Question

The atmospheric pressure held in terms of the water column is

• A. $7.5m$
• B. $8.5m$
• C. $9.81m$
• D. $10.30m$

Answer 1

The correct option is D

$10.30m$

Step 1: Given data:

Pressure = Atmospheric pressure

Step 2: Formula used:

1. The pressure would be the same if water or mercury is used; the only difference is the density and the fluid's height.
2. Mercury stands at a height of $76cm$.
3. We know that for Mercury, $P_1=h_1{\rho }_{1}g$, where $P_1,h_1,{\rho }_1,g$ are pressure, height, density, and gravity respectively.

Step 3: Pressure

1. The physical force applied to an object is known as pressure. The force, which is exerted per unit area is perpendicular to the surface of the material.
2. Mathematically, $P=\frac{\text{Force}}{\text{Area}}$ is the fundamental formula for pressure. Pascal is the unit of strain.

Step 4: Calculations:

Given, $h_1=76cm$

${\rho }_1=13.6\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^2$}\right.$ (Density of mercury)

Let us assume the height of the water column as $hm.$
Now, for water

$P_2=h_2{\rho }_{2}g$

$$\begin{gathered} \Rightarrow h_1{\rho }_{1}g=h_2{\rho }_{2}g \\ \Rightarrow h_1{\rho }_1=h_2{\rho }_2 \end{gathered}$$

Substituting the values, we get

$$\begin{gathered} h_2\times 1=76\times 13.6 \\ {h}_2=1030cm=10.30m \end{gathered}$$

Hence, the height of the water column at standard atmospheric pressure of 76 cm of mercury is $10.30m$.