Define pressure. Give the $SI$ and $CGS$ unit of pressure.

If a vessel containing a fluid of density $\rho$ up to height $h$ is accelerated vertically downwards with acceleration $a_0$,then the pressure by the fluid at the bottom of the vessel is given by the equation ........ ($p_0$ denotes the atmospheric pressure and $g$ denotes the acceleration due to gravity).

If two liquids of same volume but different densities $\rho_1$ and $\rho_2$ are mixed,then the density of the mixture is given by:

$A$ 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 ....... $g \ dyne/cm^2$.

Three liquids of equal masses are taken in three identical cubical vessels $A$,$B$,and $C$. Their densities are $\rho_{A}$,$\rho_{B}$,and $\rho_{C}$ respectively,where $\rho_{A} < \rho_{B} < \rho_{C}$. The force exerted by the liquid on the base of the cubical vessel is

An open-ended $U$-tube of uniform cross-sectional area contains water (density $10^3 \ kg \ m^{-3}$). Initially,the water level stands at $0.29 \ m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \ kg \ m^{-3}$ is added to the left arm until its length is $0.1 \ m$,as shown in the schematic figure. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-