The moment of inertia of a uniform annular disc of internal radius $r$,external radius $R$,and mass $M$ about an axis passing through its centre and perpendicular to its plane is:

Three point masses $m_1, m_2, m_3$ are located at the vertices of an equilateral triangle of side length $a$. The moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$ is:

Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

$A$ solid sphere and a solid cylinder have the same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is

$A$ non-uniform rod $OM$ (of length $l$) is kept along the $x$-axis and is rotating about an axis $AB$,which is perpendicular to the rod as shown in the figure. The rod has a linear mass density that varies with the distance $r$ from the left end $O$ of the rod according to $\lambda = \lambda_0 \left( \frac{r^3}{l^3} \right)$,where $\lambda_0$ is a constant. If the axis $AB$ is at a distance $x$ from the end $O$,what is the value of $x$ such that the moment of inertia of the rod about the axis $AB$ $(I_{AB})$ is minimum?

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