Physics - Rotation Question with Solution | TestHub

$I_1{\omega }_1=I_2{\omega }_2$

${\rho }_1\frac{4}{3}\pi r_1^3={\rho }_2\frac{4}{3}\pi r_2^3$

${\rho }_1{r}_1^3={\rho }_2{r}_2^3$

$r_2={\left(\frac{{\rho }_1}{{\rho }_2}\right)}^{\frac{1}{3}}{r}_1$

$T=\frac{2\pi }{\omega }$

$\Rightarrow \frac{T_1}{T_2}=\frac{I_1}{I_2}$

$T_2=T_1\frac{I_2}{I_1}$

$=T_1{\left(\frac{{\rho }_1}{{\rho }_2}\right)}^{\frac{2}{3}}$

$=24\left(\frac{1}{4}\right)=6\mathrm{h}$