Question

A 1.00-m-tall container is filled to the brim, partway with mercury and the rest of the way with water. The container is open to the atmosphere. What must be the depth of the mercury so that the absolute pressure on the bottom of the container is twice the atmospheric pressure?

Answer 1

Let the height of the mercury is h

height of water = 1 - h

The height of the container, h = 1.0 m

      the atmospheric pressure, P_atm = 1.01*10^5 Pa

      The density of the water, ρ_water = 1000 kg/m³

      The density of the mercury, ρ_mercury = 13600 kg/m³

For the pressure at the bottom..

13600 * 9.8 * h + 1000 * 9.8 * (1 - h) + 1.01 *10^5 = 2 * 1.01 *10^5

solving for h

h = 0.74 m (Answer)

the height of the mercury in the container is 0.74 m

I hope help you !!