Question

A narrow glass tube, 80 cm long and opens at both ends, is half immersed in mercury, now the top of the tube is closed and is taken out of mercury. a column of mercury 20 cm long remains in the tube. find atmospheric pressure
A- 20 cm of air column
B- 60 cm of Hg column
C- 60 cm of air column
D- 20 cm of Hg column

Answer 1

Hint: Here we need to find atmospheric pressure, it is the air pressure exerted by the column of air which surrounds our earth, the origin of pressure has its roots in the force which air exerts because air has weight.

Complete step by step answer:The total length of the column is 80 cm and is open at both the ends. It is initially half immersed, so 40 cm is inside and 40 cm is outside.
When the half tube is inside and is immersed in the mercury, the air pressure inside the tube should be equal to the mercury pressure in the other half.
So, \[P=\rho gh=40\rho g\]---(1)
Now, the tub is removed with the upper end to be closed, the pressure inside remains the same. The other end is open, thus, \[\Rightarrow {{P}_{0}}=P+\rho g{{h}_{1}}\]
Using eq (1) to substitute the value of P we get,
\[\begin{align}
  & {{P}_{0}}=\rho gh+\rho g{{h}_{1}} \\
\Rightarrow & \rho g(40+20) \\
\Rightarrow & 60\rho g \\
\end{align}\]
\[\therefore \] atmospheric pressure will be equal to 60 cm of Hg. So, the correct option is (B)

Note:To measure atmospheric pressure we use a barometer. It is a widely used instrument to capture the intensity of pressure at any point on the surface of the earth. There are many units to measure pressure, SI unit is Pascals.