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

Four holes of radius R are cut from a thin square plate of side 4R and

1.	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
Answer» Solution :M is the mass of the square plate before CUTTING the holes. Mass of one HOLE `m=[(M)/(16R^(2))] pi R^(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)`