Question

A cylinder is filled with a liquid of density $d$ upto a height $h$. If the beaker is at rest, then the mean pressure on the wall is :-

• A. $Zero$
• B. $hdg$
• C. $\frac{h}{2}dg$
• D. $2hdg$

Answer 1

Answer: (C)

$\frac{h}{2}dg$

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 $P=dxg$

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

Avg force across the cylinder will be,

$<F>=\frac{{\int }_0^{h}dxgk.\left(dx\right)}{kh}$

$<F>=hdg/2$