The moment of inertia of a rod of length L about an axis passing through its center of mass and perpendicular to rod is I. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its center of mass and perpendicular to its plane will be nI. Find the value of n.

Moment of inertia of rod AB about its centre and perpendicular to the length =ml212=I⇒ml2=12INow moment of inertia of the rod about the axis which is passing through O and perpendicular to the plane of hexagon Irod=ml212+mx2[From the theorem of parallel axes]=ml212+m32l2=5ml26Now the moment of inertia of system,Isystem =6×Irod=6×5ml26=5ml2Isystem =5(12I)=60I                        As ml2=12I