Two discs have the same thickness. Their radii are $R_1$ and $R_2$ and their densities are $d_1$ and $d_2$. The moment of inertia of the second disc is greater than the first if:

$Assertion$ : $A$ 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.

The moment of inertia of a circular ring of radius $r$ and mass $M$ about its diameter is:

$Assertion$ : Radius of gyration of a body is a constant quantity.
$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ are made respectively from a uniform wire. The moment of inertia of loop $Q$ about its axis is $4$ times that of loop $P$ about its axis. The value of $n$ is:

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio $1 : 3$. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio: