Water is flowing continuously from a tap having an internal diameter of $8\times {10}^{-3 }\mathrm{m}$. The water velocity as it leaves the tap is $0.4 \mathrm{m} {\mathrm{s}}^{-1}$. The diameter of the water stream at a distance $2\times {10}^{-1} \mathrm{m}$ below the tap, is close to

There is a circular tube in a vertical plane. Two liquids that do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90°$ angle at the centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{d_1}{d_2}$ is:

An open glass tube is immersed in mercury in such a way that a length of $8 \mathrm{cm}$ extends above the mercury level. The open-end of the tube is then closed and sealed and the tube is raised vertically up by an additional$46 \mathrm{cm}$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure$=76 \mathrm{cm} \text{of} \mathrm{Hg}$)

A body floats in a liquid contained in a beaker. If the whole system (shown in figure) falls under gravity then the up-thrust on the body is-

Water is filled up to a height $\mathrm{h}$ in a beaker of radius $\mathrm{R}$ 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 $ABCD$ 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