A thick hollow cylinder of length \(L\), inner radius \(R\), and outer radius \(2R\) rotates about its central axis with a constant angular speed \(\omega\). The cylinder has a non-uniform volume mass density given by \(\rho(r) = \dfrac{c}{r^2}\), where \(r\) is the radial distance from the central axis and \(c\) is a positive constant. Which of the following expressions represents the rotational kinetic energy of the cylinder?