A barometer reads 75 cm of Hg. When 2cc of air at atmpospheric pressure is introduced into the space above the mercury level, the volume of this space becomes 50 cc. The length by which the mercury column descends is
A
3 cm
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B
6 cm
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C
1.5 cm
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D
25 cm
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Solution
The correct option is A 3 cm initially barometer reads 75 cm , so atmosphere pressure Pa=ρg(0.75) gas is added at atmosphere pressure, with initial volume 2cc later volume expands to 50cc. This is isothermal process, by boyle's law P2V2=P1V1 P2=P1V1V2 since P1=Pa P2=ρg(0.75)×250 P2=ρg(0.03) applying hydro-static pressure equation(as shown in image) P2+ρgh=Pa ρg(0.03)+ρgh=ρg(0.75) h=0.72m=72cm descend in mercury column is = 75−72=3cm