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)

Given, the initial level of the water and the spirit is 10.0 cm and 12.5 cm respectively and an extra 15 cm of the water and the spirit are poured in the respective columns.

Let ρ 1 and ρ 2 be the densities of the water and the spirit respectively and h 1 and h 2 be the height of the water and the spirit in the columns respectively.

The height of the water in the column is,

h 1 =10 cm+15 cm =25 cm

The height of the spirit in the column is,

h 2 =12.5 cm+15 cm =27.5 cm

Let the difference between the height of mercury in both the columns be h'.

The hydrodynamic pressure is given by the equation,

P=ρgh'

The difference between the pressure exerted by the water and the spirit is given by the equation,

P= ρ 1 g h 1 − ρ 2 g h 2

Substituting the values in the above equation, we get:

ρgh'= ρ 1 g h 1 − ρ 2 g h 2 ρh'= ρ 1 h 1 − ρ 2 h 2

Substituting the values in the above equation, we get:

13.6 g/ cm 3 ×h'=1 g/ cm 3 ×25 cm−0.8 g/ cm 3 ×27.5 cm h'=0.221 cm

Hence, the difference in the level of mercury in the two columns is 0.221 cm.