Question

Moment of inertia of a square section with side a about the base is

Answer 1

Considering square as planar

M.I about an axis parallel to one side and intersecting other side at mid-point is (m×l^2)/12 .

Similarly for the other axis perpendicular to this is same due to symmetry of square

Therefore by applying perpendicular axis theorem the M.I of the square along an axis perpendicular to plan of square is (m×l^2)/6.

Now consider the diagonal as one axis and another diagonal perpendicular to the 1st diagonal as second MI about both the axis is same because of symmetry

Now apply perpendicular axis therom again

(m×l^2)/6=2×(MI about diagonal)

therefore MI about diagonal=(M×L^2)/12