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

$A$ container of height $10 \, cm$ is filled with water. There is a hole at the bottom. Find the pressure difference between points at the top and the bottom.

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 $g = 9.8\,m/s^2$).

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 $N$)

$A$ barometer is kept in an elevator accelerating downwards with an acceleration $a$. What is the most likely pressure reading inside the elevator?

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