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):

Find the moment of inertia of a thin,massless rod about an axis passing through its centre of mass,where a pair of masses is suspended at both ends of this rod.

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively,and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $\frac{r_2}{r_1}$ equals:

$A$ solid sphere and a thin-walled hollow sphere have the same mass and the same material. Which of them has a greater moment of inertia about its diameter? ($I_{h} =$ moment of inertia of a hollow sphere about an axis coinciding with its diameter,$I_{s} =$ moment of inertia of a solid sphere about an axis coinciding with its diameter)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Moment of inertia of a circular disc of mass $M$ and radius $R$ about $X, Y$ axes (passing through its plane) and $Z$-axis which is perpendicular to its plane were found to be $I_{x}, I_{y}$ and $I_{z}$ respectively. The respective radii of gyration about all the three axes will be the same.
Reason $R$: $A$ rigid body making rotational motion has fixed mass and shape.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ uniform solid cylinder with radius $R$ and length $L$ has moment of inertia $I_1$ about the axis of the cylinder. $A$ concentric solid cylinder of radius $R/2$ and length $L/2$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved out portion of the cylinder, then $I_1/I_2$ is (Both $I_1$ and $I_2$ are about the axis of the cylinder). (in $: 1$)