Physics - Rotation Question with Solution | TestHub

The ratio of moment of inertia of the rings

$\frac{{\mathit{I}}_1}{{\mathit{I}}_2}=\frac{{\mathit{\text{M}}}_1}{{\mathit{\text{M}}}_2}{\left(\frac{{\mathit{\text{R}}}_1}{{\mathit{\text{R}}}_2}\right)}^2=\frac{\lambda l_1}{\lambda l_2}{\left(\frac{{\mathit{\text{R}}}_1}{{\mathit{\text{R}}}_2}\right)}^2=\frac{2\pi \mathit{\text{R}}}{2\pi \mathit{\text{nR}}}{\left(\frac{\mathit{\text{R}}}{\mathit{\text{nR}}}\right)}^2$

$\lambda$= linear density of wire = constant

$\Rightarrow \frac{{\mathit{\text{I}}}_1}{{\mathit{\text{I}}}_2}=\frac{1}{{\mathit{\text{n}}}^3}=\frac{1}{8}$given

$\therefore {\mathit{\text{n}}}^3=\mathrm{8 }\Rightarrow \mathit{\text{n}}=2$