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If the air density were uniform, then the height of the atmosphere above the sea level to produce a normal atmospheric pressure of \( 1.0 \times 10^{5} \) Pa is (density of air is \( 1.3 \mathrm{kg} / \mathrm{m}^{3}, \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} \) ):

1. \( 0.77 \mathrm{km} \)
2. 7.7 km
3. \( 77 \mathrm{km} \)
4. 0.077 km

Correct answer: 7.7 km

Solution

For a uniform air density, the pressure at sea level is given by the hydrostatic relation P = ρgh. Substituting the given values gives a height of 7.7 km, which matches the correct option.

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