Four holes of radius `R` are cut from a thin square plate of side `4 R` and mass `M`. The moment of inertia of the remaining portion about z-axis is :
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Explanation

M = Mass of the square plate before the holes were cut.
`:." "` Mass of each hole `m = [M/(16R^2)] pi R^2 = (pi M)/16`
`:." "` Moment of inertia of the remaining portion.
`I = I_("square") - rI_("hole") = M/12 ( 16R^2 + 16 R^2)`
` - 4[(mR^2)/2 + m(sqrt2 R)^2] = 8/3 MR^2`
`-10 R^2 = [ 8/3 - (10 pi)/16 ]MR^2`