(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be , where is the mass of the sphere and is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

The moment of inertia of a sphere about its diameter is and is also shown in the figure,

As the the theorem of parallel axes says, M.I of a sphere about a tangent to the sphere

(b) Moment of inertia of a disc about its diameter is given as

(i)The theorem of the perpendicular axis states that the moment of inertia of a planar body about an axis passing through its center and perpendicular to the disc so we have . It is shown in the figure below,

(ii) Using the theorem of parallel axes:

Moment of inertia about an axis normal to the disc and going through a point on its circumference