Question

A sphere is just immersed in a liquid. Find the ratio of hydrostatic force acting on top and bottom half of the sphere.

Answer 1

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$F_{buoyant}=F_0-F_{s_1}$

$\rho \gamma g=Rg\rho .\pi R^2-F_{s_1}$

$F_{s_2}=\pi R^3\rho g-\rho g\gamma =\pi R^3\rho g-\rho g.\frac{2}{3}\pi R^3$

$F_{s_1}=\pi R^3\rho g\left(\frac{1}{3}\right)$

Similarly, $F_b=F_{s_2}-F_0$

$\Rightarrow F_{s_2}=F_b+F_0=\rho g.\frac{2}{3}\pi R^3+\pi R^3\rho g$

$=\frac{5}{3}\pi R^3\rho g$

$\frac{F_{s_2}}{F_{s_1}}=\frac{5}{1}$