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NEST2022PhysicsGravitation

A planet of mass M and radius R is surrounded by a thin layer of atmosphere of height H and of constant density , having pressure P and temperature T . The atmosphere consists of ideal gas molecules of only one type, each of mass m with root-mean-square speed v_ rms . Taking acceleration due to gravity to be constant within the atmosphere, at height h H from the surface

Options

  1. AP= G M h R^2
  2. BT= G M m h k_B R^2
  3. C= 3 M 4 R^3
  4. Dv_ r m s = 1 R 3 G M h

Correct answer

D. v_ r m s = 1 R 3 G M h

Step-by-step solution

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