A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, p = ar, where a is a positive constant
(a) Calculate the moment of inertia of the cylinder about a longitudinal axis through its center in terms of M and R.
(b) Is your answer greater or smaller than the moment of inertia of a cylinder of the same mass and radius but of uniform density? Explain why this result makes qualitative sense.