If G is the universal gravitational constant and $\rho$ is the uniform density of a spherical planet. Then the shortest possible period of rotation of the planet can be

Question

$$(a)\;\sqrt {\frac{\pi G}{2 \rho}} \quad (b)\;\sqrt {\frac{3 \pi G}{\rho}} \quad (c)\;\sqrt {\frac{\pi}{6 G \rho}} \quad (d)\;\sqrt {\frac{3 \pi}{G\rho}}$$