Earth is rotating about its axis with angular speed w0 and average density of earth is r. It is proposed to make a space

[answerhappygod]

Earth is rotating about its axis with angular
speed w0 and average density of earth is r. 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 n
2 G 2 8 3
+ = p r
w
, where r is
density of the earth