Chapter 1, Problem 25P

Use Archimedes' principle to develop a steady-state force balance for a spherical ball of ice floating in seawater (Fig. P1.25). The force balance should be expressed as a third-order polynomial (cubic) in terms of height of the cap above the water line $\left(h\right)$, the seawater's density $\left({\rho }_f\right)$, the ball's density ${\rho }_s$, and the ball's radius $\left(r\right)$.

FIGURE P1.25