The atmospheric pressure at a place is $10^5 \,Pa$. If tribromomethane (specific gravity $= 2.9$) is employed as the barometric liquid,the barometric height is .......... $m$. (in $.52$)

The pressure at the bottom of a tank containing a liquid does not depend on

$A$ submarine has a window of area $30 \times 30 \,cm^2$ on its ceiling and is at a depth of $100 \,m$ below sea level. If the pressure inside the submarine is maintained at the sea-level atmospheric pressure,then the force acting on the window is ............. $N$ (consider density of sea water $\rho = 1.03 \times 10^3 \,kg/m^3$,acceleration due to gravity $g = 10 \,m/s^2$).

$(a)$ 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.

On what factors does the pressure at any place depend? Explain.

$A$ sudden drop in the mercury level by $10 \,mm$ or more is a sign of ..........