Two loops $P$ and $Q$ of radii $R_1$ and $R_2$ are made from uniform metal wire of the same material. If $I_P$ and $I_Q$ are the moments of inertia of loops $P$ and $Q$ respectively,then the ratio $R_1 / R_2$ is (Given $I_P / I_Q = 27$) (in $:1$)

The figure shows two solid discs with radius $R$ and $r$ respectively. If the mass per unit area is the same for both,what is the ratio of the moment of inertia $(MI)$ of the bigger disc about axis $AB$ (which is perpendicular to the plane of the disc and passing through its centre) to the $MI$ of the smaller disc about one of its diameters lying on its plane? Given $M$ is the mass of the larger disc.

If a spherical planet of mass $M$ and radius $R$ suddenly shrinks to half its size,and its mass reduces to half,what is the new moment of inertia of the planet about its diameter?

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}: \sqrt{K}$. The value of $K$ is

$5$ particles,each of mass $2 \ kg$,are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of this system about an axis passing through the center and perpendicular to its plane is ........... $kg \cdot m^{2}$.

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 $= \lambda$).