The shortest period of rotation of a planet (considered to be a sphere of uniform density $$\rho$$) about its own axis, such that any mass $$m$$ kept on its equator is just about to fly off the surface, is

A

$$T = \sqrt{\frac{5\pi}{3G\rho}}$$

B

$$T = \sqrt{\frac{3\pi}{G\rho}}$$

C

$$T = \sqrt{\frac{3\pi}{ G\rho}}$$

D

$$T = \sqrt{\frac{5\pi}{G\rho}}$$