Chapter 5, Problem 19P

According to Archimedes principle, the buoyancy force is equal to the weight of fluid displaced by the submerged portion of an object. For the sphere depicted in Fig. P5.19, use bisection to determine the height h of the portion that is above water. Employ the following values for your computation: $r=1\text{m,}{\rho }_s=$ density of sphere $=200{\text{ kg/m}}^3,\text{and }{\rho }_w={\text{ density of water =100 kg/m}}^3$. Note that the volume of the above-water portion of the sphere can be computed with

$V=\frac{\pi h^2}{3}\left(3r-h\right)$

FIGURE P5.19