The Earth's atmosphere is a mixture of gases such as nitrogen

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The Earth's atmosphere is a mixture of gases such as nitrogen, oxygen, tiny amounts of carbon dioxide and traces of other gases. Because of the pull of gravity, these gases tend to accumulate near the surface of the Earth. The weight of these gases causes an atmospheric pressure of about 10510^5 Pa on the surface of the Earth. Because the density of air decreases with height (hh above the surface of the Earth), the atmospheric pressure (PP) decreases with hh. In fact PP varies with hh as P=P0e−h/h0P = P_0 e^{-h/h_0} where P0P_0 = atmospheric pressure at sea level (h=0h = 0) and h0h_0 is a constant. The height at which the atmospheric pressure is half its value at sea level is: (A) h=h0h = h_0 (B) h=2h0h = 2h_0 (C) h=h0log⁡e(2)h = h_0 \log_e(2) (D) h=h0e−1/2h = h_0 e^{-1/2}

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