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