Physics - Rotation Question with Solution | TestHub

Given, mass ratio of two disc ${\mathrm{m}}_1:{\mathrm{m}}_2=1:2\text{ i.e. }\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}=\frac{1}{2}$ and diameter ratio $\frac{{\mathrm{d}}_1}{{\mathrm{d}}_2}=\frac{2}{1}\Rightarrow \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{2}{1}$ $\therefore$ Ratio of their moment of inertia, $\begin{array}{ll}\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=& \frac{\frac{{\mathrm{m}}_1{\mathrm{r}}_1^2}{2}}{\frac{{\mathrm{m}}_2{\mathrm{r}}_2^2}{2}}=\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\cdot {\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2=\frac{1}{2}{\left(\frac{2}{1}\right)}^2=\frac{2}{1}\\ \therefore {\mathrm{I}}_1:{\mathrm{I}}_2=2:1& \end{array}$