Pressure gradient in a static fluid is represented by $z$-direction is vertically upwards, and $x$-axis is along horizontal, $d$ is density of fluid):

The vessel shown in the figure has two sections of the area of cross-section $A_1$ and $A_2$. A liquid of density $\mathrm{\rho }$ fills both the sections, up to height $h$ in each. Neglecting atmospheric pressure.

A wooden block with a coin placed on its top, floats in water as shown in figure. The distance $l$ and $\mathrm{h}$ are shown here. After some time the coin falls into the water. Then :

A cylindrical vessel of$90 \mathrm{cm}$height is kept filled up to the brim as shown in the figure. It has four holes $1, 2, 3, 4$which are respectively at heights of $20 \mathrm{cm}, 30 \mathrm{cm}, 40 \mathrm{cm}$ and $50 \mathrm{cm}$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from

Statement-$1$: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

Statement-$2$: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$  are connected by a string. They are fully immersed in a fluid of density $d_F.$ They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if