The moment of inertia of a sphere (mass $M$ and radius $R$) about its diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about the axis $XX'$ will be (in $,I$)

Find the moment of inertia of a plate cut in the shape of a right-angled triangle of mass $M$ and sides $AC = BC = a$,about an axis perpendicular to the plane of the plate and passing through the midpoint of the side $AB$.

$A$ thin uniform square lamina of side $a$ is placed in the $xy$-plane with its sides parallel to $X$ and $Y$-axes and with its centre coinciding with the origin. Its moment of inertia about an axis passing through a point on the $Y$-axis at a distance $y = 2a$ and parallel to the $X$-axis is equal to its moment of inertia about an axis passing through a point on the $X$-axis at a distance $x = d$ and perpendicular to the $xy$-plane. Then the value of $d$ is:

$A$ sphere of mass $10\; kg$ and radius $0.5\; m$ rotates about a tangent. The moment of inertia of the sphere is

$A$ thin wire of length $L$ and linear mass density $m$ is bent into a circular ring (in $x-y$ plane) with centre $C$ as shown in the figure. The moment of inertia of the ring about an axis $yy'$ will be:

$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is: