Question

The given figure shows a mercury barometer. The atmospheric pressure is 101,293 Pa. Find the pressure at points A, B and C.
(Density of mercury = 13.6 g/cc)

• A. $P_A=0$
• B. $P_B$ = 66640 Pa
• C. $P_C$ = 101293 Pa
• D. $P_C$ = 82987 Pa

Answer 1

Answer: (A), (B), (C)

The correct options are
A $P_A=0$
B $P_B$ = 66640 Pa
C $P_C$ = 101293 Pa

We know, pressure of vacuum is equal to zero, $P_A$ = 0

Pressure at point B = $P_B$ = pressure for 50 cm of mercury column
Atmospheric pressure = 101,293 Pa = 76 cm of Hg
So for 50 cm of Hg $P_B$ = $\frac{50}{76}\times 101,293$ = 66,640 Pa
Or we can also calculate as
Pressure at point B = $P_B$ = $\rho g{h}_B$
where $\rho$ = density of mercury
and $h_B$ = height of the mercury column from zero pressure to point B = 50 cm
So, $P_B$ = $13600\times 9.8\times 0.5$ = 66640 Pa

Similarly, pressure at point C = $P_C$ = $\rho$ g$h_C$
where $h_C$ = height of mercury column from zero pressure line = 50 + 26 cm = 76 cm
So, $P_C$ = $13600\times 9.8\times 0.76$ = 101293 Pa
Or
Since, Point C lies horizontal to the left arm of the barometer so the pressure will be 76 cm of Hg.