Suppose the density of air at Madras is ρ_o and atmospheric pressure is P₀. 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_ogz, 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?

Open in App

Solution

Using the equation P_o − P = ρ_ogz, we get:
P = P_o − ρ_ogz
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.

Suggest Corrections

Similar questions

The pressure variation equation of a sound wave propagating in a medium with pressure amplitude $P_{0}$ is

$P = P_{0} s i n ω (t - \frac{x}{v})$

Inference:

In the tube where this wave is propagating if we measure pressure, then the maximum pressure measured will be _{$P_{0}$}atm and Minimum pressure measured will be _{$- P_{0}$}atm as maximum $&$ minimum values of sin $θ$ is (+1/-1).

Q. A beaker containing a liquid of density

ρ

moves up with an acceleration

^{'} a^{'}

. The pressure in the liquid at a depth

h

below the free surface of the liquid is (consider atmospheric pressure to be

P_{0}

)

Q. For the pressure variation in a longitudinal wave represented as

P = P_{o} cos (ω t - k x)

, the density

(ρ)

equation for the given medium is best represented by
(

ρ_{o}

is the density of the medium at pressure

P_{o}

)

If we are said to find pressure at sea level of 3000m,shall we consider the atmospheric pressure also

Q. Why does the atmospheric pressure go on decreasing as we go higher up above the earth's surface?

Join BYJU'S Learning Program