A uniform thin rod of mass $M = 3.23$ kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass $m = 0.239$ kg, are attached to the ends of the rod. What must the length $L$ of the rod be so that the moment of inertia of the three-body system with respect to the described axis is $I = 0.975$ kg-m$^2$?