$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moments of inertia of the plate about axes $AB, BC,$ and $CA$ respectively. Which one of the following relations is correct?

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass,about a tangential axis perpendicular to the plane is

$A$ wire of mass $m$ and length $l$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is:

We have two spheres,one solid and one hollow. Their moments of inertia about their respective diameters are equal. The ratio of their radii will be:

Let $M$ be the mass and $L$ be the length of a thin uniform rod. In the first case,the axis of rotation passes through the center and is perpendicular to the length of the rod. In the second case,the axis of rotation passes through one end and is perpendicular to the length of the rod. The ratio of the radius of gyration in the first case to the second case 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 four times that of loop $P$ about its axis. The value of $n$ is