To what extent the atmosphere is extended above the surface of the Earth, assuming the density of air to be uniform [1.3 kg/m³] and pressure at the surface of Earth to be 10⁵ Pa. (Also assume the Earth to be perfectly spherical and no variation in 'g' due to height.)

6 km < h < 7 km

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Solution

Consider a squareplate of side 1m, kept horizontally on the surface of the Earth as shown,

Now make a cuboid considering this area plate as its base and height as the height of atmosphere
Now the volume of air contained in this cuboid,V= A $\times$ h
Where, A = Base Area

H = height of atmosphere

If the density of air $ρ$
Mass of air contained = $ρ V$
Neglecting the variation in acceleration due to gravity when the height varies,
Weight of air contained = $ρ V g$ = $ρ A h g$
Pressure= $\frac{F o r c e}{A r e a} = \frac{ρ A h g}{A} = ρ h g$
$ρ h g = 10^{5}$
$1.3 \times 10 \times h = 10^{5}$
h= $\frac{10^{5}}{13}$ =7692.30m(approx)

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To what extent the atmosphere is extended above the surface of the Earth, assuming the density of air to be uniform [1.3 kg/m3] and pressure at the surface of Earth to be 105 Pa. (Also assume the Earth to be perfectly spherical and no variation in 'g' due to height.) 6 km < h < 7 km

To what extent the atmosphere is extended above the surface of the Earth, assuming the density of air to be uniform [1.3 kg/m³] and pressure at the surface of Earth to be 10⁵ Pa. (Also assume the Earth to be perfectly spherical and no variation in 'g' due to height.)

6 km < h < 7 km