(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 `2 MR^(2)//5, where M` is the mass of the sphere and `R` is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass `M` and radius `R` about any of its diameters to be `(1)/(4)MR^(2)`, find the moment of inertia about an axis normal to the disc passing through a point on its edge.

Explanation

(a) Moment of inertia of sphere about any diameter `= (2)/(5)MR^(2)`
Applying theorem of parallel axes,
Moment of inertia of sphere about a tangent to the sphere `= (2)/(5)MR^(2) + M(R )^(2) = (7)/(5)MR^(2)`
(b) We are given, moment of inertia of the disc about any of its diameters `= (1)/(4)MR^(2)`
(i) Using theorem of perpendicular axes, moment of inertia of the disc about an axis passing through its centre and normal to the disc `= 2 xx (1)/(4) MR^(2) = (1)/(2)MR^(2)`
(ii) Using theorem of parallel axes, moment of inertia of the disc passing through a point on its edge and normal to the disc `= (1)/(2)MR^(2) + MR^(2) = (3)/(2)MR^(2)`