Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ is:

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

For the adjoining diagram,the incorrect relation between $I_{1}, I_{2}$ and $I_{3}$ is ($I$ = moment of inertia).

One quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

Four particles each of mass $M$ are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

What is the radius of gyration? Write its unit and dimensional formula.