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

Depth of a river is $100 \ m$. Magnitude of compressibility of the water is $0.5 \times 10^{-9} \ N^{-1} \ m^2$. The fractional compression in water at the bottom of the river is (Acceleration due to gravity $= 10 \ m/s^2$)

The relative density of Kerosene is $0.8$. Find its density. (in $kg/m^3$)

$A$ hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. The sphere is moving horizontally with an acceleration $2g,$ where $g$ is the acceleration due to gravity. If the minimum pressure of the liquid is $P_0$,then what is the pressure at the centre of the sphere?

$A$ bubble from the bottom of a lake rises to its surface. Its volume doubles in the process. Assuming isothermal conditions, atmospheric pressure $= 75 \, cm$ of $Hg$, and the ratio of the densities of mercury and water $= 40/3$. The depth of the lake will be ..... $m$.

$A$ cylinder stands vertically in two immiscible liquids of densities $\rho$ and $2\rho$. The heights of the two liquids are shown in the figure. Find the difference in pressure at point $A$ and point $B$.