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Archimedes Principle

To what exten...

Question

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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5 km < h < 6 km

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7 km < h < 8 km

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8 km < h < 9 km

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Solution

The correct option is C
7 km < h < 8 km

Consider a square plate 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 is $ρ$
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.)

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.)