Earth is rotating about its axis with angular speed `Omega_(0)`and average density of earth is `rho`. It is proposed to make a space elevator by placing a long rod with uniform mass density extending from just above the surface for the earth out to a radius nR (R is radius of the earth). Prove that the rod can remain above the same point on the equator all time if, `n^(2)+n=(8piGp)/(3omega^(2))` density of the earth