Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1\; \mathrm{mm}$ and $2\; \mathrm{mm}$, respectively. They are made to fall vertically (from rest) in a viscous medum whose coefficient of viscosity equals $\eta$ and whose denstry is $0.1 \mathrm{\rho}_{2} .$ The ratio of their terminal velocitites would be
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Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end having many small holes. Consider one such fountain which is produced by a pipe of internal diameter $2$ $cm$ in which water flows at a rate $3$ $ms^{^{-1}}$. The enclosure has $100$ holes each of diameter $0.05$ $cm$. The velocity of water coming out of the holes ids ( in $ms^{^{-1}}$)
A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the
A liquid is kept in a cylindrical vessel which rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$ , The difference in the height of the liquid at the centre of the vessel and its sides will be .............. $\mathrm{cm}$ $(\pi ^2 = 10)$
A $U-$ tube containing a liquid moves with a horizontal acceleration a along a direction joining the two vertical limbs. The separation between these limbs is $d$ . The difference in their liquid levels is
A rectangular box has water in it. It is being pulled to the right with an acceleration $a$. Which of the following options shows the correct shape of water surface on it ?
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \mathrm{~N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is_________.${N}$.
A fully loaded boeing aircraft has a mass of $5.4 \times 10^5\,kg$. Its total wing area is $500\,m ^2$. It is in level flight with a speed of $1080\,km / h$. If the density of air $\rho$ is $1.2\,kg\,m ^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be $\left( g =10\,m / s ^2\right)$
A cubical block of wood of edge $10$ $cm$ and mass $0.92$ $kg$ floats on a tank of water with oil of rel. density $0.6$ to a depth of $4$ $cm$ above water. When the block attains equilibrium with four of its sides edges vertical