There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^o$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{{{d_1}}}{{{d_2}}}$ is
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A horizontal pipe line carries water in a streamline flow.At a point along the tube where the cross-sectional area is $10^{-2}$ $m^2$, the water velocity is $2$ $ms^{^{-1}}$ and the pressure is $8000 $ $Pa$. The pressure of water at another point where the cross-sectional area is $0.5$ $\times 10^{-2}$ $m^2$ is ........ $Pa$
A boat having a length of $3\,metre$ and breadth $2\,metre$ is floating on a lake. The boat sinks by one cm when a man gets on it. Mass of the man is ....... $kg$
A uniformly tapering vessel is filled with a liquid of density $900 kg/m^3.$ The force that acts on the base of the vessel due to the liquid is ......... $N$. $(g = 10\,m{s^{ - 2}})$
A large cylindrical tank of cross-sectional area $1\ m^2 $ is filled with water. It has a small hole at a height of $1\ m $ from the bottom. $A$ movable piston of mass $5$ $kg$ is fitted on the top of the tank such that it can slide in the tank freely without friction. A load of $45$ $kg$ is applied on the top of water by piston, as shown in figure. The value of $v$ when piston is $7$ $m$ above the bottom is $(g = 10\ m/s^2)$ ....... $m/s$
A small metal sphere of radius $a$ is falling with a velocity $v$ through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is $\eta $ , then the sphere encounters an opposing force of
In an experiment, a small steel ball falls through a Iiquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... $cm/s$
The top of a water tank is open to air and its water level is maintained. It is giving out $0.74\,m^3$ water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$