An inverted tube barometer is kept on a lift moving downward with a deceleration $\alpha$. The density of mercury is $\rho$ and the acceleration due to gravity is $g$. If the atmospheric pressure is $P_0$,then:

Show that the pressure produced due to a fluid column depends on the height of the fluid column and the density of the fluid.

Why does food cook faster in a pressure cooker?

The density of the liquid filled in the container is $900 \ kg/m^{3}$. Calculate the force exerted on the bottom of the container. (Given: $g = 10 \ m/s^{2}$) (in $N$)

$A$ tank is filled with a liquid of density $\rho$ up to a height $H$. The average pressure on the walls of the container is:

$(a)$ Pressure decreases as one ascends the atmosphere. If the density of air is $\rho$,what is the change in pressure $dp$ over differential height $dh$?
$(b)$ Considering the pressure $P$ to be proportional to the density,find the pressure $P$ at a height $h$ if the pressure on the surface of the earth is $P_{0}$.
$(c)$ If $P_{0} = 1.03 \times 10^5 \text{ N/m}^2$,$\rho_0 = 1.29 \text{ kg/m}^3$,and $g = 9.8 \text{ m/s}^2$,at what height will the pressure drop to $\frac{1}{10}$ of the value at the surface of the earth?
$(d)$ This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.