Question

A boy can reduce the pressure in his lungs to 750 mm of mercury. Using a straw, he can drink water from glass up to the maximum depth of (atmospheric pressure = 760 mm of mercury; density of mercury = $13.6gc{m^{ - 3}}$)
(A) 13.6 cm
(B) 9.8 cm
(C) 10 cm
(D) 76 cm
(E) 1.36 cm

Answer 1

Pressure drop in the lungs is used to pull the fluid in a straw. We will first calculate the pressure difference of the lungs of the student and atmosphere. Then we will use $P = \rho \,h\,g$ to calculate he can drink water from glass up to the maximum depth.

Complete step by step answer:
Static fluid pressure:
It is pressure exerted by fluids on the walls of the container when it is at rest. It is independent of the shape, mass and surface of the container. It only depends on density of fluid, depth of container, and acceleration due to gravity.
In general pressure is force per unit area.
Pressure = $\frac{{Force}}{{Area}}$
$\Rightarrow P = \frac{{mass \times acceleration}}{{Area}}$
$\left[ {density\,\,(\rho ) = \frac{{mass\,(m)}}{{volume\,\,(V)}}} \right]$
$\Rightarrow m = \rho V$
Using mass formula in pressure formula, we get
Also,
$volume = area\, \times \,height$
Height=h
Area=A
Acceleration due to gravity= g
$P = \,\frac{{m \times \,g}}{A}$
$\Rightarrow P = \frac{{\rho V \times g}}{A}$
$\Rightarrow P = \frac{{\rho \times A \times h \times g}}{A}$
$\Rightarrow P = \rho \,h\,g$
Pressure of lungs of student = 750 mm of Hg
Atmospheric pressure = 760 mm of Hg
Difference in pressure of lungs of student and atmosphere = (760 mm - 750 mm) of Hg
= 10 mm of Hg
(1 mm = 0.1 cm)
= 1 cm of Hg
This pressure difference helps the student to take water inside his body.
Pressure created due to water column = 1 cm of Hg
Now we can compare this pressure in terms of Hg column with the pressure in terms of water column:
Density of mercury $= 13.6gc{m^{ - 3}}$
Putting the values in equation $P = \rho \,h\,g$, we get
$1 = 13.6 \times g$ … (1)
Similarly, pressure exerted by water,
$1 = 1 \times h \times g$ … (2)
Equating (1) and (2), we get
h=13.6 cm

Therefore, the correct solution is option A.

Note:
If the units are used in mm only and not converted to cm then this might create trouble and solution will get altered.
Secondly considering pressure difference (10 mm) directly as height is again a wrong concept. Option C is also wrong.
Also, the value of g is 9.8 and we know that acceleration due to gravity is not equal to the height of the container, so option B is also not correct.
Therefore, the correct option is A.