$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1, I_2, I_3$ and $I_4$,respectively (the square $ABCD$ circumscribes the circle). The distance of the centre of mass of the disc from its geometrical centre is given by

$A$ thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma (r) = kr^2$,where $r$ is the distance from its centre. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

The moment of inertia of a ring about a diameter is

$Assertion$ : $A$ judo fighter,in order to throw his opponent onto the mat,tries to initially bend his opponent and then rotate him around his hip.
$Reason$ : As the mass of the opponent is brought closer to the fighter's hip,the moment of inertia of the opponent about the axis of rotation decreases,which makes it easier to rotate the opponent.

Two discs have densities $d_1 = 7.2 \ g/cm^3$ and $d_2 = 8.9 \ g/cm^3$. Both discs have the same mass and the same thickness. Find the ratio of their moments of inertia.