Question

What length of water column has an equivalent pressure to $0.86\text{m}$ of mercury column if the density of mercury is $13.6$ times that of water? (Assume both the liquids are in identical tubes) $\left[1\text{mark}\right]$

A. $11.696\text{m}$
B. $10.696\text{m}$
C. $13.423\text{m}$
D. $12.696\text{m}$

Answer 1

Correct answer: option A $-$ $11.696\text{m}$

Given:
Height of mercury column,
$h_1$ $=0.86\text{m}$
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.

Acceleration due to gravity$=g$

Pressure of water must equal to the pressure of mercury in both the columns.

${\rho }_{2}g{h}_2={\rho }_{1}g{h}_1$

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

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

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