At every point of a liquid at rest,the tangential stress is zero. Explain with reason.

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

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

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 $= 10 \ m/s^2$)

$A$ nurse measures the blood pressure of a seated patient to be $190 \,mm$ of $Hg$.

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends a $90^o$ angle at the centre. The radius joining their interface makes an angle $\alpha$ with the vertical. The ratio $\frac{d_1}{d_2}$ is