An open $U$-tube contains mercury. When $13.6 \,cm$ of water is poured into one of the arms of the tube,then the mercury rise in the other arm from its initial level is ....... $cm$

In which layer of the atmosphere is water vapour present?

$A$ cylinder stands vertically in two immiscible liquids of densities $\rho$ and $2\rho$. The heights of the two liquids are shown in the figure. Find the difference in pressure at point $A$ and point $B$.

$A$ tank $5 \ m$ high is half-filled with water and then is filled to the top with oil of density $0.85 \ g/cm^3$. The pressure at the bottom of the tank,due to these liquids is ....... $g \ dyne/cm^2$.

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill up to a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases? If so,why do the vessels filled with water to that same height give different readings on a weighing scale?

$A$ vessel with a square cross-section and a height of $6 \ m$ is vertically partitioned. $A$ small window of $100 \ cm^2$ with a hinged door is fitted at a depth of $3 \ m$ in the partition wall. One part of the vessel is filled completely with water and the other side is filled with a liquid having a density of $1.5 \times 10^3 \ kg/m^3$. What force needs to be applied on the hinged door so that it does not open (in $N$)? (Acceleration due to gravity $= 10 \ m/s^2$)