A vessel has the shape shown in figure. Water, which has density ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, is filled in the vessel. The pressure at the point $A$, ignoring the atmospheric pressure, is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

$1 \mathrm{m}$ height of water level is maintained in a container which is placed on a platform of height $2 \mathrm{m}$. A hole is punched at a height $h$ from the ground. For which value of $h$ given in options, the water falls at maximum distance from the base?

Figure shows five identical open-top container filled upto the brim with water. In figure $\left(b\right)$, toy duck is floating, in figure $\left(c\right)$ a heavy toy duck sinks and touches the bottom, in figure $\left(d\right)$ a heavy toy duck is suspended from a string and in figure $\left(e\right)$ a light toy duck is tied with a massless string. If all the five containers are put on weighing machine, the correct order of their reading will be

A non-viscous ideal fluid is flowing vertically downwards in a pipe. The area of cross-section at section $A$ is double that at section $B$. Vertical distance between section $A$ and section $B$ is $h$ and the height of water column in tube $\left(2\right)$ is more than that in tube $\left(1\right)$ by $\frac{\mathrm{h}}{2}$ distance. Velocity of the fluid at section $\mathrm{A}$ is

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 $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)