$A$ circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2}=2$,then $\frac{T_1}{T_2}=\frac{1}{\alpha}$. The value of $\alpha$ is . . . . . . .

Let $l$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to:

The ratio of the radius of gyration of a circular disc to that of a circular ring,each of the same mass and radius,about their respective central axes is:

For a cube of side $a$ and mass $M$,the moment of inertia is minimum about which axis?

The linear mass density of a thin rod $AB$ of length $L$ varies from $A$ to $B$ as $\lambda(x) = \lambda_{0}(1 + \frac{x}{L})$,where $x$ is the distance from $A$. If $M$ is the mass of the rod,then its moment of inertia about an axis passing through $A$ and perpendicular to the rod is $......ML^{2}$.

One circular ring and one circular disc,both having the same mass and radius. The ratio of their moments of inertia about the axis passing through their centers and perpendicular to their planes will be: