In the given figure,about which axis will the moment of inertia of the triangular frame be maximum? [Given: $AB < BC < AC$]

Find the moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane.

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

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

The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,m$ rotating about one of its diameters is

$A$ quarter circular sector is cut from a uniform circular disc. The mass of this sector is $M$. It is rotated about an axis passing through the center of the original disc and perpendicular to its plane. The moment of inertia of this sector about the axis of rotation is: