An Air Column of 12cm lenght is trapped by a mercury column of 16cm long in a cappillary tube of uniform bore what would the lenght of the air column when the tube is kept vertically with its open end down?

Question

anonymous · Answer

The atmospheric pressure is equivalent to 76 cm of Hg column.

Initially when it was kept upright -
     The upward pressure due to the air column of 12 cm length(say p1)= Atmospheric pressure + pressure due to the mercury column 

  So, p1 = 76 + 16 = 92cm of Hg column.

When it is flipped over-
 Atmospheric pressure = pressure due to mercury column+ pressure due to the air column of unknown length(say p2)

that gives, p2=60cm Hg

Initial volume(v1)=12*A where A is area of the capillary tube
Final volume(v2)=x*A where x is the final length of the air column

p1*v1=p2*v2

which gives x=18.4cm

anonymous · Answer

@Diwakar  the options are  9.9cm    13.8cm    14.6cm    15.2cm

anonymous · Answer

Got it!
I took the tube to be standing vertically with its mouth above in the previous solution.
If we took the tube to be lying horizontally in the initial case, the pressure due to the air column would have been equal to atmospheric pressure = 76cm

The final presasure would have been the same=92cm
Application of Boyle's law now would give us x=15.2cm.

anonymous · Answer

@Diwakar

anonymous · Answer

Yes.

shubhamsrg · Answer

just a slight correction,
final pressure = 60 and not 92, diwakar must be knowing this, just a silly mistake on his part..
on that substitution, we get the ans as predicted by him..

anonymous · Answer

Thank you  for pointing that out shubhamsrg. I am sorry for that.

shubhamsrg · Answer

lol..sorry kya bhai,,chalta hai,,me,,am the king of blunders! :D