The height of the water column will be greater than the height of the mercury column.
To understand why, we can use the basic principle of hydrostatic pressure, which is defined as:
P = h × ρ × g
Where P is the pressure, h is the height of the liquid column, ρ is the density of the liquid, and g is the acceleration due to gravity. For mercury, the density is approximately 13.6 g/cm³.
Given that we want the pressure from a water column to equal the pressure exerted by a 760 mm height of mercury, we can set up the equation:
760 mm Hg = h_water × 0.9976 g/cm³ × g / (13.6 g/cm³)
Rearranging this equation, we can solve for h_water:
h_water = (760 mm Hg × 13.6 g/cm³) / 0.9976 g/cm³ = approximately 10,333 mm of water.
This clearly shows that the height of water required to exert the same pressure as a 760 mm column of mercury is much greater than 760 mm. Thus, the height of the water column will indeed be greater.