A solid non$-$rotating spherical planet of mass M and radius R is covered uniformly in a thin ocean of depth D $$ R $($no continents or other land masses with nooks and crannies$).$ Now suppose this same planet is rotating uniformly $($w$.$r$.$t$.$ inertial frames$)$ about its polar axis $($z$-$axis$)$ with angular velocity $=0$ z$.$ Put an origin at the center of the planet. Let denote the usual polar angle in spherical polar coordinates $($so the angle between the z$-$axis and a position vector emanating from the origin$).$

a$)$ Determine h$($$),$ the height above the planet$$s surface of sea level as a function of $($if the planet were not rotating, the function would be the constant function h$($$)=$ D$.$

b$)$ At what value of $0$ will the ocean floor first be exposed at the poles?