The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass 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

Two circular discs of iron have the same thickness. The diameter of disc $A$ is twice that of disc $B$. The moment of inertia of $A$ will be ........ times that of $B$.

$A$ solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio of $I_1/I_2$ is given by

$Assertion$ : Radius of gyration of a body is a constant quantity.
$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.

Two half rings are joined as shown in the figure. Each half ring has a radius $R$ and mass $M$. The moment of inertia of the system about the axis $XX'$ is