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)

Explanation

Let density of water `rho_(1)=1g cm^(-3)` , density of spirit `rho_(2)=0.8gcm^(-3)` , density of mercury
`rho_(3)=13.6g cm^(-3)` , height of water column
`h_(1)=25cm` , height of spirit column `h_(2)=27.5`cm
and let `h_(3)` be the difference between the levels of mercury in the two arms.
Since pressure at A and B are same,
`thereforeP_(0)+h_(1)rho_(1)g=P_(0)+h_(2)rho_(2)g+h_(3)rho_(3)g`
where `P_(0)=` atmospheric pressure.
`thereforeh_(1)rho_(1)=h_(2)rho_(2)+h_(3)rho_(3)` ....(1)

`thereforeh_(3)rho_(3)=h_(1)rho_(1)-h_(2)rho_(2)`
`thereforeh_(2)xx13.6=25xx1-27.5xx0.8`
`thereforeh_(3)=(25-22)/(13.6)`
`thereforeh_(3)=(3)/(13.6)=0.221cm`
Hence , the difference between the levels of mercury in the two arms is 0.221 cm