Five solid spheres,each of mass $m$ and radius $r$,are arranged as shown in the figure. The axis of rotation $A-A'$ passes through the centers of three spheres. Calculate the moment of inertia of the system about the axis of rotation $A-A'$. (in $m r^2$)

$A$ slender rod of mass $M$ and length $L$ is hinged at one end to swing freely in a vertical plane. Its density is non-uniform and varies linearly from the hinged end to the free end,doubling its value. The moment of inertia of the rod about the rotation axis passing through the hinge point is:

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

Two rings of same mass $M$ and radius $R$ are placed such that their centers coincide and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the center and perpendicular to any one ring 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:

$A$ person is sitting on a rotating table with their arms outstretched. If they suddenly pull their arms inward,then: