A satellite can be in a geostationary orbit around the earth at a distance r from the center. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the center is

Question

$$(a)\;\frac{n}{2} \quad (b)\;\frac{r}{2 \sqrt 2} \quad (c)\;\frac{r}{(2)^{1/3}} \quad (d)\;\frac{n}{(4)^{1/3}}$$