In the previous problem, if $15.0 \;cm$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury$= 13.6$)
In the previous problem, if $15.0 \;cm$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury$= 13.6$)
Height of the spirit column, $h_{1}=12.5 cm =0.125 m$
Height of the water column, $h_{2}=10 cm =0.1 m$
$P_{0}=$ Atmospheric pressure
$\rho_{1}=$ Density of spirit
$\rho_{2}=$ Density of water
Pressure at point $B =P_{0}+h_{1} \rho_{1} g$
Pressure at point $D =P_{0}+h_{2} \rho_{2} g$
Pressure at points $B$ and $D$ is the same. $P_{0}+h_{1} \rho_{1} g =h_{2} \rho_{2} g$
$\frac{\rho_{1}}{\rho_{2}}=\frac{h_{2}}{h_{1}}$
$=\frac{10}{12.5}=0.8$
Therefore, the specific gravity of spirit is $0.8 .$
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