The L-shaped object in Figure $10-21$ can be rotated in one of the following three ways: case $1,$ rotation about the $x$ axis; case $2,$ rotation about the $y$ axis; and case $3,$ rotation about the $z$ axis (which passes through the origin perpendicular to the plane of the figure). Rank these three cases in order of increasing moment of inertia. Indicate ties where appropriate.