Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984 \;kg m^{-3}$. Determine the height (in $m$) of the wine column for normal atmospheric pressure.
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Density of mercury, $\rho_{1}=13.6 \times 10^{3} kg / m ^{3}$
Height of the mercury column, $h_{1}=0.76 m$
Density of French wine, $\rho_{2}=984 kg / m ^{3}$
Height of the French wine column $=h_{2}$
Acceleration due to gravity, $g=9.8 m / s ^{2}$
The pressure in both the columns is equal, i.e.,
Pressure in the mercury column
$=$ Pressure in the French wine column
$\rho_{1} h_{1} g =\rho_{2} h_{2} g$
$h_{2}=\frac{\rho_{1} h_{1}}{\rho_{2}}$
$=\frac{13.6 \times 10^{3} \times 0.76}{984}$
$=10.5 m$
Hence, the height of the French wine column for normal atmospheric pressure is $10.5\; m$
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