A small hole of area of cross-section $2\; \mathrm{mm}^{2}$ is present near the bottom of a fully filled open tank of height $2\; \mathrm{m} .$ Taking $\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2},$ the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \;m^{3} /s$
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A sphere of solid material of relative density $9$ has a concentric spherical cavity and floats having just sinked in water. If the radius of the sphere be $R$, then the radius of the cavity $(r)$ will be related to $R$ as :-
A small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?
A space $2.5\ cm$ wide between two large plane surfaces is filled with oil. Force required to drag very thin plate of area $0.5\ m^2$ just midway the surfaces at a speed of $0.5\ m/sec$ is $1\ N$ The coefficient of viscosity in $kg-s/m^2$ is :
A cylindrical vessel of height $500 \mathrm{~mm}$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height $\mathrm{H}$. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being $200 \mathrm{~mm}$. Find the fall in height (in ${m m}$ ) of water level due to opening of the orifice.
|Take atmospheric pressure $=1.0 \times 10^5 \mathrm{~N} / \mathrm{m}^2$, density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ and $g=10 \mathrm{~m} / \mathrm{s}^2$. Neglect any effect of surface tension.]
A streamlined body falls through air from a height $h$ on the surface of a liquid. If $d$ and $D(D > d) $ represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is
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 cylindrical vessel of $90 cm$ height is kept filled upto the brim. It has four holes $ 1, 2, 3, 4$ which are respectively at heights of $20 cm, 30 cm, 45 cm $ and $50 cm$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from
A triangular lamina of area $A$ and height h is immersed in a liquid of density $\rho $ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is