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

Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

$Assertion$ : 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.

What is the radius of gyration of a circular disc of radius $R$ about an axis passing through its center and perpendicular to its plane?

The moment of inertia of a uniform thin rod of mass $m$ and length $\ell$ about a perpendicular axis passing through one end is $I_{1}$. The same rod is bent into a ring and its moment of inertia about a diameter is $I_{2}$. If $\frac{I_{1}}{I_{2}} = \frac{x \pi^{2}}{3}$,then the value of $x$ will be ...............

Three identical rods each of mass $M$ and length $L$ are joined to form a symbol $H$. The moment of inertia of the system about one of the sides of $H$ is