Question

At a given place, a barometer records 70 cm of mercury. If the mercury in the barometer is replaced by water, what would be the resulting reading? Take density of mercury = 13600 kg/m³ and density of water = 1000 kg/m³.

Answer 1

Step 1. Given data

Height of the mercury column, $h_m=70cm=0.7m$,

Density of mercury, ${\rho }_m=13600kg/m^3$,

Density of water, ${\rho }_w=1000kg/m^3$, and

To find, Height of water column, $h_w$

Acceleration due to gravity, $g=9.8m/s^2$

Step 2. Formula used
Atmospheric pressure measured by the barometer before and after replacing the barometer with water will remain the same because atmospheric pressure at a place remains constant and therefore

${\rho }_w\times g\times h_w={\rho }_m\times g\times h_m$

Step 3. Calculation

${\rho }_w\times g\times h_w={\rho }_m\times g\times h_m$

Substituting the given values in equation (a), we get

$$\begin{gathered} 1000kg/m^3\times g\times h_w=13600kg/m^3\times g\times 0.7m \\ {h}_w=\frac{13600kg/m^3\times 0.7m}{1000kg/m^3} \\ {h}_w=9.52m \end{gathered}$$

Step 4. Final answer

The height of the water column is equal to 9.52 m.