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Question

A thin tube of uniform cross-section is sealed at both ends. It lies horizontally. The middle 5cm contains Hg and two equal ends contain air at the same pressure P0. When the tube is held at an angle of 60o with the vertical, the length of the air column above and below the Hg are 46cm and 44.5cm. Calculate pressure P0 in cm of Hg. Assume temperature of the system to be constant.

A
55cm of Hg
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B
65cm of Hg
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C
70.4cm of Hg
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D
75.4cm of Hg
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Solution

The correct option is D 75.4cm of Hg
As the length of the tube remains constant, thus
2L+5=46+5+44.5
or
L=45.25cm
In case (ii) PA=PB+5cos60o
or PAPB=2.5cm of Hg
PA(44.5)=PB(46)
or (4644.51)PB=2.5
or PB=2.5×44.51.5
P0(44.25)=PB×46
Thus P0=PB4645.25=2.51.5×44.5×4645.25
=75.4cm of Hg
140027_139752_ans_50a6c4c5ad0244d9a603cea161bd896d.png

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