Question

The surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as p(r) = A + Br. Find its moment of inertia about the line perpendicular to the plane of the disc through its centre.

Answer 1

The surface density of a circular disc of radius a depends upon the distance from the centre as
P(r) = A + Br
Therefore the mass of the ring of radius r will be
 θ= (A + Br) × 2πr dr × r²
Therefore moment of inertia about the centre will be