$A$ vertical $U$-tube of uniform cross-section contains water in both the arms. $A$ $10 \, cm$ glycerine column $(R.D. = 1.2)$ is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be ...... $cm$.

Three different liquids are filled in a $U$-tube as shown in the figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ respectively. From the figure, we may conclude that:

At shallow depth $h$,the pressure in the ocean is simply given by $P = P_0 + \rho gh$,in which $\rho$ is the density of water and $P_0$ is the air pressure. As we go deeper,the high pressure causes the water to compress and become denser. Which of the following sketches illustrates the correct dependence of the pressure on the depth $h$ ?

Two liquids of densities $\rho_{1}$ and $\rho_{2}$ (where $\rho_{2} = 2\rho_{1}$) are filled behind a vertical wall of height $10 \; m$ and width $w$,as shown in the figure. Each liquid has a height of $h = 5 \; m$. The ratio of the force exerted by the upper liquid on the part $MN$ to the force exerted by the lower liquid on the part $NO$ is (Assume that the liquids do not mix):

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

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 ........ $g/cm^3$.