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Question

A long U tube is filled with a liquid of density ‘ρ ’ such that length of the tube above liquid is ‘a’ in both arm. One side of tube (right arm) is sealed and the tube is inverted (‘P0’ atmospheric pressure).


A

Liquid will spill out the left tube if a<P04ρg

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B

Liquid will not spill out the left tube for any value of ‘a’

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C

Liquid surface in left arm will not move if a=P02ρg

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D

Liquid surface in right arm will come down

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Solution

The correct options are
A

Liquid will spill out the left tube if a<P04ρg


C

Liquid surface in left arm will not move if a=P02ρg


Let pressure of gas in right arm in inverted position be ‘P’.

P(a+x)=P0.a …(i)

P+2xρg=P0 …(ii)

From (i) and (ii)

x={P02ρga}


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