Question

What length of water column in a given tube has equivalent pressure to $0.86m$ of mercury column? The density of mercury is $13.6$ times the density of water.

• A. $11.696m$
• B. $10.696m$
• C. $11.423m$
• D. $12.696m$

Answer 1

The correct option is A

$11.696m$

Given:
Height of mercury column,
$h_1$ $=0.86m$
Let $h_2$ be the height of water column which will produce the same pressure as height $h_1$ of the mercury column.
${\rho }_1$ and ${\rho }_2$ are densities of mercury and water respectively.
Weight $=W$
mass $=m$
Volume $=V$
Acceleration due to gravity$=g$

Weight of water must equal to the weight of mercury in the column.
$W_{water}=W_{mercury}$
$m_{water}g=m_{mercury}g$
${\rho }_2{V}_{water}g={\rho }_1{V}_{mercury}g$
${\rho }_{2}A{h}_{2}g={\rho }_{1}A{h}_{1}g$

$h_2$ = $\frac{h_1{\rho }_1}{{\rho }_2}$

Given, ${\rho }_1=13.6\times {\rho }_2$

$\frac{{\rho }_1}{{\rho }_2}=13.6$
Hence,
$h_2=13.6\times 0.86$$=11.696m$.