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Q.

A tube of length /r, which is wide enough to male surface tension effects negligible, is closed at one end. It is then lowered into a tank of mercury to a depth.h as shown in fig. (4), so that mercury rises a distance x into the tube. If the mercury barometer stands at i also, then

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a

(2h−x)(h−x)=h2

b

h(h−x)=h2

c

(2h−x)(h+x)=h2

d

2h(h−x)=h2

answer is A.

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Detailed Solution

At atmospheric pressure, the air fills the tube. Its volume is h a, where a is area of cross section of the tube. Whenthe tube is pushed into mercury, the air volume is (h-x) a  Applying Boyle's law, we haveh⋅ha=(2h−x)(h−x)a or h2=(2h−x)(h−x)
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