The ratio of the radius of gyration of a circular disc about an axis in its plane and tangent to it,to the radius of gyration of a circular ring about an axis in its plane and tangent to it is .........

Four point masses $m, 2m, 3m$ and $4m$ are kept at the corners $A, B, C$ and $D$ respectively of a square $ABCD$ of side '$b$'. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through the point $D$ is (in $mb^2$)

List-$I$	List-$II$
$(a)$ $MI$ of the rod (length $L$,mass $M$,about an axis $\perp$ to the rod passing through the midpoint)	$(i) \frac{8ML^2}{3}$
$(b)$ $MI$ of the rod (length $L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends)	$(ii) \frac{ML^2}{3}$
$(c)$ $MI$ of the rod (length $2L$,mass $M$,about an axis $\perp$ to the rod passing through its midpoint)	$(iii) \frac{ML^2}{12}$
$(d)$ $MI$ of the rod (length $2L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends)	$(iv) \frac{2ML^2}{3}$

Choose the correct answer from the options given below:

The moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod is $2400 \,g \,cm^2$. The length of the $400 \,g$ rod is nearly: (in $\,cm$)

Two circular discs of iron have the same thickness. The diameter of disc $A$ is twice that of disc $B$. The moment of inertia of $A$ will be ........ times that of $B$.

Two circular loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $R_1$ and $R_2$ respectively. The moments of inertia about their own axis are $I_{P}$ and $I_{Q}$ respectively. If $\frac{I_{P}}{I_{Q}}=\frac{1}{8}$,then $\frac{R_2}{R_1}$ is