Find the moment of inertia of a uniform square plate of mass m and edge α about one of its diagonals.
Let us assume that at a distance of x, there is a small cross sectional area along AB.
Now mass of that cross sectional area will be-
Now, moment of inertia along AB becomes-
Therefore, for two lines, the
Now, considering diagonals, the moment of inertia for pair of perpendicular diagonals becomes –
Therefore, by perpendicular axis theorem, moment of inertia becomes-