Question

At sea level, the atmospheric pressure is 76cm of Hg. If air pressure falls by 10mm of Hg per 120m of ascent, what is the height of a hill where the barometer reads 70cm of Hg?
A. 720m
B. 760m
C. 720cm
D. 760cm

Answer 1

Hint: We are given the pressure fall with every 120m of ascent, from which we get the ascent for the fall in pressure of 1cm of Hg. We could find the total pressure difference between the sea level and the top of the hill from the given values. Now you could multiply this difference with the ascent caused above to get the height of the hill.

Complete step-by-step solution
In the question, we are given the atmosphere pressure (P) as 76cm of Hg. We are also told that the air pressure falls by 10mm of Hg with every 120m of ascent. We are also given the barometer reading $\left( P' \right)$ at the top of a hill as 70cm of Hg. With all this given information, we are asked to find the height of a hill.
So the rate at which the pressure falls is given as 10mm of Hg for every 120m of ascent, that is, 1cm of Hg for every 120m ascent.
Total fall in pressure from the sea level to the top of the hill could be obtained from the difference of the pressure measured at sea level and that at the top of the hill. Therefore, the total fall in pressure is given by,
$P-P'=76-70=6cmHg$
If pressure fall of 1cm of Hg indicates ascent of 120m, that is,
$1cmHg\to 120m$
$\Rightarrow 6cmHg\to 6\times 120m$
$\therefore 6cmHg\to 720m$
That is, the height of the hill is found to be 720m.
Hence, option A is the correct answer to the given question.

Note: The collision of the air molecules with surface results in atmospheric pressure. We know that the atmospheric pressure falls with the increase in altitude. This happens because, with the increase of altitude, the number of molecules decreases and so does the pressure. It is due to this reason that we pressurize the aircraft that fly at high altitudes to aid breathing for the passengers.