Question

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

• A. $6km<h<7km$
• B. $5km<h<6km$
• C. $7km<h<8km$
• D. $8km<h<9km$

Answer 1

The correct option is C

$7km<h<8km$

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