A solid cylinder of mass \(M\) and radius \(R\) rests on a rough horizontal table. A light string is attached to a frictionless axle at the center of the cylinder. The string passes over a light, frictionless pulley at the edge of the table and is attached to a hanging block of mass \(m\). The rotational inertia of a solid cylinder about its center is \(I = \dfrac{1}{2}MR^2\). The system is released from rest, and the cylinder rolls without slipping along the table. Let \(g\) represent the acceleration due to gravity.