Calculate the approximate height (h) of Earth's atmosphere extending above the surface of the Earth, assuming the density of air to be uniform [ $1.3 k g m^{- 3}$ ] and pressure at the surface of Earth to be $10^{5} P a$ . (Assume the Earth to be perfectly spherical and no variation in 'g' due to height).

$6 k m < h < 7 k m$

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$5 k m < h < 6 k m$

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$7 k m < h < 8 k m$

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$8 k m < h < 9 k m$

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Solution

The correct option is C
$7 k m < h < 8 k m$

Let the height of the atmosphere be $h$ .
Using the formula for pressure at a depth,
$P = ρ g h$
$10^{5} = 1.3 \times 10 \times h$
$h = 7692.30 m$ (approximately)

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