Physics · JEE Main, NEET, Olympiad (NSEP)

Fluid Mechanics

192 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

147MCQ45Numerical25With diagram
Start with question 1 See it move: Fluid mechanics
  1. 1Water flows through a horizontal pipe of non-uniform cross-section. At point AA the velocity is 2 m/s2\,\text{m/s} and pressure is PAP_A. At point BB, where diameter is halved, velocity is:JEE Main/MCQ/Medium
  2. 2Raindrops attain a constant terminal velocity due to:NEET/MCQ/Medium
  3. 3Water flows out of a small hole of area aa at the base of a large cylindrical tank of cross-sectional area AA filled to height HH. Time taken to empty the tank completely is:Olympiad (NSEP)/MCQ/Hard
  4. 4A spherical ball of radius rr falls with terminal velocity vv in a viscous liquid. The viscous drag force acting on the ball is proportional to:JEE Main/MCQ/Medium
  5. 5An air bubble of volume 2.9 cm32.9 \mathrm{~cm}^{3} rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17∘C17^{\circ} \mathrm{C}. The volume of the bubble when it reaches the surface, where the water temperature is 27∘C27^{\circ} \mathrm{C}, is ____\_\_\_\_ cm3\mathrm{cm}^{3}.
    (g=10 m/s2\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right., density of water =103 kg/m3=10^{3} \mathrm{~kg} / \mathrm{m}^{3}, and 1 atm pressure is 105 Pa)\left.10^{5} \mathrm{~Pa}\right)    JEE Main/MCQ/Medium/Pressure and thrust
  6. 6A plane is in level flight at constant speed and each of its two wings has an area of 40m2.40{m}^{2}. If the speed of the air is 180kmh−1180km{h}^{-1} over the lower wing surface and 252kmh−1252km{h}^{-1} over the upper wing surface, the mass of the plane is ________kg.kg. (Take air density to be 1kgm–31kg{m}^{–3} and g=10ms–2g=10m{s}^{–2})JEE Main/Numerical/Medium/Pressure and thrust
  7. 7Given below are two statements:
    Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
    Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
    In the light of the above statements, choose the most appropriate from the options given below    JEE Main/MCQ/Medium/Pressure and thrust
  8. 8Given below are two statements:
    Statement I: Pressure in a reservoir of water is same at all points at the same level of water.
    Statement II: The pressure applied to enclosed water is transmitted in all directions equally.
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Pressure and thrust
  9. 9A hydraulic automobile lift is designed to lift vehicles of mass 5000kg5000kg. The area of cross section of the cylinder carrying load is 250cm2250{cm}^{2}. The maximum pressure the smaller piston would have to bear is [Assume g=10ms−2g=10m{s}^{-2}]JEE Main/MCQ/Medium/Pressure and thrust
  10. 10An air bubble of volume 1cm31{cm}^{3} rises from the bottom of a lake 40m40m deep to the surface at a temperature of 12∘C.12^{\circ}C. The atmospheric pressure is 1×105Pa,1\times {10}^{5}Pa, the density of water is 1000kgm−31000kg{m}^{-3} and g=10ms−2.g=10m{s}^{-2}.There is no difference of the temperature of water at the depth of 40m40m and on the surface. The volume of air bubble when it reaches the surface will beJEE Main/MCQ/Medium/Pressure and thrust
  11. 11A glass tumbler having inner depth of 17.5cm17.5cm is kept on a table. A student starts pouring water (μ=43)\left(\mu =\dfrac{4}{3}\right) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ?JEE Main/MCQ/Medium/Pressure and thrust
  12. 12A light cylindrical vessel is kept on a horizontal surface. Area of the base is A.A. A hole of cross-sectional area aa is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is
    JEE Main/MCQ/Medium/Pressure and thrust/With diagram
  13. 13The pressure acting on a submarine is 3×105Pa3\times {10}^{5}Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is 1×105Pa1\times {10}^{5}Pa density of water is 103kgm−3,g=10ms−2{10}^{3}kg{m}^{-3},g=10{ms}^{-2})JEE Main/MCQ/Medium/Pressure and thrust
  14. 14A hollow spherical shell at outer radius RR floats just submerged under the water surface. The inner radius of the shell is r.r. If the specific gravity of the shell material is 278\dfrac{27}{8} with respect to water, the value of rr is:JEE Main/MCQ/Medium/Pressure and thrust
  15. 15Consider a solid sphere of radius RR and mass density ρ(r)=ρ0(1−r2R2),0<r≤R.\rho \left(r\right)={\rho }_{0}\left(1-\dfrac{{r}^{2}}{{R}^{2}}\right),0\lt r\leq R. The minimum density of a liquid in which it will float is:JEE Main/MCQ/Medium/Pressure and thrust
  16. 16A leak proof cylinder of length 1m,1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0oC{0}^{o}C such that its height above the water surface is 20cm.20cm. When the temperature of water is increased to 4oC,{4}^{o}C, the height of the cylinder above the water surface becomes 21cm.21cm. The density of water at T=4oC,T={4}^{o}C, relative to the density at T=0oCT={0}^{o}C is close to:JEE Main/MCQ/Medium/Pressure and thrust
  17. 17A submarine experiences a pressure of 5.05×106Pa5.05\times {10}^{6}Pa at a depth of d1{d}_{1} in a sea. When it goes further to a depth of d2{d}_{2} , it experiences a pressure of 8.08×106Pa8.08\times {10}^{6}Pa . Then d2−d1{d}_{2}-{d}_{1} is approximately (density of water =103kg/m3={10}^{3}kg/{m}^{3} and acceleration due to gravity =10ms−2=10m{s}^{-2} ):JEE Main/MCQ/Medium/Pressure and thrust
  18. 18When an air bubble of radius rr rises from the bottom to the surface of a lake, its radius becomes 5r4\frac{5 \mathrm{r}}{4}. Taking the atmospheric pressure to be equal to 10 m10 \mathrm{~m} height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):JEE Main/MCQ/Medium/Pressure and thrust
  19. 19A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ1{\rho }_{1} and ρ2(ρ1>ρ2),{\rho }_{2}({\rho }_{1}\gt {\rho }_{2}), fill half the circle. The angle θ\theta between the radius vector passing through the common interface and the vertical is:JEE Main/MCQ/Medium/Pressure and thrust
  20. 20A thin uniform tube is bent into a circle of radius rr in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ρ1\rho_1 and ρ2(ρ1>ρ2)\rho_2\left(\rho_1\gt \rho_2\right) fill half the circle. The angle θ\theta between the radius vector passing through the common interface and the vertical isJEE Main/MCQ/Medium/Pressure and thrust
  21. 21A thin tube sealed at both ends is 100 cm100 \mathrm{~cm} long. It lies horizontally, the middle 20 cm20 \mathrm{~cm} containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced ?


