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  4. The moment of inertia of a thin square plate A B C D, of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is where I1, I2, I3 and I4 are respectively moments of inertia about axes 1,2,3 and 4 which are in the plane of the plate

Q. The moment of inertia of a thin square plate , of uniform thickness about an axis passing through the centre and perpendicular to the plane of the plate is where and are respectively moments of inertia about axes and which are in the plane of the plate Physics Question Image

 3858  181 IIT JEEIIT JEE 1992System of Particles and Rotational Motion Report Error

Solution:

Since, it is a square lamina

and (by symmetry)
From perpendicular axes theorem.
Moment of inertia about an axis perpendicular to square plate and passing from is

or
Hence,
Rather we can say
Therefore, can be obtained by adding any two i.e.