Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis along any one side of the triangle is:

Two discs $A$ and $B$ of same material and thickness have radii $R$ and $3R$ respectively. Their moments of inertia about their axis will be in the ratio

The moment of inertia of a straight thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its one end,is

From a uniform wire, two circular loops are made: $(i)$ $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$). (in $\sqrt{2}$)

Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is:

Two rings of same mass $m$ and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is ............