A light, inextensible string is wrapped around the outer rim of a uniform solid cylinder of mass \(M\) and radius \(R\) that is mounted on a fixed horizontal axle through its center. The free end of the string is attached to a block of mass \(m\). A constant frictional torque \(\tau_f\) opposes the rotation of the cylinder about the axle. The block is released from rest and the string unwinds without slipping. What is the magnitude of the downward linear acceleration of the block in terms of \(m\), \(M\), \(R\), \(\tau_f\), and fundamental constants?