An infinitely long non-conducting solid cylinder of radius \(R\) has a non-uniform volume charge density given by \(\rho(r) = \rho_0 \dfrac{r}{R}\) for \(r \le R\), where \(\rho_0\) is a positive constant and \(r\) is the radial distance from the central axis. A particle of mass \(m\) and negative charge \(-q\) (where \(q > 0\)) moves in a stable circular orbit of radius \(r < R\) inside the cylinder, centered on and perpendicular to the central axis. Which of the following expressions correctly represents the orbital speed \(v\) of the particle in terms of \(r\), \(R\), \(\rho_0\), \(q\), \(m\), and fundamental constants?