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

$A$ tube is bent into an $L$ shape and kept in a vertical plane. If these three liquids are kept in equilibrium by the piston of area $A$,the value of $\frac{F}{A}$ is:

Two liquids having densities $d_1$ and $d_2$ are mixed in such a way that both have the same mass. The density of the mixture is ............

Consider a vessel filled with a liquid up to height $H$. The bottom of the vessel lies in the $X-Y$ plane passing through the origin. The density of the liquid varies with the $Z$-axis as $\rho(z) = \rho_0 \left[ 2 - \left( \frac{z}{H} \right)^2 \right]$. If $P_1$ and $P_2$ are the pressures at the bottom surface and top surface of the liquid respectively,the magnitude of $(P_1 - P_2)$ is:

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends a $90^o$ angle at the centre. The radius joining their interface makes an angle $\alpha$ with the vertical. The ratio $\frac{d_1}{d_2}$ is

Pressure at the bottom of a tank of water is $3P$,where $P$ is atmospheric pressure. If water is drawn out till the level of water is lowered by one-fifth,then the pressure at the bottom of the tank is