On account of the melting of ice at the North Pole,the moment of inertia of the spinning Earth:

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

$A$ straight rod of length $L$ is made of a material having mass per unit length $m(x) = \lambda|x|$, where $x$ is measured from the center of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is to be calculated. Given $L = 1 \ m$ and $\lambda = 16 \ kg/m^2$.

Three thin uniform rods,each of mass $M$ and length $L$,are placed along the three Cartesian axes such that one end of each rod is at the origin. Find the moment of inertia of this system about the $z$-axis.

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is: