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Four holes of radius R are cut from a th...

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

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M is the mass of the square plate before cutting the holes.
Mass of one hole
`m=[(M)/(16R^(2))]piR^(2)=(pi)/(16)M`
`:.` Moment of inertia of remaining portion.
`I_("square")-4I_("nole")`
`I=(M)/(12)[16R^(2)+16R^(2)]-4[(mR^(2))/(2)+m(2R)^(2)]`
`=(8)/(3)MR^(2)-18mR^(2)` `I=((8)/(3)-(10pi)/(16))MR^(2)`
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