Four identical solid spheres each of mass $m$ and radius $a$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about one side of the square is:

From a uniform circular thin disc of mass $9 M$ and radius $R$,a small disc of radius $\frac{R}{3}$ is removed. The centre of the small disc is at a distance $\frac{2 R}{3}$ from the centre of the original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc of radius $R$ is

Seven identical discs each of mass $M$ and radius $R$ are arranged in a hexagonal plane pattern so as to touch each neighbour disc as shown in the figure. The moment of inertia of the system of seven discs about an axis passing through the centre of the central disc and normal to the plane of all discs is

For which of the following objects can the moment of inertia $NOT$ be found using the perpendicular axis theorem?

$ABC$ is a plane lamina in the shape of an equilateral triangle. $D$ and $E$ are the midpoints of $AB$ and $AC$,respectively,and $G$ is the centroid of the lamina. The moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I_{0}$. If the part $ADE$ is removed,the moment of inertia of the remaining part about the same axis is $\frac{NI_{0}}{16}$,where $N$ is an integer. The value of $N$ is

Two rings of the same radius and mass are placed such that their centers coincide and their planes are mutually perpendicular. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is ...... (where mass $= m$,radius $= r$)