Two solid cylinders, Cylinder A and Cylinder B, both have total mass \(M\), radius \(R\), and length \(L\).

• Cylinder A is made of a uniform material.
• Cylinder B is made of a material such that its volume mass density \(\rho\) increases with radial distance \(r\) from the central axis according to the function \(\rho(r) = \beta r\), where \(\beta\) is a positive constant.

Both cylinders are placed at rest at the top of a rough incline of angle \(\theta\) and roll without slipping down the incline.