On pouring 15 cm of water and spirit each into the respective arms of the U-tube, the mercury level will rise in the arm containing the spirit.
ρm= density of mercury.
Let us select two points A and B lying in the same horizontal plane asshown.
Thus according to Pascal’s law,
Pressure at A= Pressure at B
or P0+hwρwg=P0+hsρsg+hmρmg
where P0= atmospheric pressure
or hwρw=hsρs+hmρm
or hmρm=hwρw−hsρs
Here, hw= height of water column =10+15=25 cm
hs= height of spirit column =12.5+15=27.5 cm
ρw=1g cm−3;ρs=0.8 g cm−3
ρm= density of mercury =13.6 g cm−3
∴ Substituting in equation (i), we get
hm×13.6=25×1−27.5×0.8
or hm=

25−22.00

13.6

=0.2206 cm
=0.221 cm or hm=0.221 cm
i.e. mercury will rise in the arm containing spirit, by 0.221 cm