A thin square plate is of mass m and the length of each of its sides is I. Find the moment of inertia of the plate when it is rotating about an axis (i) passing through its centre and perpendicular to its plane and (ii) passing through one of its corners and perpendicular to its plane.

A thin square plate is of mass m and the length of each of its sides i

1.	A thin square plate is of mass m and the length of each of its sides is I. Find the moment of inertia of the plate when it is rotating about an axis (i) passing through its centre and perpendicular to its plane and (ii) passing through one of its corners and perpendicular to its plane.
Answer» Solution :Passing through its centre and perpendicular to its plane : `I=(m(l^(2)+l^(2))/(12)=(2ML)/(12)=(ml^(2))/(6))` (ii)Passing through one of its CORNERS and perpendicular to its plane `I=I_(G)+Mr^(2)` `I=(ml^(2))/(6)+(ml^(2))/(2)=(ml^(2)+3ml^(2))/(6) rArr I=(4ml^(2))/(6)=(2ml^(2))/(3)`