$A$ liquid of mass $1 \ kg$ is filled in a flask as shown in the figure. The force exerted by the flask on the liquid is $(g = 10 \ m/s^2)$ [Neglect atmospheric pressure]:

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.

Gauge pressure is defined as:

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 $= 10 \ m/s^2$)

$A$ siphon in use is demonstrated in the following figure. The density of the liquid flowing in the siphon is $1.5 \text{ g/cm}^3$. The pressure difference between the points $P$ and $S$ will be

In the arrangement shown, both the vessels $A$ and $B$ are identical, but the amount of water in $B$ is double that in $A$. The vessels are closed by identical leak-proof pistons at the same height. The pistons are connected to the ends of a lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now, the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube?