(II) How high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?
We have to determine the height of the atmosphere upto which it would be extended considering it to be uniformly distributed having density half of the present density at sea level.
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The pressure at the bottom point due to air of density , having the height of the air column taking the density of the atmosphere to be uniform,is given as,
Where Pressure at the topmost point
Acceleration due to gravity