Two rings of radius R and nR made up of same material have the ratio of moment of inertia about an axis passing through centre as 1 : 8. The value of n is :

mass of a ring is proportional to its circumference and circumference is proportional to radius r

hence moment of inertia 

$$\begin{gathered} I=m{r}^2 \\ I\propto m{r}^2 ; hence I\propto r^3 \\ if \frac{I_1}{I_2}={\left(\frac{r_1}{r_2}\right)}^3=\frac{1}{8} \\ \frac{r_1}{r_2}=\frac{1}{n} n=2 \end{gathered}$$