Question

If mercury is replaced with water in barometer, what would be the height of water column at standard atmospheric pressure, i.e., $76cm$ of mercury? (Specific gravity of mercury $=13.6$)

• A. $1033.6m$
• B. $1033.6cm$
• C. $1033.6mm$
• D. $10336cm$

Answer 1

The correct option is B

$1033.6cm$

Let ${\rho }_m$, $h_m$ and ${\rho }_w$, $h_w$ be the densities and heights of the columns of mercury and water respectively.
Let $P_0$ be the atmospheric pressure.
For mercury:
$P_0={\rho }_{m}g{h}_m$
For water:
$P_0={\rho }_{w}g{h}_w$

$⟹{\rho }_{m}g{h}_m={\rho }_{w}g{h}_w$
$h_w=\frac{{\rho }_m{h}_m}{{\rho }_w}---\left(1\right)$
Given, specific gravity of mercury is $13.6$. Hence,
$\frac{{\rho }_m}{{\rho }_w}=13.6$
Substituting in (1) we get:
$h_w=13.6\times 76cm$
$h_w=1033.6cm$