Physics - Fluid Question with Solution | TestHub

Force due to atmospheric pressure = ρ₀A = ρ​gH × bH

F₁= ​ρgbH²

​${\text{Force due to mercury on side wall, F}}_2=\frac{\text{ρ}\text{g}\text{b}{\text{H}}^2}{2}$

This force acts at a height H₁= H/2 from bottom

This force acts at a height H₂= H/3 from bottom.

$\therefore \text{distance of net force from bottom}=\frac{{\text{F}}_1{\text{H}}_2+{\text{F}}_2{\text{H}}_2}{{\text{F}}_1+{\text{F}}_2}$

$=\frac{\text{ρ}\text{g}\text{b}{\text{H}}^2\times \frac{\text{H}}{2}+\text{ρ}\text{gb}\times \frac{{\text{H}}^2}{2}\times \frac{\text{H}}{3}}{\text{ρ}\text{gb}{\text{H}}^2+\text{ρ}\text{gb}\frac{{\text{H}}^2}{2}}=\frac{4}{9}\text{H}=\text{32 cm.}$