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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 `4 R` and mass `M`. The moment of inertia of the remaining portion about z-axis is :
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Text Solution

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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=I_("square")-4l_("hole")`
`I=M/12[16R^(2)+16R^(2)]-4[(mR^(2))/2+m(2R^(2))]`
`=8/3MR^(2)-10 mR^(2)=(8/3-(10pi)/16) MR^(2)`
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