A solid disk-shaped pulley of total mass \(M = 3.0 \text{ kg}\) and radius \(R = 0.100 \text{ m}\) is mounted on a horizontal axle. The pulley is manufactured such that its area mass density \(\sigma\) (in \(\text{kg/m}^2\)) increases with the radial distance \(r\) from the center according to the equation \(\sigma(r) = cr\), where \(c\) is a positive constant. Given that the total mass of the pulley is \(M\), the constant \(c\) can be expressed as \(c = \dfrac{3M}{2\pi R^3}\).