The surface density (mass/area) of a circular disc of radius α 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.
The moment of inertia = 
Given
The radius of the circular disc is “a”, and the distance from the center to the edge of the disc is given as
. Hence to find moment of inertia we find the relationship mass and moment of inertia in terms of area.
Formula Used
The inertia of the body for a point of mass is the product of the square of the radius with the mass of the body. The formula is
where
I is the moment of Inertia, A is the area of the object and r is the radius of the object.
Explanation
The moment of inertia of a disc is
2