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Q30 (NDA-I/2008) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

Let us assume that air density (0.0013 gm/cm3) remains constant as we go up in the atmosphere. In such a hypothetical case, what is the approximate height of atmosphere to have 1 atmospheric pressure?

Result
Your answer: —  ·  Correct: B
Explanation

To find the height of a hypothetical constant-density atmosphere, we use the hydrostatic equation: P = ρgh [t1][t7]. Given the air density (ρ) is 0.0013 gm/cm³, we first convert this to SI units: 0.0013 gm/cm³ equals 1.3 kg/m³ [t2]. Standard atmospheric pressure (P) at sea level is approximately 101,325 Pascals (Pa) or 1034 gm/cm² [c1][t3]. Using the acceleration due to gravity (g) as approximately 9.8 m/s², the height (h) is calculated as h = P / (ρg). Substituting the values: h = 101,325 / (1.3 × 9.8) ≈ 101,325 / 12.74 ≈ 7,953 meters. This value rounds to approximately 8 km [t6]. This hypothetical 'scale height' represents the thickness the atmosphere would have if it were incompressible and maintained sea-level density throughout its vertical extent [t5][t8].

Sources

  1. [1] https://www.aoml.noaa.gov/ftp/hrd/annane/prelim_notes/hypsometric_equation.pdf
  2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 23: Pressure Systems and Wind System > 23.1. Atmospheric Pressure > p. 304
  3. [3] https://en.wikipedia.org/wiki/Density_of_air
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