Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$,then the relation between $h_A$ and $h_B$ is

Three liquids of densities $d, 2d$,and $3d$ are mixed in equal volumes. Then 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:

$A$ liquid mixture of volume $V$ has two liquids as its ingredients with densities $\alpha$ and $\beta$. If the density of the mixture is $\sigma$,then the mass of the first liquid in the mixture is ............

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

At every point of a liquid at rest,the tangential stress is zero. Explain with reason.