The moment of inertia of a regular circular disc of mass $0.4\, kg$ and radius $100\, cm$ about an axis perpendicular to the plane of the disc and passing through its centre is ...... $kg\, m^2$.

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 centre 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 $nr$). (in $\sqrt{2}$)

The moment of inertia of a cylinder of mass $M$,length $L$,and radius $R$ about an axis passing through its centre and perpendicular to the axis of the cylinder is $I = M \left(\frac{R^2}{4} + \frac{L^2}{12}\right)$. If such a cylinder is to be made for a given mass of material,the ratio $L/R$ for it to have the minimum possible $I$ is

$A$ rod has a length of $1 \ m$ and a mass of $0.12 \ kg$. The moment of inertia about an axis passing through its center and perpendicular to its length is ...... $kg \cdot m^2$.

$A$ flywheel is constructed such that its entire mass is concentrated at its rim,because......

Two rings made of the same material and having the same thickness have radii of $0.2 \ m$ and $0.6 \ m$. The ratio of their moments of inertia is: