A mercury barometer reads 744 mm on the roof of a building and 769 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building.

To determine the height of the building, we can use the concept of pressure difference and the formula for hydrostatic pressure.

The pressure at a given point in a fluid column is determined by the height of the fluid above that point and the density of the fluid. The pressure difference between two points in a fluid column is directly proportional to the difference in height between those two points.

In this case, we have a difference in pressure readings between the roof and the ground. The difference in pressure is caused by the difference in height between those two points.

Let's calculate the pressure difference first:

Pressure difference = Pressure at the ground - Pressure at the roof
= 769 mm mercury - 744 mm mercury

Now, we need to convert the pressure difference from millimeters of mercury to pascals, as Pascal is the SI unit of pressure. We can use the conversion factor that 1 mmHg = 133.322 pascals.

Pressure difference = (769 - 744) mmHg * 133.322 pascals/mmHg

With this pressure difference, we can now use the hydrostatic pressure formula:

Pressure difference = density * acceleration due to gravity * height

We are given the density of air as 1.29 kg/m^3. The acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, we can rearrange the formula to solve for height:

Height = Pressure difference / (density * acceleration due to gravity)

Substituting the values we have:

Height = (Pressure difference) / (density * acceleration due to gravity)
= (Pressure difference) / (1.29 kg/m^3 * 9.8 m/s^2)

Now, we can calculate the height of the building by plugging in the values for the pressure difference, density, and acceleration due to gravity.

Height = (Pressure difference) / (1.29 kg/m^3 * 9.8 m/s^2)