Answer
$M=5\times 10^{24}Kg$
Work Step by Step
We know that:
$g=a_g-{\omega}^2R$
When $g=0$, then
$0=a_g-{\omega}^2R$
But we also know that $a_g=\frac{GM}{R^2}$.
Thus, by substitution, the above equation becomes $0=\frac{GM}{R^2}-{\omega^2R}$
Rearranging this equation,
$M=\frac{R^3{\omega^2}}{G}$
$\omega=2{\pi}\frac{rad}{s}$
We then plug in the known values to obtain:
$M=\frac{(20000)^3\times (2{\pi)^2} }{6.67\times 10^{-11}}$
$M=4.7\times 10^{24}$
$M=5\times 10^{24}Kg$
