Suppose the density of air at Madras is ρ_{o} and atmospheric pressure is P_{0}. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10 km above Madras. If we use the equation P_{o} − P = ρ_{o}gz, will we get a pressure more than the actual or less than the actual? Neglect the variation in g. Does your answer change if you also consider the variation in g?

#### Solution

Using the equation P_{o} − P = ρ_{o}gz, we get:

P = P_{o} − ρ_{o}gz

The pressure calculated by using this equation will be more than the actual pressure because density at a height of 10 km above Madras will be less than ρ_{o}.

Yes, the answer will change if we also consider the variation in g. Because g decreases with height, it will have the same effect on pressure as that of density.