The height of the mountain would be 1002.048 m
The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
The mathematical expression for the pressure
Pressure = Force /Area
As given in the problem the reading of a mercury barometer is 75.58cm at the base of a mountain and 66.37cm at the summit.
density of mercury =13.6g/m³
=13600 kg/m³
density of air =1.25kg/m³
the gauge pressure of the mercury = the gauge pressure of the air
ρgH for the mercury = ρgH for the air
13600×9.81×(75.58-66.37) = 1.25 ×9.81 ×(height of the mountain )
(height of the mountain) = 100204.8 cm
= 1002.048 m
Thus, the height of the mountain would be 1002.048 m
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