$A$ barometer kept in a stationary elevator reads $76 \ cm$. If the elevator starts accelerating upwards,the reading will be:

The pressure at half the depth of a lake is $2/3$ of the pressure at its bottom. What is the depth of the lake in $m$?

What does it mean when the height of a barometer is rising?

What are the difficulties arising from using water in a barometer instead of mercury?

$(a)$ 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.

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