Two rings have their masses in ratio $1 : 2$ and their diameters are in the ratio $2 : 1$. The ratio of their moments of inertia is

An annular ring has mass $10 \ kg$ and inner and outer radii are $5 \ m$ and $10 \ m$ respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

$A$ uniform solid cylinder of length $L$ and radius $R$ has a moment of inertia about its axis equal to $I_1$. $A$ small co-centric cylinder of length $L/2$ and radius $R/3$ is carved from this cylinder. The moment of inertia of this small carved cylinder about the same axis is $I_2$. The ratio $I_1/I_2$ is . . . . . . .

$A$ solid cylinder of mass $20 \ kg$ has length $1 \ m$ and radius $0.2 \ m$. Then its moment of inertia (in $kg \cdot m^2$) about its geometrical axis is

The moment of inertia of a uniform rectangular plate about an axis passing through its center and parallel to its length $(l)$ is ($b =$ width of the rectangular plate):