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?

Why is the dam of a water reservoir thick at the bottom?

$A$ $U$-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are initially in level with $10.0 \; cm$ of water in one arm and $12.5 \; cm$ of spirit in the other. If $15.0 \; cm$ of water and spirit each are further poured into the respective arms of the tube,what is the difference in the levels (in $cm$) of mercury in the two arms? (The specific gravity of spirit is $0.8$.)

In Guericke's experiment to show the effect of atmospheric pressure,two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create a vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$,then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is

Is pressure a scalar or a vector quantity? Explain.

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: