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Question

The atmospheric pressure held in terms of the water column is


A

7.5m

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B

8.5m

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C

9.81m

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D

10.30m

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Solution

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, P1=h1ρ1g, where P1,h1,ρ1,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=ForceArea is the fundamental formula for pressure. Pascal is the unit of strain.

Step 4: Calculations:

Given, h1=76cm

ρ1=13.6gcm2 (Density of mercury)

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

P2=h2ρ2g

h1ρ1g=h2ρ2gh1ρ1=h2ρ2

Substituting the values, we get

h2×1=76×13.6h2=1030cm=10.30m

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


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