A spherical planet of uniform density ρ \rho\,ρ rotates about its axis. Loose material at the equator is on the verge of losing contact with the surface. What is the period of rotation of the planet?
3πGρ\sqrt{\frac{3\pi}{G\rho}}Gρ3π
34πGρ\sqrt{\frac{3}{4\pi G\rho}}4πGρ3
2π3Gρ2\pi\sqrt{\frac{3}{G\rho}}2πGρ3
Gρ3π\sqrt{\frac{G\rho}{3\pi}}3πGρ
