From a circular disc of radius $R$ and mass $9M$,a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

Two discs of the same thickness but different radii are made of two different materials such that their masses are equal. The densities of the materials are in the ratio $1:3$. The ratio of the moments of inertia of the discs about the axes passing through their centers and perpendicular to their planes is:

Four hollow spheres,each with a mass of $1\, kg$ and a radius $R = 10\, cm$,are connected with massless rods to form a square with a side of length $L = 50\, cm$. In case-$1$,the masses rotate about an axis that bisects two sides of the square. In case-$2$,the masses rotate about an axis that passes through the diagonal of the square,as shown in the figure. Compute the ratio of the moments of inertia $I_1/I_2$ for the two cases.

The ratio of the radii of two solid spheres of same mass is $2:3$. The ratio of the moments of inertia of the spheres about their diameters is

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

Five masses,each of $2\, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its center. All masses are equidistant from the axis at a distance of $10\, cm$. Calculate the moment of inertia of the whole system in $gm-cm^2$. (Assume the disc has negligible mass.)