Question

A beaker is filled with a liquid of density $\rho$ upto a height h. If the beaker is at rest , the mean pressure on the walls is

• A. $0$
• B. $h\rho g$
• C. $\frac{h\rho g}{2}$
• D. $2h\rho g$

Answer 1

Answer: (C)

$\frac{h\rho g}{2}$

Let the atmospheric pressure be considered as negligible.

From the surface of water as we move downwards , the pressure will keep on increasing.

Pressure at any depth $x$ will be $P=\rho xg$

The force exerted on any area will be $kdx$ where $k$ is the perimeter of the cylinder, $dF=PdA=\rho xgk.\left(dx\right)$

Average force across the cylinder will be,

$F=\frac{{\int }_0^h\rho xgk.\left(dx\right)}{kh}$

$F=\frac{h\rho g}{2}$