The pressure at the bottom of a column of mercury of density 13600 kg/m³ is 50 N/m². Calculate the height of the mercury column.

To calculate the height of the mercury column, we can use the formula for pressure:

P = ρgh

Where:
P = pressure at the bottom of the column (50 N/m²)
ρ = density of mercury (13600 kg/m³)
g = acceleration due to gravity (9.81 m/s²)
h = height of the mercury column

Plugging in the values, we get:

50 = 13600 * 9.81 * h
50 = 133416h
h = 50 / 133416
h ≈ 0.000375 m

Therefore, the height of the mercury column is approximately 0.000375 meters.

Given:

- Density of mercury, ρ = 13600 kg/m³
- Pressure at the bottom of the column, P = 50 N/m²

To find:

- Height of the mercury column, h

Formula:

Pressure due to a liquid column = ρgh

where,

- g is the acceleration due to gravity (9.81 m/s²)
- h is the height of the liquid column

Solution:

Substituting the given values into the formula, we get:

50 N/m² = 13600 kg/m³ - 9.81 m/s² - h

Solving for h:

h = 50 N/m² / (13600 kg/m³ - 9.81 m/s²)

h ≈ 0.0364 m

Therefore, the height of the mercury column is approximately 0.0364 meters.