Question

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill​

Answer 1

Here the pressure difference between the sea level and the hill and that due to atmospheric pressure would be same.

So,

Pressure difference between sea level and the hill would be

dP1 = dh1 X ρm X g (1)

where dh = h1 (sea level mercury height = 75 cm) - h2 (hill top mercury height = 50 cm)

ρm is the density of mercury

and the pressure difference in atmospheric pressure would be

dP2 = dh2 X ρa X g (2)

where dh2 is the height of the hill, ρa is the density of air

now, we know that (1) = (2), so

dh1 X ρm X g = dh2 X ρa X g

by substituting appropriate values and rearranging, we get

dh2 = 0.25 X (ρm/ ρa) = 0.25 X 104 m

or dh2 = 2500 m

thus, the height of the hill is

dh2 = 2500m = 2.5 km