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Question

A 100cm long thin tube (sealed at both ends) lies horizontally, in the middle 0.1m containing mercury and the two ends containing air at standard atmospheric pressure. If the tube is turned to a vertical position, by what amount will the mercury be displaced?

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Solution

When the tube is horizontally placed:(shown in fig.)
When the tube is vertically placed:(shown in fig.)
Let the area of the tube be 'a'
Boyle's law:P1V1=P2V2
For the chamber A: (76×45a)=PA×(45+d)a
PA=76×4545+d
For the chamber B: (76×45a)=PB×(45d)a
PB=76×4545d
Also PA+10=PB
=76×45+(450+10d)45+d=76×4545d
Cross multiplying we get, 10d2+6840d20250=0
d=3cm

993911_1050352_ans_9a0acf64cf714b44aa371ac5fdfcb61a.JPG

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