Five particles of mass $2 \ kg$ each are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is ........ $kg \ m^2$.

Four solid spheres,each of mass $M$ and radius $R$,are placed at the four corners of a square of side length $a$. Find the moment of inertia of the system about an axis coinciding with one of the sides of the square.

The ratio of the radius of gyration of a hollow sphere to that of a solid cylinder of equal mass,for the moment of inertia about their diameter axis $AB$ as shown in the figure,is $\sqrt{\frac{8}{x}}$. The value of $x$ is:

Four identical uniform solid spheres,each of same mass '$M$' and radius '$R$',are placed touching each other as shown in the figure with centers $A, B, C, D$. If $I_{A}, I_{B}, I_{C}, I_{D}$ are the moments of inertia of the system about axes passing through their centers $A, B, C, D$ respectively and perpendicular to the plane,then:

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

If the mass and radius of a hollow sphere are $M$ and $R$ respectively,then its moment of inertia with respect to its diameter is: