A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is $(i)$ maximum at, and $ (ii) $ minimum at

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is $P_0$. Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

In the figure shown, the heavy cylinder (radius $R$) resting on a smooth surface separates two liquids of densities $2\ \rho$ and $3\ \rho$ . The height $‘h’$ for the equilibrium of cylinder must be

Two communicating vessels contain mercury. The diameter of one vessel is $n$ times larger than the diameter of the other. A column of water of height $ h$  is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s =$ relative density of mercury and $\rho  = $ density of water) by

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area $'a'$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is $(a\,<\,<\,A)$

An open-ended U-tube of uniform cross-sectional area contains water (density $10^3 kg m ^{-3}$ ). Initially the water level stands at $0.29 m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 kg m ^{-3}$ is added to the left arm until its length is $0.1 m$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-