Consider a solid sphere of radius R and mass density ρ( r )=ρ_0(1-(r^2)/(R^2)), 0< r ≤ R. The minimum density of a liquid in which it will float is:

Consider a solid sphere of radius R and mass density $\displaystyle \rho(\mathrm{r})=\rho_0\left(1-\frac{\mathrm{r}^2}{\mathrm{R}^2}\right)$, $\displaystyle 0<\mathrm{r} \leq \mathrm{R}$. The minimum density of a liquid in which it will float is :