The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $z$-axis is

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

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

The radius of gyration of a disc of mass $100\,g$ and radius $5\,cm$,about an axis passing through its centre of gravity and perpendicular to the plane,is ....... $cm$.

$A$ solid sphere $A$ of radius $R$ and mass $M$ is attached at a point to a smaller solid sphere $B$ of radius $r < R$ and mass $m < M$. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of $A$ is $I_A$ and that calculated about a vertical axis passing through the centre of $B$ is $I_B$. The difference $I_A - I_B$ is :

Two rings have their moments of inertia in the ratio $2:1$ and their diameters are in the ratio $2:1$. The ratio of their masses is