Question

By sucking through a straw, a boy can reduce the pressure in his lungs to $750\,mm\,of\,Hg$ $(density = 13.6\,g/c{m^3})$ . Using a straw, he can drink water from a maximum depth of
A. $13.6\,cm$
B. $1.36\,cm$
C. $0.136\,cm$
D. $10\,cm$

Answer 1

In order to this question, to find the maximum depth or the height, we will first calculate the pressure difference (as we know the value of atmospheric pressure) and then we can equate the density of both the $Hg$ and water, to find the height.

Complete step by step answer:
Given that, Pressure in lungs $= 750mm\,of\,Hg$ and as we know, atmospheric pressure, ${P_{atm}} = 760mm\,of\,Hg$ (Atmospheric pressure, also known as barometric pressure, is the force exerted by an atmospheric column per unit area that is, the entire body of air above the specified area). So, we can find the pressure difference as well-
Now, Pressure difference, $\Delta P = 760 - 750 = 10mm\,of\,Hg$
Now,
$\because 1cm\,of\,Hg = {\rho _{water}}\,gh \\\ \Rightarrow 1{\rho _{Hg}}g = {\rho _{water}}\,gh \\\ \Rightarrow 13.6g = 1\,gh \\\ \therefore h = 13.6\,cm$
Therefore, the required maximum depth is $13.6\,cm$.

Hence, the correct option is A.

Note: The air travels into and out of the lungs due to the pressure difference between the lungs and the atmosphere. When the pressure inside the lungs (intrapulmonary pressure) is less than the atmospheric pressure, or when there is a negative pressure in the lungs in relation to the atmospheric pressure, inspiration occurs.