The ratio of moments of inertia of two solid spheres of same mass but densities in the ratio 1:8 is

A solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface as shown below.

The cube is free to rotate about the fixed axis $AB$. A bullet of mass $m\left(<<M\right)$ and speed $v$ is shot horizontally at the face opposite to $ABCD$ at a height $h$ above the surface to impart the cube an angular speed ${\omega }_c$, so that the cube just topples over. Then, ${\omega }_c$ is (Note the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is $\frac{2M{a}^3}{3}$)

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?

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

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

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:

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: