Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on the same horizontal plane are filled with water to the same height. If the volume of water in vessel $A$ is $3$ times the volume of water in vessel $B$,then the ratio of the pressures at the bottom of the vessels $A$ and $B$ is

$A$ vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to the water surface as shown. The force on one surface of the plate by water is (density of water is $\rho$ and atmospheric pressure is $P_0$).

In which layer of the atmosphere is water vapour present?

$A$ $U$ tube with both ends open to the atmosphere is partially filled with water. Oil,which is immiscible with water,is poured into one side until it stands at a distance of $10\, mm$ above the water level on the other side. Meanwhile,the water rises by $65\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$.

Explain the hydrostatic paradox.

Three different liquids are filled in a $U$-tube as shown in the figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ respectively. From the figure, we may conclude that: