Mercury is poured into the communicating vessels. Water was added to one vessel, the column of which was 4 cm high.

Mercury is poured into the communicating vessels. Water was added to one vessel, the column of which was 4 cm high. How high should a column of some liquid in another vessel be so that the level of mercury in both vessels was the same if the density of the liquid is 1.25 times less than the density of water?

For the level of mercury in both vessels to be the same, it is necessary that the pressure of the liquid column in the inlets be balanced by the pressure of the unknown liquid. the pressure of the liquid column is expressed by the formula:

P = d * g * h, where

d – density kg / m3,

g – acceleration of gravity, 9.8 m / s2,

h is the height of the liquid column.

Let be:

P1 = d1 * g * h1 – water column pressure,

P2 = d2 * g * h2 – pressure of a column of unknown liquid.

d1 = 1000 kg / m3,

h1 = 4 cm = 0.04 m,

1.25 * d2 = d1

P1 = P2;

d1 * g * h1 = d2 * g * h2;

1.25 * d2 * h1 = d2 * h2;

h2 = 1.25 * h1 = 1.25 * 4 = 5 cm.

Answer: The height of the unknown liquid column will be 5 cm.