A solid cylinder of mass \(M\) and radius \(R\), and a thin hoop of mass \(M\) and radius \(R\), are released from rest at the same time from the top of an incline of height \(H\). The surface of the incline is rough enough that both objects roll down the incline without slipping. The rotational inertia of a solid cylinder about its center of mass is \(I_C = \dfrac{1}{2}MR^2\), and the rotational inertia of a thin hoop about its center of mass is \(I_H = MR^2\).