A rod of length L and mass M has a nonuniform mass distribution.
The linear mass density (mass per length) is λ = cx², where x is measured from the center of the rod and c is a constant.
a. What are the units of c?
b. Find an expression for c in terms of L and M.
c. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.