What is the moment of inertia of a thin circular disc about its diameter? ($M$ is the mass and $R$ is the radius of the disc.)

$A$ circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from an iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is:

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

For the adjoining diagram,the incorrect relation between $I_{1}, I_{2}$ and $I_{3}$ is ($I$ = moment of inertia).

The ratio of the radius of gyration of a ring to that of a disc (both circular) of the same radius and mass,about a tangential axis perpendicular to the plane is

The radius of gyration of a rod of length $L$ and mass $M$ about an axis perpendicular to its length and passing through a point at a distance $L/3$ from one of its ends,is :-