    (Given : cross-section of the tube can be assumed to be uniform)    JEE Main/MCQ/Medium/Pressure and thrust/With diagram
  22. 22Air of density 1.2 kg m−31.2 \mathrm{~kg} \mathrm{~m}^{-3} is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are 150 ms−1150 \mathrm{~ms}^{-1} and 100 ms−1100 \mathrm{~ms}^{-1}, respectively. The pressure difference between the upper and lower sides of the wings, is :JEE Main/MCQ/Medium/Pressure and thrust
  23. 23The terminal velocity of a small sphere of radius aa in a viscous liquid is proportional toJEE Main/MCQ/Medium/Pressure and thrust
  24. 24Two cylindrical vessels of equal cross sectional area of 2 m22 \mathrm{~m}^2 contain water up to height 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is 103 kg/m310^3 \mathrm{~kg} / \mathrm{m}^3 and g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2)JEE Main/MCQ/Medium/Pascal's Law
  25. 25In a hydraulic lift, the surface area of the input piston is \(6 \mathrm{~cm}^2\) and that of the output piston is \(1500 \mathrm{~cm}^2\). If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ.JEE Main/Numerical/Medium/Pascal's Law
  26. 26A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is FαM\sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}} in SI unit. The value of α\alpha is __________.JEE Main/Numerical/Medium/Pascal's Law
  27. 27
    A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of     10 N10 \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.    JEE Main/Numerical/Medium/Pascal's Law/With diagram
  28. 28Mercury is filled in a tube of radius 2 cm2 \mathrm{~cm} up to a height of 30 cm30 \mathrm{~cm}. The force exerted by mercury on the bottom of the tube is _____ N.
    (Given, atmospheric pressure     =105Nm−2=10^5 \mathrm{Nm}^{-2}, density of mercury =1.36×104 kg m−=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-} 3, g=10 m s−2,π=227)\left.{ }^3, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7}\right)    JEE Main/Numerical/Medium/Pascal's Law
  29. 29Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal’s principle is observed.
    Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
    In the light of the above statements, choose the most appropriate answer from the options given below.    JEE Main/MCQ/Medium/Pascal's Law
  30. 30Two cylindrical vessels of equal cross-sectional area 16cm216{cm}^{2} contain water upto heights 100cm100cm and 150cm150cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water =103kgm−3={10}^{3}kg{m}^{-3} and g=10ms−2g=10{ms}^{-2}]JEE Main/MCQ/Medium/Pascal's Law
  31. 31A hydraulic press can lift 100kg100kg when a mass mm is placed on the smaller piston. It can lift kg when the diameter of the larger piston is increased by 44 times and that of the smaller piston is decreased by 44 times keeping the same mass mm on the smaller piston.JEE Main/Numerical/Medium/Pascal's Law
  32. 32A tub is filled with water and a wooden cube 1010 cm ×\times 1010 cm ×\times 1010 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.873.87 cm. The mass of the metal coin is _______ gram.
    (Take water density as     11 g/cm3^3 and density of wood as 0.40.4 g/cm3^3)    JEE Main/Numerical/Medium/Archmidies Principle
  33. 33A cubical block of density ρb=600 kg/m3\rho_{b}=600 \mathrm{~kg} / \mathrm{m}^{3} floats in a liquid of density ρe=900kg/m3\rho_{\mathrm{e}}=900 \mathrm{kg} / \mathrm{m}^{3}. If the height of block is H=8.0 cmH=8.0 \mathrm{~cm} then height of the submerged part is ____\_\_\_\_ cm.JEE Main/MCQ/Medium/Archmidies Principle
  34. 34A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2100 \mathrm{~cm}^2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5×103 kg/m31.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3. What force one needs to apply on the hinged door so that it does not get opened ?
    (Acceleration due to gravity     =10 m/s2=10 \mathrm{~m} / \mathrm{s}^2)    JEE Main/Numerical/Medium/Archmidies Principle
  35. 35A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ?
    (Given : density of water     =1000 kg m−3=1000 \mathrm{~kg} \mathrm{~m}^{-3} )    JEE Main/MCQ/Medium/Archmidies Principle
  36. 36A sphere of relative density σ\sigma and diameter DD has concentric cavity of diameter dd. The ratio of Dd\frac{D}{d}, if it just floats on water in a tank is :JEE Main/MCQ/Medium/Archmidies Principle
  37. 37A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil =0.8=0.8, specific gravity of ice =0.9=0.9)
    JEE Main/MCQ/Medium/Archmidies Principle/With diagram
  38. 38A small ball of mass MM and density ρ\rho is dropped in a viscous liquid of density ρ0{\rho }_{0}. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?JEE Main/MCQ/Medium/Archmidies Principle
  39. 39A fully loaded boeing aircraft has a mass of 5.4×105kg5.4\times {10}^{5}kg. Its total wing area is 500m2500{m}^{2}. It is in level flight with a speed of 1080kmh−11080km{h}^{-1}. If the density of air ρ\rho is 1.2kgm–31.2kg{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
    (    g=10ms−2g=10m{s}^{-2})    JEE Main/MCQ/Medium/Archmidies Principle
  40. 40The velocity of a small ball of mass 0.3g0.3g and density 8gcc−18g{cc}^{-1} when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3gcc−11.3g{cc}^{-1}, then the value of viscous force acting on the ball will be x×10−4Nx\times {10}^{-4}N, the value of xx is _____ .
    [use     g=10ms−2g=10m{s}^{-2}]    JEE Main/Numerical/Medium/Archmidies Principle
  41. 41A cubical block of side 0.5m0.5m floats on water with 3030% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?

