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  4. Torricelli’s barometer used mercury but Pascal duplicated it using French wine of density 984 kg m-3 . In that case, the height of the wine column for normal atmospheric pressure is (Take the density of mercury = 13.6 × 103 kg m-3 )

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Q. Torricelli’s barometer used mercury but Pascal duplicated it using French wine of density $ 984 \,kg \,m^{-3} $ . In that case, the height of the wine column for normal atmospheric pressure is (Take the density of mercury $ = 13.6 \times 10^{3} \,kg\, m^{-3} $ )

Mechanical Properties of Fluids

Solution:

As $ P =h \rho g $
Height of mercury column in Torricelli ’s barometer
$ =0.76 \, m $ of Hg,
$ \rho_{\text{mercury}}=13.6 \times10^{3}\, kg\, m^{-3} $ ,
$ \rho_{\text{french wine}}=984 \, kg \, m^{-3} $
or $ 0.76\times\left(13.6\times10^{3}\right)\times9.8=h \times984 \times9.8 $
or $ h=\frac{0.76\times13.6\times10^{3}\times9.8}{984\times9.8} $
$ =10.5\,m $