A uniform thin bar of mass 6m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

A uniform thin bar of mass 6m and length 12L is bent to make a regular

1.	A uniform thin bar of mass 6m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is
Answer» `20 mL^2` `30 mL^2` `((12)/(5)) mL^2` `6 mL^2` Solution :LENGTH of each side of hexagon = 2L and mass of each side = m . Let O be the centre of mass of hexagon . Perpendicular distance of O from each side , r = L TAN `60^(@) = L sqrt3` The desired moment of INERTIA of hexagon about O is `I = 6[I_("one side") ] = 6 [ (m (2L)^(2))/(12) + mr^(2)]` `= 6 [(mL^2)/(3) + m(Lsqrt3)^(2)] = 20 mL^(2)`