A small drop of water falls from rest through a large height $h$ in air; the final velocity is
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(d) The terminal velocity is independent of the height of launch.
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A load of mass $M\,kg$ is suspended from a steel wire of length $2\,m$ and radius $1.0\,mm$ in Searle’s apparatus experiment. The increase in length produced in the wire is $4.0\,mm.$ Now the load is fully immersed in a liquid of relative density $2$. The relative density of the material of load is $8$. The new value of increase in length of the steel wire is ........ $mm$
Consider two solid spheres $\mathrm{P}$ and $\mathrm{Q}$ each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$, respectively. Sphere $\mathrm{P}$ is dropped into a liquid of density $0.8 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=3$ poiseulles. Sphere $Q$ is dropped into a liquid of density $1.6 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=2$ poiseulles. The ratio of the terminal velocities of $\mathrm{P}$ and $\mathrm{Q}$ is
A vessel contains oil (density =$ 0.8 \;gm/cm^3$) over mercury (density = $13.6\; gm/cm^3$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $ gm/cm^3$ is
Water flows into a cylindrical vessel of large cross-sectional area at a rate of $10^{-4}$ $m^3/s$. It flows out from a hole of area $10^{-4}$ $m^2$, which has been punched through the base. How high does the water rise in the vessel?
Consider a water tank as shown in the figure. It's cross-sectional area is $0.4\, m ^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1\, cm ^{2}$. A load of $24\, kg$ is applied on the water at the top when the height of the water level is $40\, cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\, ms ^{-1}$. The value of $v$, to the nearest integer, is ......$m/s$. [Take value of $g$ to be $10 \,ms ^{-2}$ ]
$A U-$ tube having horizontal arm of length $20$ $cm$, has uniform cross-sectional area $=1\ cm^2$. It is filled with water of volume $60$ $cc$. What volume of a liquid of density $4$ $g/cc$ should be poured from one side into the $U -$ tube so that no water is left in the horizontal arm of the tube ........ $cc$ ?
Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$. If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$.
A cylindrical vessel of cross-section $A$ contains water to a height $h$ . There is a hole in the bottom of radius $'a'$ . The time in which it will be emptied is
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0\,cm ^2$. The area of cross section at the outlet is $10\,mm ^2$. If the piston is pushed at a speed of $4\,cm s ^{-1}$, the speed of outgoing fluidis $.........\,cm s ^{-1}$.
A bucket contains water filled upto a height $=$ $15 cm$. The bucket is tied to a rope which is passed over a frictionless light pulley and the other end of the rope is tied to a weight of mass which is half of that of the (bucket $+$ water). The water pressure above atmosphere pressure at the bottom is ....... $kPa$