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 $.........\,cm s ^{-1}$.
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A cubical block of side $‘a’$ and density $‘\rho ’$ slides over a fixed inclined plane with constant velocity $‘v’$. There is a thin film of viscous fluid of thickness $‘t’$ between the plane and the block. Then the coefficient of viscosity of the thin film will be:
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 liquid of density $\rho $ is coming out of a hose pipe of radius $a$ with horizontal speed $v$ and hits a mesh. $50\%$ of the liquid passes through the mesh unaffected. $25\%$ looses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mesh will be
Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if $8 \mathrm{such}$ droplets are coalesced and formed a larger drop, the new terminal velocity will be ........... $\mathrm{cm} / \mathrm{s}$.
A barometer kept in an elevator reads $76 \,cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cm$ of $Hg$ ) is ........
Two capillary of length $L $ and $2L$ and of radius $R$ and $2R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X = \pi P{R^4}/8\eta L)$
A bottle has a thin nozzle on top. It is filled with water, held horizontally at a height of $1 \,m$ and squeesed slowly by hands, so that the water jet coming out of the nozzle hits the ground at a distance of $2 \,m$. If the area over which the hands squeese it is $10 \,cm ^{2}$, the force applied by hand is close to .......... $N$ (take, $g=10 \,m / s ^{2}$ and density of water $=1000 \,kg / m ^{3}$ )