$A$ $U$-tube having a horizontal arm of length $20 \ cm$ has a uniform cross-sectional area of $1 \ cm^2$. It is filled with water of volume $60 \ cc$. What volume of a liquid of density $4 \ g/cc$ should be poured from one side into the $U$-tube so that no water is left in the horizontal arm of the tube? (Answer in $cc$)

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

The limbs of a $U$-tube are lowered into vessels $A$ and $B$,where vessel $A$ contains water. Some air is pumped out through the top of the tube at $C$. The liquids in the left limb (in vessel $A$) and the right limb (in vessel $B$) rise to heights of $10\, cm$ and $12\, cm$ respectively above the free surfaces of the liquids in the vessels. The density of liquid $B$ is ........ $g/cm^3$.

The pressure at the sea surface is .......... $P_{a}$.

Two substances of densities ${\rho _1}$ and ${\rho _2}$ are mixed in equal volumes and the relative density of the mixture is $4$. When they are mixed in equal masses,the relative density of the mixture is $3$. The values of ${\rho _1}$ and ${\rho _2}$ are

$A$ 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 $B$.