A thin uniform spherical shell of radius R is bored such that the axis of the boring rod passes through the centre of the sphere. The boring rod is a cylinder of radius `(R)/(2)`. Take the mass of the sphere before boring to be M.
(a) Find the mass of the leftover part
(b) Find the moment of inertia of the leftover part about the axis shown.

Answer

(a) `(sqrt3)/(2) M`
(b) `(3 sqrt3)/(8) MR^(2)`