A uniform solid cylinder of mass \(M\) and radius \(R\) with rotational inertia \(I = \dfrac{1}{2}MR^2\) is mounted on a fixed, horizontal, frictionless axle passing through its center of mass. A light, unstretchable string is wrapped securely around the outer rim of the cylinder and attached to a block of mass \(m\) that hangs vertically. The system is released from rest, and the string unwinds without slipping as the block accelerates downward. In terms of \(M\), \(m\), and \(g\), what is the magnitude of the upward force exerted by the axle on the cylinder while the block is falling?