    [Take, density of water     =103kg/m3={10}^{3}kg/{m}^{3} ]    JEE Main/MCQ/Medium/Archmidies Principle
  42. 42A wooden block floating in a bucket of water has 45\dfrac{4}{5} of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:JEE Main/MCQ/Medium/Archmidies Principle
  43. 43There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90o angle at centre. Radius joining their interface makes an angle α\alpha with vertical. Ratio \dfrac{{}_{}}{}d1\dfrac{{\text{d}}_{1}}{{}_{}}\dfrac{{}_{}}{} is :
    JEE Main/MCQ/Medium/Archmidies Principle/With diagram
  44. 44A ball is made of a material of density ρ\rho where ρoil <ρ<ρwater \rho_{\text {oil }} \lt \rho \lt \rho_{\text {water }} with ρoil \rho_{\text {oil }} and ρwater \rho_{\text {water }} representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?JEE Main/MCQ/Medium/Archmidies Principle
  45. 45A jar filled with two non mixing liquids 1 and 2 having densities ρ1\rho_1 and ρ2\rho_2 respectively. A solid ball, made of a material of density ρ3\rho_3, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ρ1,ρ2\rho_1, \rho_2 and ρ3\rho_3 ?
    JEE Main/MCQ/Medium/Archmidies Principle/With diagram
  46. 46A liquid of density 600600 kg/m3^3 flowing steadily in a tube of varying cross-section. The cross-section at a point AA is 1.01.0 cm2^2 and that at BB is 2020 mm2^2. Both the points AA and BB are in same horizontal plane, the speed of the liquid at AA is 1010 cm/s. The difference in pressures at AA and BB points is ________ Pa.JEE Main/MCQ/Medium/Hydrodynamics
  47. 47A water spray gun is attached to a hose of cross sectional area 3030 cm2^2. The gun comprises of 1010 perforations each of cross sectional area 1515 mm2^2. If the water flows in the hose with the speed of 5050 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)JEE Main/MCQ/Medium/Hydrodynamics
  48. 48Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at AA and BB are 6 cm26 \mathrm{~cm}^{2} and 3 cm23 \mathrm{~cm}^{2} respectively. The rate of flow will be ____\_\_\_\_ cm3/s\mathrm{cm}^{3} / \mathrm{s}. (take g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^{2})
    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  49. 49Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m20.5 \mathrm{~m}^2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g=10 m/s2)\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)JEE Main/MCQ/Medium/Hydrodynamics
  50. 50Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1P_1. The reading of the pressure gauge falls to P2P_2 when the valve is opened. The speed of water flowing in the pipe is proportional toJEE Main/MCQ/Medium/Hydrodynamics
  51. 51

    A tube of length     LL is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s2 \mathrm{~m} / \mathrm{s}, then velocity of water leaving the point (2) will be    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  52. 52Correct Bernoulli's equation is (symbols have their usual meaning) :JEE Main/MCQ/Medium/Hydrodynamics
  53. 53Given below are two statements:
    Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation     P1−P2=ρg(h2−h1)P_1-P_2=\rho g\left(h_2-h_1\right).
    Statement II : In ventury tube shown     2gh=v12−v222 \mathrm{gh}=v_1^2-v_2^2

    In the light of the above statements, choose the most appropriate answer from the options given below.    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  54. 54In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70ms−170m{s}^{-1} and 65ms−165m{s}^{-1} respectively. If the wing area is 2m22{m}^{2}, the lift of the wing is _______NN. (Given density of air =1.2kgm−3=1.2kg{m}^{-3})JEE Main/Numerical/Medium/Hydrodynamics
  55. 55The reading of pressure metre attached with a closed pipe is 4.5×104Nm−24.5\times {10}^{4}N{m}^{-2}. On opening the valve, water starts flowing and the reading of pressure metre falls to 2.0×104Nm−22.0\times {10}^{4}N{m}^{-2}. The velocity of water is found to be Vms−1\sqrt{V}m{s}^{-1}. The value of VV is _________.JEE Main/Numerical/Medium/Hydrodynamics
  56. 56
    The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross-sectional areas at     AA is 1.5cm2,1.5{cm}^{2}, and BB is 25mm2,25{mm}^{2}, if the speed of liquid at BB is 60cms−160cm{s}^{-1} then (PA–PB)({P}_{A}–{P}_{B}) is
    (Given     PA{P}_{A} and PB{P}_{B} are liquid pressures at AA and BB points.
    Density     ρ=1000kgm−3\rho =1000kg{m}^{-3}
    AA and BB are on the axis of tube)    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  57. 57Glycerin of density 1.25×103kgm–31.25\times {10}^{3}kg{m}^{–3} is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are 10cm210{cm}^{2} and 5cm25{cm}^{2} and pressure drop across its length is 3Nm–23N{m}^{–2}. The rate of flow of glycerine through the pipe is x×10–5m3s–1x\times {10}^{–5}{m}^{3}{s}^{–1}. The value of xx is _____.JEE Main/Numerical/Medium/Hydrodynamics
  58. 58Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0cm22.0{cm}^{2}. The area of cross section at the outlet is 10mm210{mm}^{2}. If the piston is pushed at a speed of 4cms−14cm{s}^{-1}, the speed of outgoing fluid is _____ cms−1cm{s}^{-1}
    JEE Main/Numerical/Medium/Hydrodynamics/With diagram
  59. 59A liquid of density 750kgm−3750kg{m}^{-3} flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1=1.2×10−2m2{A}_{1}=1.2\times {10}^{-2}{m}^{2} to A2=A12{A}_{2}=\dfrac{{A}_{1}}{2}. The pressure difference between the wide and narrow sections of the pipe is 4500Pa4500Pa. The rate of flow of liquid is _____ ×10−3m3s−1\times {10}^{-3}{m}^{3}{s}^{-1}.JEE Main/Numerical/Medium/Hydrodynamics
  60. 60An ideal fluid of density 800kgm−3800kg{m}^{-3}, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to a2\dfrac{a}{2}. The pressure difference between the wide and narrow sections of pipe is 4100Pa4100Pa. At wider section, the velocity of fluid is x6ms−1\dfrac{\sqrt{x}}{6}{ms}^{-1} for x=x=_____ . (Given g=10ms−2g=10{ms}^{-2})
    JEE Main/Numerical/Medium/Hydrodynamics/With diagram
  61. 61Two narrow bores of diameter 5.0mm5.0mm and 8.0mm8.0mm are joined together to form a U−U-shaped tube open at both ends. If this U−U-tube contains water, what is the difference in the level of two limbs of the tube.
    [Take surface tension of water     T=7.3×10−2Nm−1T=7.3\times {10}^{-2}N{m}^{-1}, angle of contact =0,g=10ms−2=0,g=10{ms}^{-2} and density of water=1.0×103kgm−3]\left.=1.0\times {10}^{3}kg{m}^{-3}\right]    JEE Main/MCQ/Medium/Hydrodynamics
  62. 62Consider a water tank as shown in the figure. It's cross-sectional area is 0.4m20.4{m}^{2}. The tank has an opening BB near the bottom whose cross-section area is 1cm21{cm}^{2}. A load of 24kg24kg is applied on the water at the top when the height of the water level is 40cm40cm above the bottom, the velocity of water coming out the opening BB is vms−1vm{s}^{-1}. The value of vv, to the nearest integer, is ___ .[Take the value of gg to be 10ms−210{ms}^{-2}]
    JEE Main/Numerical/Medium/Hydrodynamics/With diagram
  63. 63A fluid is flowing through a horizontal pipe of varying cross-section, with vms−1v {ms}^{-1} at a point where the pressure is PP Pascal. At another point where pressure P2\dfrac{P}{2} Pascal its speed is Vms−1V{ms}^{-1}. If the density of the fluid is ρkg−m−3\rho kg-{m}^{-3} and the flow is streamline, then VV is equal toJEE Main/MCQ/Medium/Hydrodynamics
  64. 64Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density dd. The area of the base of both vessels is SS but the height of liquid in one vessel is x1{x}_{1} and in the other x2{x}_{2}. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :JEE Main/MCQ/Medium/Hydrodynamics
  65. 65Water flows m a horizontal tube (see figure). The pressure of water changes by 700Nm−2700N{m}^{-2} between AA and BB where the area of cross section are 40cm240c{m}^{2} and 20cm2,20c{m}^{2}, respectively. Find the rate of flow of water through the tube. (density of water =1000kgm−3=1000kg{m}^{-3} )

    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  66. 66An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm6.4cm and 4.8cm4.8cm , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:JEE Main/MCQ/Medium/Hydrodynamics
  67. 67Water from a tap emerges vertically downwards with an initial speed of 1.0ms−11.0m{s}^{-1} . The cross −- sectional area of the tap is 10−4m2{10}^{-4}{m}^{2} . Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross −- sectional area of the stream, 0.15m0.15m below the tap would be:
    (Take     g=10ms−2g=10m{s}^{-2} )    JEE Main/MCQ/Medium/Hydrodynamics
  68. 68A liquid of density ρ\rho is coming out of a hose pipe of radius a with horizontal speed vv and hits a mesh. 50%50 \% of the liquid passes through the mesh unaffected. 25%25 \% looses all of its momentum and 25%25 \% comes back with the same speed. The resultant pressure on the mesh will be:JEE Main/MCQ/Medium/Hydrodynamics
  69. 69Water flows into a large tank with flat bottom at the rate of 10−4m3s−1.{10}^{-4}{m}^{3}{s}^{-1}. Water is also leaking out of a hole of area 1cm21c{m}^{2} at its bottom. If the height of the water in the tank remains steady then this height is:JEE Main/MCQ/Medium/Hydrodynamics
  70. 70Two tubes of radii r1{r}_{1} and r2{r}_{2} and lengths l1{l}_{1} and l2,{l}_{2,} respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1{P}_{1} and P2{P}_{2} are pressure differences across the two tubes. If P2{P}_{2} is 4P14{P}_{1} and l2{l}_{2} is l14\dfrac{{l}_{1}}{4} then the radius r2{r}_{2} will be equal to :JEE Main/MCQ/Medium/Hydrodynamics
  71. 71
    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)\left(r\lt \lt R\right) 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:    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  72. 72
    In the diagram shown, the difference in the two tubes of the manometer is     5cm5cm, the cross-section of the tube at AA and BB is 6mm26{mm}^{2} and 10mm210{mm}^{2} respectively. The rate at which water flows through the tube is (g=10ms−2)\left(g=10m{s}^{-2}\right)    JEE Main/MCQ/Medium/Hydrodynamics/With diagram
  73. 73A cylindrical vessel of cross-section A contains water to a height h\mathrm{h}. There is a hole in the bottom of radius ' aa '. The time in which it will be emptied is:JEE Main/MCQ/Medium/Hydrodynamics
  74. 74The average mass of rain drops is 3.0×10−5 kg3.0 \times 10^{-5} \mathrm{~kg} and their avarage terminal velocity is 9 m/s9 \mathrm{~m} / \mathrm{s}. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm100 \mathrm{~cm} of rain in a year.JEE Main/MCQ/Medium/Hydrodynamics
  75. 75Water is flowing through a horizontal tube having cross-sectional areas of its two ends being AA and A′A^{\prime} such that the ratio A/A′A / A^{\prime} is 5 . If the pressure difference of water between the two ends is 3×3 \times 105 N m−210^5 \mathrm{~N} \mathrm{~m}^{-2}, the velocity of water with which it enters the tube will be (neglect gravity effects)JEE Main/MCQ/Medium/Hydrodynamics
  76. 76A square hole of side length ℓ\ell is made at a depth of h\mathrm{h} and a circular hole of radius r\mathrm{r} is made at a depth of 4 h4 \mathrm{~h} from the surface of water in a water tank kept on a horizontal surface. If ℓ<<h,r<<h\ell\lt \lt h, r\lt \lt h and the rate of water flow from the holes is the same, then rr is equal toJEE Main/MCQ/Medium/Hydrodynamics/With diagram
  77. 77Water is flowing continuously from a tap having an internal diameter 8×10−3 m8 \times 10^{-3} \mathrm{~m}. The water velocity as it leaves the tap is 0.4 ms−10.4 \mathrm{~ms}^{-1}. The diameter of the water stream at a distance 2×10−1 m2 \times 10^{-1} \mathrm{~m} below the lap is close to :JEE Main/MCQ/Medium/Hydrodynamics
  78. 78A cylindrical vessel of 4040 cm radius is completely filled with water and its capacity is 528528 dm3^3 (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 7070 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm.JEE Main/MCQ/Medium/Efflux of liquid
  79. 79The surface of water in a water tank of cross section area 750cm2750{cm}^{2} on the top of a house is hmhm. above the tap level. The speed of water coming out through the tap of cross section area 500mm2500{mm}^{2} is 30cms−130cm{s}^{-1}. At that instant, dhdt\dfrac{dh}{dt} is x×10−3ms−1x\times {10}^{-3}m{s}^{-1}. The value of xx will be ______.JEE Main/Numerical/Medium/Efflux of liquid
  80. 80Consider a cylindrical tank of radius 1m1m is filled with water. The top surface of water is at 15m15m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5m5m from the bottom. A force of 5×105N5\times {10}^{5}N is applied an the top surface of water using a piston. The speed of efflux from the hole will be :
    (given atmospheric pressure     PA=1.01×105Pa{P}_{A}=1.01\times {10}^{5}Pa, density of water ρw=1000kgm−3{\rho }_{w}=1000kg{m}^{-3} and gravitational acceleration g=10ms−2g=10m{s}^{-2})
    JEE Main/MCQ/Medium/Efflux of liquid/With diagram
  81. 81A pressure-pump has a horizontal tube of cross-sectional area 10cm210{cm}^{2} for the outflow of water at a speed of 20ms−120m{s}^{-1}. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water =1000kgm−3=1000kg{m}^{-3}]JEE Main/MCQ/Medium/Efflux of liquid
  82. 82The area of cross-section of a large tank is 0.5m20.5{m}^{2}. It has a narrow opening near the bottom having area of cross-section 1cm21{cm}^{2}. A load of 25kg25kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40cm40cm above the bottom, will be _____ cms−1cm{s}^{-1}.
    [Take     g=10ms−2g=10{ms}^{-2} ]    JEE Main/Numerical/Medium/Efflux of liquid
  83. 83The top of a water tank is open to air and its water level is maintained. It is giving out 0.74m30.74{m}^{3} water per minute through a circular opening of 2cm2cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:JEE Main/MCQ/Medium/Efflux of liquid
  84. 84A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.80.8 ). The height of water is 3 m3 \mathrm{~m} and that of kerosene 2 m2 \mathrm{~m}. When the hole is opened the velocity of fluid coming out from it is nearly: (take g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2} and density of water =103 kg m−3)\left.=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\right)JEE Main/MCQ/Medium/Efflux of liquid
  85. 85In a cylindrical water tank, there are two small holes AA and BB on the wall at a depth of h1h_1, from the surface of water and at a height of h2h_2 from the bottom of water tank. Surface of water is at height of h2h_2 from the bottom of water tank. Surface of water is at heigh HH from the bottom of water tank. Water coming out from both holes strikes the ground at the same point SS. Find the ratio of h1h_1 and h2h_2
    JEE Main/MCQ/Medium/Efflux of liquid/With diagram
  86. 86A cylinder of height 20 m20 \mathrm{~m} is completely filled with water. The velocity of efflux of water (in ms−1\mathrm{ms}^{-1} ) through a small hole on the side wall of the cylinder near its bottom isJEE Main/MCQ/Medium/Efflux of liquid
  87. 87Eight mercury drops, each of radius rr, coalesce to form a bigger drop. The surface energy released in this process is _______. (SS is the surface tension of mercury).JEE Main/MCQ/Medium/Surface tension
  88. 88The surface tension of a soap solution is 3.5×10−23.5 \times 10^{-2} N/m. The work required to increase the radius of a soap bubble from 11 cm to 22 cm is α×10−6\alpha \times 10^{-6} J. The value of α\alpha is _____. (π=22/7\pi = 22/7)JEE Main/Numerical/Medium/Surface tension
  89. 89The surface tension of a soap bubble is 0.030.03 N/m. The work done in increasing the diameter of bubble from 22 cm to 66 cm is απ×10−4\alpha \pi \times 10^{-4} J. The value of α\alpha is _______. (Take π=3.14\pi = 3.14)JEE Main/MCQ/Medium/Surface tension
  90. 90A liquid drop of diameter 22 mm breaks into 512512 droplets. The change in surface energy is α×10−6\alpha \times 10^{-6} J. The value of α\alpha is _______. (Take surface tension of liquid =0.08= 0.08 N/m)JEE Main/MCQ/Medium/Surface tension
  91. 91A soap bubble of surface tension 0.04 N/m0.04 \mathrm{~N} / \mathrm{m} is blown to a diameter of 7 cm. If (15000−x)μJ(15000-x) \mu \mathrm{J} of work is done in blowing it further to make its diameter 14 cm, then the value of xx is ____\_\_\_\_. (π=22/7\pi=22 / 7)JEE Main/Numerical/Medium/Surface tension
  92. 92When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height hh. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1%1 \% each, then the height of the liquid in the tube will change by %\%.JEE Main/MCQ/Medium/Surface tension
  93. 93Given below are two statements:
    Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
    Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
    In the light of the above statements, choose the correct answer from the options given below    JEE Main/MCQ/Medium/Surface tension
  94. 94Surface tension of two liquids (having same densities), T1T_{1} and T2T_{2}, are measured using capillary rise method utilizing two tubes with inner radii of r1r_{1} and r2r_{2} where r1>r2r_{1}\gt r_{2}. The measured liquid heights in these tubes are h1h_{1} and h2h_{2} respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h1h_{1} and h2h_{2} and surfaces tensions T1T_{1} and T2T_{2} satisfy the relation:JEE Main/MCQ/Medium/Surface tension
  95. 95A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70dyn/cm70 \mathrm{dyn} / \mathrm{cm} and glass water contact angle ≃0∘\simeq 0^{\circ}) with 30∘30^{\circ} inclined with vertical. The length of water risen in the capillary is ________ cm.
    (\left(\right. Take g=9.8 m/s2)\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)    JEE Main/MCQ/Medium/Surface tension
  96. 96Two liquids A and B have θA\theta_{\mathrm{A}} and θB\theta_{\mathrm{B}} as contact angles in a capillary tube. If K=cos⁡θA/cos⁡θBK=\cos \theta_A / \cos \theta_B. then identify the correct statement:JEE Main/MCQ/Medium/Surface tension
  97. 97The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is nn times the volume of the bubble BB, then, the value of nn is ___.JEE Main/Numerical/Medium/Surface tension
  98. 98Two water drops each of radius 'r' coalesce to from a bigger drop. If ' T ' is the surface tension, the surface energy released in this process is :JEE Main/MCQ/Medium/Surface tension
  99. 99A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____ π×10−13 m3/s\pi \times 10^{-13} \mathrm{~m}^3 / \mathrm{s}.JEE Main/Numerical/Medium/Surface tension
  100. 100An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m31000 \mathrm{~kg} / \mathrm{m}^3. If the pressure inside the bubble is 2100 N/m22100 \mathrm{~N} / \mathrm{m}^2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )JEE Main/MCQ/Medium/Surface tension
  101. 101The amount of work done to break a big water drop of radius ' RR ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will beJEE Main/MCQ/Medium/Surface tension
  102. 102An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J/m20.095 \mathrm{~J} / \mathrm{m}^2 and density 103 kg/m310^3 \mathrm{~kg} / \mathrm{m}^3. The difference between pressure inside the bubble and atmospheric pressure is _____ N/m2\mathrm{N} / \mathrm{m}^2. (Take g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )JEE Main/Numerical/Medium/Surface tension
  103. 103Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ .JEE Main/Numerical/Medium/Surface tension
  104. 104The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:JEE Main/MCQ/Medium/Surface tension
  105. 105A liquid column of height 0.04 cm0.04 \mathrm{~cm} balances excess pressure of a soap bubble of certain radius. If density of liquid is 8×103 kg m−38 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3} and surface tension of soap solution is 0.28Nm−10.28 \mathrm{Nm}^{-1}, then diameter of the soap bubble is _____ cm\mathrm{cm}. (if g=10 m s−2g=10 \mathrm{~m} \mathrm{~s}^{-2} )JEE Main/Numerical/Medium/Surface tension
  106. 106Pressure inside a soap bubble is greater than the pressure outside by an amount :
    (given :     R=\mathrm{R}= Radius of bubble S=\mathrm{S}= Surface tension of bubble)    JEE Main/MCQ/Medium/Surface tension
  107. 107A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is 10x\frac{10}{x}. The value of xx is __________JEE Main/Numerical/Medium/Surface tension
  108. 108Given below are two statements :
    Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be     0∘0^{\circ}.
    Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
    In the light of the above statement, choose the correct answer from the options given below.    JEE Main/MCQ/Medium/Surface tension
  109. 109Given below are two statements :
    Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
    Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Surface tension
  110. 110A soap bubble is blown to a diameter of 7 cm.36960erg7 \mathrm{~cm} .36960 \mathrm{erg} of work is done in blowing it further. If surface tension of soap solution is 40dyne/cm40 \mathrm{dyne} / \mathrm{cm} then the new radius is______ cm\mathrm{cm} Take (π=227)\left(\pi=\frac{22}{7}\right)JEE Main/Numerical/Medium/Surface tension
  111. 111A big drop is formed by coalescing 10001000 small droplets of water. The surface energy will become :JEE Main/MCQ/Medium/Surface tension
  112. 112A big drop is formed by coalescing 10001000 small identical drops of water. If E1{E}_{1} be the total surface energy of 10001000 small drops of water and E2{E}_{2} be the surface energy of single big drop of water, the E1{E}_{1} : E2{E}_{2} is x:1x:1, where x=x=________.JEE Main/Numerical/Medium/Surface tension
  113. 113A small liquid drop of radius RR is divided into 2727 identical liquid drops. If the surface tension is TT, then the work done in the process will be :JEE Main/MCQ/Medium/Surface tension
  114. 114There is an air bubble of radius 1.0mm1.0mm in a liquid of surface tension 0.075Nm–10.075N{m}^{–1} and density 1000kgm–31000kg{m}^{–3} at a depth of 10cm10cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ Pa(g=10ms−2)Pa\left(g=10m{s}^{-2}\right).JEE Main/Numerical/Medium/Surface tension
  115. 1156464 identical drops each charged upto potential of 10mV10mV are combined to form a bigger drop. The potential of the bigger drop will be _____ mVmV.JEE Main/Numerical/Medium/Surface tension
  116. 116The surface tension of soap solution is 3.5×10−2Nm−13.5\times {10}^{-2}N{m}^{-1}. The amount of work done required to increase the radius of soap bubble from 10cm10cm to 20cm20cm is _____×10−4J\times {10}^{-4}J . (take π=227\pi =\dfrac{22}{7})JEE Main/Numerical/Medium/Surface tension
  117. 117Eight equal drops of water are falling through air with a steady speed of 10cms−110cm{s}^{-1}. If the drops coalesce, the new velocity is:-JEE Main/MCQ/Medium/Surface tension
  118. 118A mercury drop of radius 10–3m{10}^{–3}m is broken into 125125 equal size droplets. Surface tension of mercury is 0.45Nm–10.45N{m}^{–1} . The gain in surface energy is:JEE Main/MCQ/Medium/Surface tension
  119. 119If 10001000 droplets of water of surface tension 0.07Nm−10.07N{m}^{-1}. having same radius 1mm1mm each, combine to from a single drop. In the process the released surface energy is-
    (Takeπ=227)\left(\text{Take}\pi =\dfrac{22}{7}\right)    JEE Main/MCQ/Medium/Surface tension
  120. 120The height of liquid column raised in a capillary tube of certain radius when dipped in liquid AA vertically is, 5cm5cm. If the tube is dipped in a similar manner in another liquid BB of surface tension and density double the values of liquid AA, the height of liquid column raised in liquid B would be ______ mm.JEE Main/MCQ/Medium/Surface tension
  121. 121Surface tension of a soap bubble is 2.0×10−2Nm−12.0\times {10}^{-2}N{m}^{-1} . Work done to increase the radius of soap bubble from 3.5cm3.5cm to 7cm7cm will be : [Take π=227\pi =\dfrac{22}{7} ]JEE Main/MCQ/Medium/Surface tension
  122. 122A spherical drop of liquid splits into 10001000 identical spherical drops. If ui{u}_{i} is the surface energy of the original drop and uf{u}_{f} is the total surface energy of the resulting drops, the (ignoring evaporation), ufui=(10x)\dfrac{{u}_{f}}{{u}_{i}}=\left(\dfrac{10}{x}\right). Then value of xx is ______:JEE Main/Numerical/Medium/Surface tension
  123. 123Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.
    Reason (R) : Because the angle of contact between the oil/ grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.    JEE Main/MCQ/Medium/Surface tension
  124. 124A spherical soap bubble of radius 3cm3cm is formed inside another spherical soap bubble of radius 6cm6cm. If the internal pressure of the smaller bubble of radius 3cm3cm in the above system is equal to the internal pressure of the another single soap bubble of radius rcmrcm. The value of rr is _____JEE Main/Numerical/Medium/Surface tension
  125. 125A water drop of radius 1cm1cm is broken into 729729 equal droplets. If surface tension of water is 75dynecm−175dyne{cm}^{-1}, then the gain in surface energy upto first decimal place will be
    [Given     π=3.14\pi =3.14]    JEE Main/MCQ/Medium/Surface tension
  126. 126A drop of liquid of density ρ\rho is floating half immersed in a liquid of density σ\sigma and surface tension 7.5×10−4Ncm−17.5\times {10}^{-4}N{cm}^{-1}. The radius of drop in cmcm will be : (Take : g=10ms−2g=10{ms}^{-2})JEE Main/MCQ/Medium/Surface tension
  127. 127A water drop of diameter 2cm2cm is broken into 6464 equal droplets. The surface tension of water is 0.075Nm−10.075N{m}^{-1}. In this process the gain in surface energy will beJEE Main/MCQ/Medium/Surface tension
  128. 128A soap bubble of the radius 3cm3cm is formed inside another soap bubble of radius, 6cm6cm. The radius of an equivalent soap bubble that has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is____cm.cm.JEE Main/Numerical/Medium/Surface tension
  129. 129Two small drops of mercury each of radius RR coalesce to form a single large drop. The ratio of total surface energy before and after the change isJEE Main/MCQ/Medium/Surface tension
  130. 130Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01cm30.01{cm}^{3} of oleic acid per cm3{cm}^{3} of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4cm24{cm}^{2} by considering 100100 spherical drops of radius (340π)13×10−3cm.{\left(\dfrac{3}{40\pi }\right)}^{\dfrac{1}{3}}\times {10}^{-3}cm. Then the thickness of oleic acid layer will be x×10−14mx\times {10}^{-14}m. Where xx is ________ .JEE Main/Numerical/Medium/Surface tension
  131. 131When two soap bubbles of radii aa and bb(b>a)(b\gt a) coalesce, the radius of curvature of common surface is:JEE Main/MCQ/Medium/Surface tension
  132. 132A large number of water drops, each of radius rr, combine to have a drop of radius RR. If the surface tension is TT and mechanical equivalent of heat is JJ, the rise in heat energy per unit volume will be:JEE Main/MCQ/Medium/Surface tension
  133. 133A air bubble of radius 1cm1\text{cm} in water has an upward acceleration of 9.8cms–29.8{\text{cms}}^{–2}. The density of water is 1gm cm–31{\text{gm cm}}^{–3} and water offers negligible drag force on the bubble. The mass of the bubble is (g=980cm/s2)\left(g=980\text{cm}/{\text{s}}^{2}\right).JEE Main/MCQ/Medium/Surface tension
  134. 134When a long glass capillary tube of radius 0.015cm0.015cm is dipped in a liquid, the liquid rises to a height of 15cm15cm within it. If the contact angle between the liquid and glass to close to 0∘0^{\circ}, the surface tension of the liquid, in milliNewton m−1,{m}^{-1}, is [ρ(liqued)=900kgm−3,g=10ms−2]\left[{\rho }_{\text{(liqued)}}=900kg{m}^{-3},g=10m{s}^{-2}\right] (Given answer in closed integer)JEE Main/Numerical/Medium/Surface tension
  135. 135Pressure inside two soap bubbles are 1.011.01 and 1.021.02 atmosphere, respectively. The ratio of their volumes is :JEE Main/MCQ/Medium/Surface tension
  136. 136A capillary tube made of glass of radius 0.15mm0.15mm is dipped vertically in a beaker filled with methylene iodide (surface tension =0.05Nm−1=0.05N{m}^{-1}, density =667kgm−3=667kg{m}^{-3}) which rises to height hh in the tube. It is observed that the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60º60º with one another. Then hh is close to (g=10ms−2g=10m{s}^{-2})JEE Main/MCQ/Medium/Surface tension
  137. 137A small spherical droplet of density dd is floating exactly half immersed in a liquid of density ρ\rho and surface tension T.T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):JEE Main/MCQ/Medium/Surface tension
  138. 138
    Two liquids of densities     ρ1{\rho }_{1} and ρ2(ρ2=2ρ1){\rho }_{2}\left({\rho }_{2}=2{\rho }_{1}\right) are filled up behind a square wall of side 10m10m as shown in figure. Each liquid has a height of 5m.5m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):    JEE Main/MCQ/Medium/Surface tension/With diagram
  139. 139The ratio of surface tensions of mercury and water is given to be 7.57.5, while the ratio of their densities is 13.613.6. Their contact angles, with glass, are close to 135∘135^{\circ} and 0∘0^{\circ}, respectively. If it is observed that mercury gets depressed by an amount hh in a capillary tube of radius r1{r}_{1}, while water rises by the same amount hh in a capillary tube of radius r2{r}_{2}, then the ratio r1r2\dfrac{{r}_{1}}{{r}_{2}} is close toJEE Main/MCQ/Medium/Surface tension
  140. 140If ′M′'M' is the mass of water that rises in a capillary tube of radius ′r′'r' , then mass of water which will rise in a capillary tube of radius ′2r′'2r' is:JEE Main/MCQ/Medium/Surface tension
  141. 141A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:JEE Main/MCQ/Medium/Surface tension
  142. 142A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P2{P}_{2} be the pressure inside the inner bubble and P0{P}_{0}, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2−P0{P}_{2}-{P}_{0} between its inside and outside would be:JEE Main/MCQ/Medium/Surface tension
  143. 143If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by:

    JEE Main/MCQ/Medium/Surface tension/With diagram
  144. 144A large number of liquid drops each of radius rr coalesce to form a single drop of the radius RR. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid TT, density ρ\rho)JEE Main/MCQ/Medium/Surface tension
  145. 145Two soap bubbles coalesce to form a single bubble. If V\mathrm{V} is the subsequent change in volume of contained air and S\mathrm{S} change in total surface area, T\mathrm{T} is the surface tension and P\mathrm{P} atmospheric pressure, then which of the following relation is correct?JEE Main/MCQ/Medium/Surface tension
  146. 146An air bubble of radius 0.1 cm0.1 \mathrm{~cm} is in a liquid having surface tension 0.06 N/m0.06 \mathrm{~N} / \mathrm{m} and density 103 kg/m310^3 \mathrm{~kg} / \mathrm{m}^3. The pressure inside the bubble is 1100Nm−21100 \mathrm{Nm}^{-2} greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g=9.8 ms−2)\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)JEE Main/MCQ/Medium/Surface tension
  147. 147A capillary tube is immersed vertically in water and the height of the water column is x⁡x⁡. When this arrangement is taken into a mine of depth d, the height of the water column is y⁡y⁡. If R is the radius of earth, the ratio x⁡y⁡\dfrac{x⁡}{y⁡} is :JEE Main/MCQ/Medium/Surface tension
  148. 148An open glass tube is immersed in mercury in such a way that a length of 8cm8cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46cm46cm. What will be length of the air column above mercury in the tube now ?
