Two liquids of densities $\rho_1 = 1$ and $\rho_2 = 2$ are mixed in equal masses. What is the density of the resulting mixture?

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \text{ g/cm}^3$) standing initially $20 \text{ cm}$ from the bottom in each arm. An immiscible liquid of density $4.0 \text{ g/cm}^3$ is added to one arm until a layer $5 \text{ cm}$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_A, \rho_B$ and $\rho_C$ (where $\rho_A > \rho_B > \rho_C$). The pressure at the bottom of the vessels is:

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

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).

$A$ 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 $= 10 \ m/s^2$)