NEET-XII-Physics

13: Fluid Mechanics

with Solutions - page 2
Qstn# ii-11 Prvs-QstnNext-Qstn
  • #11
    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
    digAnsr:   d
    Ans : (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, `` {\,\mathrm{\,P\,}}_{0}>0``.
    Using this relation, we get:
    `` {P}_{\,\mathrm{\,atm\,}}={P}_{0}+\,\mathrm{\,\rho \,}gh``
    `` \,\mathrm{\,Here\,},``
    `` \,\mathrm{\,\rho \,}=\,\mathrm{\,Density\,}\,\mathrm{\,of\,}\,\mathrm{\,mercury\,}``
    `` h=\,\mathrm{\,Height\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,mercury\,}\,\mathrm{\,column\,}``
    `` \because {P}_{0}>0``
    `` \,\mathrm{\,And\,},``
    `` {P}_{\,\mathrm{\,atm\,}}>\,\mathrm{\,\rho \,}gh``
    `` \therefore 76\,\mathrm{\,cm\,}\,\mathrm{\,of\,}\,\mathrm{\,Hg\,}>\,\mathrm{\,\rho \,}gh``
    `` \,\mathrm{\,or\,},h<76\,\mathrm{\,cm\,}``
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