Question

The column of mercury in a barometer is 76mm of Hg. Calculate the atmospheric pressure if the density of mercury $ = 13600kg{m^{ - 3}} $ . (Take $ g = 10m/{s^2} $ )
(A) $ 1.03 \times {10^5}Pa $
(B) $ 1.03 \times {10^3}Pa $
(C) $ 1.03 \times {10^4}Pa $
(D) $ 1.03 \times {10^6}Pa $

Answer 1

Hint
The atmospheric pressure can be calculated by the formula $ P = h\rho g $ . So we can substitute the values of the height of mercury in the barometer, density, and gravity in the formula and then calculate the value of the atmospheric pressure from there.
In the solution to this question, we use the following formulas,
$\Rightarrow P = h\rho g $
where $ P $ is the atmospheric pressure, $ h $ is the height of mercury in the barometer, $ \rho $ is the density of mercury and $ g $ is the acceleration due to gravity.

Complete step by step answer
In a barometer, as the air pressure pushes down the level of the mercury bath, the height of the mercury in the tube rises and we can measure the height of the mercury. As we are given the values of the density of the mercury and the acceleration due to gravity, so by using the formula for the pressure we can find the atmospheric pressure as,
$\Rightarrow P = h\rho g $
We are provided that the height of mercury in the barometer is, $ h = 76mm = 76 \times {10^{ - 3}}m $
The density of mercury is given as, $ \rho = 13600kg{m^{ - 3}} = 13.6 \times {10^3}kg{m^{ - 3}} $
And the acceleration due to gravity is taken as, $ g = 10m{s^{ - 2}} $
So by substituting these values in the equation we get,
$\Rightarrow P = 76 \times {10^{ - 3}} \times 13.6 \times {10^3} \times 10 $
On doing this product, we get the value of atmospheric pressure as,
$\Rightarrow P = 10336Pa $
This can be written as,
$\Rightarrow P = 1.03 \times {10^4}Pa $
So the atmospheric pressure is $ 1.03 \times {10^4}Pa $ .
Hence the correct option is (C). $ 1.03 \times {10^4}Pa $ .

Note
A barometer is a scientific instrument that can be used to measure the atmospheric pressure in any environment. It consists of an inverted glass tube placed in a bath of mercury. Now as the air pressure on the mercury bath increases, the mercury is pushed upwards in the tube. The height that the mercury rises in the tube gives the value of $ h $ .