Calculate the moment of inertia of
a. a ring of mass `M` and radius `R` about an axis coinciding with the diameter of the ring.
b. a thin disc about an axis coinciding with the diameter.

Explanation

Let X and Y axes be along two perpendicular diameters of the ring. By symmetry, `I_x=I_y and I_x+I_y` But we know that `I_z=MR^2` `MR^2=I_x+I_y` ,`MR^2=2I_x` `I_x=I_y=(MR^2)/2`Similarly for a thin disc (i.e., a circular plate) Moment of inertia about a diameter is `=I=1/2(1/2MR^2)=1/4MR^2`.