Q15 of 149 Page 195

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-





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