Comparison of Rotational Kinetic Energies on an Inclined Plane

[urapeach]

Here's a question:

A solid cylinder and hollow cylinder of the same mass and radius, both initally at rest, roll down the same inclined plane without slipping.

1) How do their rotational kinetic energies about the center of mass compare at the bottom?

2) If the plane was frictionless, which would reach the bottom first?

Thanks!

 

[Harmony]

Consider the mass distribution. If both cylinder have the same mass and radius, which one will have the larger value of I?

 

[Kurdt]

Also remember in rotational problems such as this the total energy is that of the kinetic and rotational energy summed. Just thought that might help in the second part of the question.