Question

The atmospheric pressure held in terms of water column is
A) $7.5{\text{ m}}$
B) $8.5{\text{ m}}$
C) $9.81{\text{ m}}$
D) $10.30{\text{ m}}$

Answer 1

Hint: The term "density" refers to the amount of mass per unit of volume. An object's average density is proportional to its total mass divided by its total volume. In the given question, the atmospheric pressure will remain the same, only the density of the water and height of the water column will be different from that of mercury.

Complete step by step answer:
The physical force applied on an object is known as pressure. The force exerted per unit area is perpendicular to the surface of the material.
$P = \dfrac{{{\text{Force}}}}{{\text{Area}}}$ is the fundamental formula for pressure. Pascal is the unit of strain. Absolute, atmospheric, differential, and gauge pressures are examples of pressure types.
The pressure would be the same if mercury or water is used; the only distinction is the density of the solvent and the fluid's height. Mercury stands at a height of 76 cm. We know that for Mercury,
${P_1} = {h_1}{\rho _1}g$
Given ${h_1} = 76{\text{ cm}}$
${\rho _1} = 13.6{\text{ g/c}}{{\text{m}}^3}$ -- Density of Mercury
Let the height of the water column be assumed as hm
Now, for water
${P_2} = {h_2}{\rho _2}g$
where Density of water ${\rho _2} = 1{\text{ g/c}}{{\text{m}}^3}$
Since,
${P_1} = {P_2}$
$ \Rightarrow {h_1}{\rho _1}g = {h_2}{\rho _2}g$
Substituting the values we get,
${h_2} \times 1 = 76 \times 13.6$
${h_2} = 1030{\text{ cm}}$
${h_2} = 10.30{\text{ m}}$
Hence, the height of the water column at standard atmospheric pressure of $76{\text{ cm}}$
of mercury is $10.30{\text{ m}}$

Note:
A barometer is a scientific device that measures air pressure in a specific area. Short-term weather variations can be predicted using pressure trends. Surface weather mapping employs a variety of atmospheric pressure sensors to locate surface troughs, pressure systems, and frontal borders.