The moment of inertia of a rod of length `l` about an axis passing through its centre 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 centre of mass and perpendicular to its plane will be

Explanation

`M.I.` of rod `AB` about its centre and perpendicular to length `=(ml^(2))/12=I rArrml^(2)=12 I`

Now moment of inertia of rod about the axis which is passing through `O` and perpendicular to the plane of hexagon
`I_(rod)=(ml^(2))/12+mx^(2)`[from parallel axes theoram ]
`=(ml^(2))/12+m[(sqrt(3))/2l]^(2)=(5ml^(2))/6`
Now moment of inertia of system
`I_("System")=6xxI_(rod)=5ml^(2)=5xx2I=60 I`