A square plate of side / has mass M. What is its moment of inertia about one of its diagonals ?

A square plate of side / has mass M. What is its moment of inertia abo

1.	A square plate of side / has mass M. What is its moment of inertia about one of its diagonals ?
Answer» `(Ml^2)/(6)` `(Ml^2)/(12)` `(Ml^2)/(3)` `(Ml^2)/(4)` Solution :Moment of inertia of a SQUARE about an axis through its centre and perpendicular to its PLANE `I_(O) = (M)/(12) (l^(2) + l^(2)) = (Ml^(2))/(6)` ACCORDING to theorem of perpendicular axes , we get `I_(1) + I_(2) = I_(O) = (Ml^(2))/(6)` But `I_1 = I_2` (By SYMMETRY) `therefore 2I_(1) = (Ml^(2))/(6) or I_(1) = (MI^(2))/(12)`