There is a square plate of side length a. It is divided into nine identical squares each of side `(a)/(3)` and the central square is removed (see fig. (i)). Now each of the remaining eight squares of side length `(a)/(3)` are divided into nine identical squares and central square is removed from each of them (see fig. (ii)).
(a)
Mass of the plate with one big and eight small holes is M. Find its moment of inertia about an axis passing through its centre and perpendicular to its plane.

Answer

`(91)/(486) Ma^(2)`