Question

two solid spheres of different materials have the same moments of inertia about their diameters . if r1 and r2 are their radii ratio of their densities is

Answer 1

Dear student
$$\begin{gathered} I_1=I_2 \\ \frac{2}{5}{m}_1{r^2}_1=\frac{2}{5}{m}_2{r^2}_2 \\ \frac{2}{5}\left(\frac{4\pi {r^3}_1\times {\rho }_1}{3}\right){r^2}_1=\frac{2}{5}\left(\frac{4\pi {r^3}_2\times {\rho }_2}{3}\right){r^2}_2 \\ \left(\frac{{r^3}_1\times {\rho }_1}{1}\right){r^2}_1=\left(\frac{{r^3}_2\times {\rho }_2}{1}\right){r^2}_2 \\ {\rho }_1\times {r^5}_1={\rho }_2\times {r^5}_2 \\ \frac{{\rho }_1}{{\rho }_2}=\frac{{r^5}_2}{{r^5}_1} \\ Regards \end{gathered}$$