How high a column of air would be necessary to cause the barometer to read 76 cm of Hg, if the atmosphere were of uniform density #1.2Kg/m^3#? The density of Hg = #13.6*10^3Kg/m^3#

A: 8613 m
B: 8613 cm
C: 8.613 m
D: 8613 mm

1 Answer
Aug 6, 2017

The height is option #(A)=8613m#

Explanation:

The pressure is

#p=rho g h#

The density is #rhokgm^-3#

The height is #hm#

and #g=9.8ms^-2#

Height of the column of air is #h_(air)#

Height of the column of mercury is #h_(Hg)#

Therefore,

#rho_(air)gh_(air)=rho_(Hg) gh_(Hg)#

#h_(air)=(rho_(Hg) h_(Hg))/(rho_(air))=(13.6*10^3*0.76)/1.2=8613m#