Consider a disc of radius $R$ and mass $M$. A hole of radius $\frac{R}{3}$ is created in the disk such that the center of the hole is $\frac{R}{3}$ away from centre of the disk. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $X{X}^{\mathit{\prime }}$ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about $X{X}^{\mathit{\prime }}$ axis is:

Which one of the following four graphs best depict the variation with $x$ of the moment of inertia $I$ of a uniform triangular lamina about an axis parallel to its base at a distance $x$ from it

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$(see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

A mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?