The density of mercury is 13.5 times greater than the density of water. If you were to build a barometer that used water instead of mercury to record the standard pressure at sea level, what would be the height of that barometer?

Height of barometer using water column = 10.26 m

Explanation:

Pressure can be written as p = h d g

Where ,

h= Height of liquid column

d=Density of liquid

g= Acceleration due to gravity

Case 1 - Mercury in the barometer

h1= Height of mercury column

d1=Density of mercury

Case 2 - Water in the barometer

h2= Height of water column

d2=Density of water

Since atmospheric pressure is same for water and mercury column.

Atmospheric pressure = h1d1g = h2d2 g

or, h1d1 = h2d2

Given

h1 = 0.76 m (Atmospheric pressure corresponding to mercury column)

d1=13.5d2

Hence, h2 = h1 x 13.5 = 0.76 x 13.5=10.26 m

Height of barometer using water column = 10.26 m

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