$A$ circular disc is to be made by using iron and aluminium,so that it acquires a large moment of inertia about its geometrical axis. This is possible with:

$A$ circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$,and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{t}{4}$. The ratio of the moment of inertia $\frac{I_Y}{I_X}$ is:

The ratio of the radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of a thin hollow sphere of the same mass and radius about its axis is:

$A$ uniform solid cylinder with radius $R$ and length $L$ has a moment of inertia $I_1$ about its central axis. $A$ concentric solid cylinder of radius $R' = \frac{R}{2}$ and length $L' = \frac{L}{2}$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved-out portion of the cylinder about the same axis,then $\frac{I_1}{I_2} = ..........$

If $I_1$,$I_2$,and $I_3$ are the moments of inertia of a solid sphere,a hollow cylinder,and a ring,respectively,all having the same mass and radius,which of the following statements is correct?

$A$ wheel of mass $10 \ kg$ has a moment of inertia of $160 \ kg \cdot m^2$ about its own axis. The radius of gyration is ........ $m.$