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

Explanation

M is the mass of the square plate before cutting the holes.
Mass of one hole
`m=[(M)/(16 R^(2))]pi R^(2)=(pi)/(16)M`
`therefore` 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)`