Question

What length of water column is equivalent to $0.86m$ of mercury column?

Given: density of mercury is $13.6$ times the density of water.

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

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 the water column which will produce the same pressure as height $0.86m$ of the mercury column.

If pressures are equal $h_1{\rho }_{1}g=h_2{\rho }_{2}g$

Then $h_2$ = $\frac{h_1{\rho }_1}{{\rho }_2}$ ( ${\rho }_1$ and ${\rho }_2$ are densities of mercury and water respectively.)

It is given that ${\rho }_1=13.6\times {\rho }_2$

$\Rightarrow \frac{{\rho }_1}{{\rho }_2}=13.6$
Hence, $h_2=13.6\times 0.86$

So, length of water column required = $11.696m$.