$A$ 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 ........ $m.$

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

From a uniform wire,two circular loops are made: $(i)\ P$ of radius $r$ and $(ii)\ Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its center and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).

Two solid spheres of iron have radii in the ratio $1 : 2$. Their moments of inertia will be in the ratio

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is:

Two circular rings $A$ and $B$ of radii $nR$ and $R$ are made from the same wire. The moment of inertia of $A$ about an axis passing through the centre and perpendicular to the plane of $A$ is $64$ times that of the ring $B$. The value of $n$ is: