A disc of radius R is removed from the centre of the square plate of area $4 R^{2}$ and mass M. What is the moment of inertia of the remaining material with respect to an axis passing through its centre and perpendicular to the plate?

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Square plate, side 2R I pl a t e ​ = 6 M ( 2 R ) 2 ​ = 3 2 ​ M R 2 Mass of removed disc m = 4 R 2 M ​ π R 2 = 4 π M ​ I d i sc ​ = 2 m R 2 ​ = 8 π ​ M R 2 I = M R 2 [ 3 2 ​ − 8 π ​ ] Answer: A

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