The moment of inertia of a uniform circular ring,having a mass $M$ and a radius $R$,about an axis tangential to the ring and perpendicular to its plane,is

For the given uniform square lamina $ABCD$,whose centre is $O$,

The moment of inertia of a square frame about an axis passing through its center of mass and perpendicular to its plane is $20 \ kg \cdot m^2$. The moment of inertia about an axis touching its side and lying in the plane of the frame is ........ $kg \cdot m^2$.

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

$A$ solid sphere of radius $R$ has a moment of inertia $I$ about its geometrical axis. It is melted into a disc of radius $r$ and thickness $t$. If its moment of inertia about the tangential axis (which is perpendicular to the plane of the disc) is also equal to $I$,then the value of $r$ is equal to: