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:

Two discs have densities $d_1 = 7.2 \ g/cm^3$ and $d_2 = 8.9 \ g/cm^3$. Both discs have the same mass and the same thickness. Find the ratio of their moments of inertia.

Consider the following statements:
Assertion $(A)$: The moment of inertia of a rigid body reduces to its minimum value as compared to any other parallel axis when the axis of rotation passes through its centre of mass.
Reason $(R)$: The weight of a rigid body always acts through its centre of mass in a uniform gravitational field.
Of these statements:

Four point masses,each of value $m$,are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

$A$ ring of mass $m$ and radius $r$ is melted and recast into a sphere. The moment of inertia of the sphere will be:

$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moments of inertia of the plate about axes $AB, BC,$ and $CA$ respectively. Which one of the following relations is correct?