Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σr=A+Br . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its center is:

Go at distance of r and take an element of thickness dr.​Area of element = dA=2πrdr​Given : Surface mass density = α=A+Br Mass of element = dm=αdA​∴Total mass=∫dm=∫A+Br2πrdrMoment of Inertia about center = I=∫dm r2 =∫0aA+Br2πr3dr =2πAa44+Ba55=2πa4A4+aB5