Consider a mercury-filled tube as shown in the figure below. Which of the following options about the pressures at the lettered locations $(A, B, C, D)$ is true?

An open $U$-tube contains mercury. When $13.6 \,cm$ of water is poured into one of the arms of the tube,then the mercury rise in the other arm from its initial level is ....... $cm$

Three identical vessels are filled to the same height with three different liquids $A, B$ and $C$ $(\rho_A > \rho_B > \rho_C)$. The pressure at the base will be

When two metals of equal volume are mixed,the relative density of the mixture is $4$. When equal masses of these two metals are mixed,the relative density of the mixture is $3$. What are the relative densities of the two metals?

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

At a depth of $1000 \; m$ in an ocean:
$(a)$ What is the absolute pressure?
$(b)$ What is the gauge pressure?
$(c)$ Find the force acting on the window of area $20 \; cm \times 20 \; cm$ of a submarine at this depth,the interior of which is maintained at sea-level atmospheric pressure. (The density of sea water is $1.03 \times 10^3 \; kg \; m^{-3}$,$g = 10 \; m \; s^{-2}$.)