A uniform solid cylinder of mass \(M\) and radius \(R\) is placed on a rough horizontal surface. A light string is attached to a frictionless axle that passes through the center of mass of the cylinder. The string is pulled horizontally to the right, passes over a light, frictionless pulley at the edge of the surface, and is attached to a hanging block of mass \(m\), as shown in Figure 1. The rotational inertia of a uniform solid cylinder about its center is \(I = \dfrac{1}{2}MR^2\). The system is released from rest, and the cylinder rolls to the right without slipping.