Two immiscible liquids are poured in a $U$-tube having densities ${\rho }_1=1.0\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and ${\rho }_2=3.0\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Find the ratio of heights (of the liquids above their interface) $\frac{h_1}{h_2}$.

The given container is in contact with vertical wall. The container has liquid of density $\rho$. There is a small hole of cross-section area of $A$. At the given moment ground can exert maximum friction force $\rho Agh$ on the container. At given instant the normal force exerted by the vertical wall on container is $x\rho Agh$, find the value of $x$.

A simple open $U$-tube contains mercury. Now water is poured slowly up to height $27.2 \mathrm{cm}$ in the left arm. How high (in $\mathrm{cm}$) does the mercury rise in the right arm from its initial level in equilibrium state? (Take density of mercury $=13600 \mathrm{kg} {\mathrm{m}}^{-3}$ and that of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)