Consider a solid sphere of radius \( R \) and mass density \( \rho(r)=\rho_{0}\left(1-\frac{r^{2...

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Consider a solid sphere of radius \( R \) and mass density \( \rho(r)=\rho_{0}\left(1-\frac{r^{2}}{R^{2}}\right), 0r \leq R \). The minimum density of a liquid in which it will float is
(a) \( \frac{\rho_{0}}{3} \)
(b) \( \frac{2 \rho_{0}}{5} \)
(c) \( \frac{2 \rho_{0}}{3} \)
(d) \( \frac{\rho_{0}}{5} \)
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