Question

The density of air on the Earth decreases almost linearly with height from 1.22kgm–3 at sea level

to 0.74 kgm–3 at an altitude of 5000m.
Atmospheric pressure at the Earth’s surface on a particular day is 100000Pa. The value of g
between the Earth’s surface and an altitude of 5000 m can be considered to have a constant
value of 9.7ms–2.
What will be the atmospheric pressure at an altitude of 5000m?
the answer is 52000 Pa

Answer 1

P = 10^5 - ρ (average)gh

where ρ (average) = average air density between 0 and 5000 m = (1.22+0.74)/2 = 0.98

we know g & h

I get P = 52470 Pa