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

$A$ thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........

$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. Their moments of inertia about their diameters are $I_A$ and $I_B$ respectively. Which of the following relations is correct?

Two loops $A$ and $B$ of radii $R_1$ and $R_2$ are made from a uniform wire. If the moment of inertia of $A$ is $I_A$ and that of $B$ is $I_B$,then find the ratio $R_2 / R_1$ given that $I_A / I_B = 27$.

The adjoining figure shows a disc of mass $M$ and radius $R$ lying in the $X-Y$ plane with its centre on the $X$-axis at a distance $a$ from the origin. Then the moment of inertia of the disc about the $X$-axis is

Two rings of radius $R$ and $nR$ made of the same material have a ratio of moment of inertia about an axis passing through their centers and perpendicular to their planes as $1:8$. The value of $n$ is (mass per unit length $= \lambda$).