Derive an expression for the buoyant force on a spherical balloon as it is submerged in water as a function of the depth below the surface, the volume of the balloon at the surface, the pressure at the surface, and the density of the water. (Assume water temperature does not change with depth.) (b) Does the buoyant force increase or decrease as the balloon is submerged? (c) At what depth does the buoyant force decrease to one-half the surface value?