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A solid sphere of radius $r$ is floating at the interface of two immiscible liquids of densities $\rho_1$ and $\rho_2\,\, (\rho_2 > \rho_1),$ half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is $h.$ The force exerted on the sphere by the upper liquid is $($ atmospheric pressure $= p_0\,\,\&$ acceleration due to gravity is $g) $
$p_0\pi r^2 + (h -2/3r)\pi r^2\rho_1g$
$(h -2/3r)\pi r^2\rho_1g$
$2/3r\pi r^2\rho_1g$
$p_0\pi r^2$
Solution
$\mathrm{PA}-\mathrm{F}=\mathrm{F}_{\mathrm{B}}=\frac{2 \pi}{3} \mathrm{r}^{3} \rho_{1} \mathrm{g}$
$\left(\mathrm{P}_{0}+\rho_{1} \mathrm{gh}\right) \pi \mathrm{r}^{2}-\mathrm{F}$
$=\frac{2 \pi}{3} \mathrm{r}^{3} \rho_{1} \mathrm{g}$
$\mathrm{F}=\mathrm{P}_{0} \pi \mathrm{r}^{2}+\left(\mathrm{h}-\frac{2}{3} \mathrm{r}\right) \pi \mathrm{r}^{2} \rho_{1} \mathrm{g}$
