The ratio of the radii of gyration of a circular disc to that of a circular ring,each of same mass and radius,around their respective axes is

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:

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

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:

$A$ 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 :

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