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Question

To construct a barometer, a tube of length 1 m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76 cm. Suppose a 1 m tube is filled with mercury up to 76 cm and then closed by a cork. It is inverted in a mercury cup and the cork is removed. The height of mercury column in the tube over the surface in the cup will be
(a) zero
(b) 76 cm
(c) > 76 cm
(d) < 76 cm

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Solution

(d) < 76 cm

Because of the trapped air, the pressure at the upper end of the mercury column inside the tube is not zero.
In other words, P0>0.
Using this relation, we get:
Patm=P0+ρghHere,ρ=Density of mercuryh=Height of the mercury columnP0>0And,Patm>ρgh76 cm of Hg>ρghor, h<76 cm

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