Spherical balls of radius $ 'r'$ are falling in a viscous fluid of viscosity '$\eta$' with a velocity $ 'v'. $ The retarding viscous force acting on the spherical ball is
AIEEE 2004, Easy
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(b)$F = 6\,\pi \eta \,rv$
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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 cylindrical tank has a hole of $1 cm^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 cm^3/sec$. then the maximum height up to which water can rise in the tank is .......... $cm$
Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure) . Through a hole of radius $r$ $(r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x.$ Then
A solid sphere of density $\eta$ $( > 1)$ times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
A cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury ar $\rho _s$ and $\rho _m$ . The height of the block above the mercury level is given by
Two identical cylindrical vessels with their bases at same level, each contains a liquid of density $d$ . The height of the liquid in one vessel is $ h_1$ and that in the other vessel is $h_2$ . The area of either base is $A$ . The work done by gravity in equalizing the levels when the two vessels are connected 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 $.........\,cm s ^{-1}$.
Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
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