(a) Derive an expression for the buoyant force on a spherical balloon, submerged in water, as a function of the depth h below the surface, the volume Vi of the balloon at the surface, the pressure P0 at the surface, and the density rw of the water. Assume the water temperature does not change with depth. (b) Does the buoyant force increase or decrease as the balloon is submerged?
(c) At what depth is the buoyant force onehalf the surface value?