A rigid cylinder of mass \(M\) and radius \(R\) has an internal mass distribution that yields a rotational inertia \(I = \beta M R^2\) about its central axis, where \(\beta > 0\) is a dimensionless parameter. The cylinder is released from rest on a plane inclined at an angle \(\theta\) above the horizontal and rolls down the incline without slipping. Which of the following correctly describes the magnitude of the linear acceleration \(a\) of the cylinder's center of mass and the magnitude of the static friction force \(f_s\) exerted on the cylinder in the theoretical limit as \(\beta \to \infty\)?