A square plate is of mass M and length of edge 2a. Its M.I about its centre of mass axis, perpendicular to its plane is equal to I(1). Four identical disks of diameter a are cut from the plane. The MI of leftover square about the same axis?
1) MI of square plate of edge length a- Ma^2/6
2) MI of disk of radius R- MR^2/2
3) I about a point P, x distance from COM is I about COM + Mx^2
The Attempt at a Solution
I first calculated MI of original square plate using formula 1 as (2/3)Ma^2=I(1). Mass of one disc as (pi/16)M=M(d). MI of one disc about the COM of disk=M(d)a^2/8=I(disc). MI of one disk about CM of square=I(disc)+(M(d)*a^2)/2=I(2). The MI of leftover square should be I(1)-4I(2) but I'm getting the wrong value every time, can you point out my mistake and write out the calculations in case I'm making a mistake somewhere?