Variation of atmospheric pressure with height from the Earth is ................

$A$ barometer tube,containing mercury,is lowered in a vessel containing mercury until only $50 \, cm$ of the tube is above the level of mercury in the vessel. If the atmospheric pressure is $75 \, cm$ of mercury,what is the pressure at the top of the tube?

During a blood transfusion,a needle is inserted into a vein where the gauge pressure is $2000\,Pa$. At what height must the blood container be placed so that blood may just enter the vein (in $,m$)? (Density of blood $= 1.06 \times 10^3\,kg/m^3$ and take $g = 9.8\,m/s^2$).

Write the formula of pressure at depth $h$ in a liquid.

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? $(g = 9.81 \ m/s^2)$

In a cylindrical container open to the atmosphere from the top,a liquid is filled up to a $10\, m$ depth. The density of the liquid varies with depth $h$ from the surface as $\rho(h) = 100 + 6h^2$,where $h$ is in meters and $\rho$ is in $kg/m^3$. The pressure at the bottom of the container will be: (Atmospheric pressure $P_0 = 10^5\, Pa$,$g = 10\, m/s^2$)