A uniform hemisphere has mass M and radius a. A spinning top is made by fitting the hemisphere with a light spindle AB which passes through the hemisphere and is fixed along its axis of symmetry with the curved surface of the hemisphere facing away from the end A.
The distance of A from the point where the spindle enters the flat surface is equal to the radius a of the hemisphere. Find the principal moments of inertia of the top at the end A of the spindle.