Physics - Fluid Question with Solution | TestHub

The pressure at the top surface of the liquid (just below the piston) is the sum of the atmospheric pressure and the pressure exerted by the weight of the piston.

$P_{\text{top}}=P_0+\frac{mg}{A}=P_0+\frac{mg}{\pi r^2}$

The pressure at the bottom of the cylinder is the pressure at the top surface plus the pressure due to the liquid column of height $h$.

$P_{\text{bottom}}=P_{\text{top}}+\rho gh=P_0+\frac{mg}{\pi r^2}+\rho gh$

The force at the bottom of the cylinder is the pressure at the bottom multiplied by the area of the base.

$F=P_{\text{bottom}}\times A=\left(P_0+\frac{mg}{\pi r^2}+\rho gh\right)\pi r^2$

Answer: $\left(P_0+\frac{mg}{\pi r^2}+\rho gh\right)\pi r^2$