The density of the atmosphere is $1.29 \ kg/m^3$. If the atmospheric pressure is $1.013 \times 10^5 \ Pa$,how high would the atmosphere extend if the density were uniform? $(g = 9.81 \ m/s^2)$

$A$ 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 $g = 10 \,m/s^2$).

What would be the absolute pressure at a depth of $1 \,km$ below the ocean surface? [Given: density of water $\rho = 10^{3} \,kg/m^{3}$,$g = 10 \,m/s^{2}$,$1 \,atm = 1.01 \times 10^{5} \,N/m^{2}$]

The value of $g$ at a place decreases by $2\%$. The barometric height of mercury:

By sucking through a straw,a student can reduce the pressure in his lungs to $750\, mm$ of $Hg$ (density $= 13.6\, g/cm^3$). Using the straw,he can drink water from a glass up to a maximum depth of ....... $cm$.

Water stands up to height $h$ behind a dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. The density of water is $\rho$ and the acceleration due to gravity is $g$. If the atmospheric pressure force is also considered,the point of application of the total force acting on the dam due to water above $O$ is: