Suppose we put a third tiny sphere of mass m at the center of the rod in Problem 10.32. Determine the new moment of inertia about an axis perpendicular to the rod passing through its center, in terms of m and L.

Problem 10.32

Picture a rigid rod of length L having negligible mass. It has two identical tiny spheres both of mass m, one at each end of the rod. Determine the moment of inertia about an axis perpendicular to the rod passing through its center, in terms of m and L.