0\). The string is pulled downward through the hole very slowly until the radius of the circular path decreases to \(\dfrac{1}{2}R_0\). Which of the following correctly identifies the final angular momentum \(L_f\), the final tension in the string \(T_f\), and the total work \(W\) done by the string tension on the block during this process?