    (Atmospheric pressure =     76cm76cm of Hg)    JEE Main/MCQ/Medium/Surface tension
  149. 149On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
    (density of water is     ρw{\rho }_{\text{w}})

    JEE Main/MCQ/Medium/Surface tension/With diagram
  150. 150Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact θ\theta and the height hh upto which water rises change. These changes are :JEE Main/MCQ/Medium/Surface tension
  151. 151This question has Statement-1 and Statement- 2 . Of the four choices given after the Statements, choose the one that best describes the two Statetnents.
    Statement-1: A capillary is dipped in a liquid and liquid rises to a height     hh in it. As the temperature of the liquid is raised, the height hh increases (if the density of the liquid and the angle of contact remain the same).
    Statement-2: Surface tension of a liquid decreases with the rise in its temperature.    JEE Main/MCQ/Medium/Surface tension
  152. 152Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is TT, the density of the liquid isρ\rho and LL is its latent heat of vaporisation.)JEE Main/MCQ/Medium/Surface tension
  153. 153A large number of droplets, each of radius, rr coalesce to form a bigger drop of radius, RR. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( T=T= surface tension, ρ=\rho= density)JEE Main/MCQ/Medium/Surface tension
  154. 154A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5×10−2 N1.5 \times 10^{-2} \mathrm{~N} (see figure). The length of the slider is 30 cm30 \mathrm{~cm} and its weight negligible. The surface tension of the liquid film is
    JEE Main/MCQ/Medium/Surface tension/With diagram
  155. 155Work done in increasing the size of a soap bubble from a radius of 3 cm3 \mathrm{~cm} to 5 cm5 \mathrm{~cm} is nearly (Surface tension of soap solution =0.03Nm−1=0.03 \mathrm{Nm}^{-1} ):JEE Main/MCQ/Medium/Surface tension
  156. 156A capillary tube (A)(\mathrm{A}) is dropped in water. Another identical tube (B)(\mathrm{B}) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
    JEE Main/MCQ/Medium/Surface tension/With diagram
  157. 157A 20 cm20 \mathrm{~cm} long capillary tube is dipped in water. The water rises up to 8 cm8 \mathrm{~cm}. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will beJEE Main/MCQ/Medium/Surface tension
  158. 158If two soap bubbles of different radii are connected by a tube,JEE Main/MCQ/Medium/Surface tension
  159. 159A spherical liquid drop of radius RR acquires the terminal velocity v1v_1 when falls through a gas of viscosity η\eta. Now the drop is broken into 6464 identical droplets and each droplet acquires terminal velocity v2v_2 falling through the same gas. The ratio of terminal velocities v1/v2v_1/v_2 is ________.JEE Main/MCQ/Medium/Viscosity
  160. 160If an air bubble of diameter 22 mm rises steadily through a liquid of density 20002000 kg/m3^3 at a rate of 0.50.5 cm/s, then the coefficient of viscosity of liquid is _______ Poise. (Take g=10g = 10 m/s2^2)JEE Main/MCQ/Medium/Viscosity
  161. 161Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s10 \mathrm{~cm} / \mathrm{s} coalesce to form a bigger drop. The terminal velocity of bigger drop is ____\_\_\_\_ cm/s\mathrm{cm} / \mathrm{s}.JEE Main/Numerical/Medium/Viscosity
  162. 162A small metallic sphere of diameter 2 mm and density 10.5 g/cm310.5 \mathrm{~g} / \mathrm{cm}^{3} is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm31.5 \mathrm{~g} / \mathrm{cm}^{3} respectively. The terminal velocity attained by the sphere is ____\_\_\_\_ cm/s\mathrm{cm} / \mathrm{s}.
    (    π=227\pi=\frac{22}{7} and g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^{2})    JEE Main/MCQ/Medium/Viscosity
  163. 163The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s20 \mathrm{~cm} / \mathrm{s}. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ____\_\_\_\_ cm/s\mathrm{cm} / \mathrm{s}.JEE Main/Numerical/Medium/Viscosity
  164. 164A spherical body of radius rr and density σ\sigma falls freely through a viscous liquid having density ρ\rho and viscosity η\eta and attains a terminal velocity v0v_{0}. Estimated maximum error in the quantity η\eta is : (Ignore errors associated with σ,ρ\sigma, \rho and gg, gravitational acceleration)JEE Main/MCQ/Medium/Viscosity
  165. 165A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45×10−2 m/s2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s} while falling under gravity through an oil of density 925 kg m−3925 \mathrm{~kg} \mathrm{~m}^{-3}. Take density of steel as 7825 kg m−37825 \mathrm{~kg} \mathrm{~m}^{-3} and g as 9.8 m/s2\mathrm{m} / \mathrm{s}^2. The viscosity of the oil in SI unit isJEE Main/MCQ/Medium/Viscosity
  166. 166Consider following statements:
    A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
    B. As the temperature of liquid rises, the coefficient of viscosity increases.
    C. As the temperature of gas increases, the coefficient of viscosity increases
    D. The onset of turbulence is determined by Reynold's number.
    E. In a steady flow two stream lines never intersect.
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Viscosity
  167. 167In the experiment for measurement of viscosity ' η\eta ' of given liquid with a ball having radius RR, consider following statements.
    A. Graph between terminal velocity V and R will be a parabola.
    B. The terminal velocities of different diameter balls are constant for a given liquid.
    C. Measurement of terminal velocity is dependent on the temperature.
    D. This experiment can be utilized to assess the density of a given liquid.
    E. If balls are dropped with some initial speed, the value of     η\eta will change.
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Viscosity
  168. 168Given below are two statements:
    Statement I: The hot water flows faster than cold water
    Statement II: Soap water has higher surface tension as compared to fresh water.
    In the light above statements, choose the correct answer from the options given below    JEE Main/MCQ/Medium/Viscosity
  169. 169A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)JEE Main/MCQ/Medium/Viscosity
  170. 170A spherical ball of radius 1×10−4 m1 \times 10^{-4} \mathrm{~m} and density 105 kg/m310^5 \mathrm{~kg} / \mathrm{m}^3 falls freely under gravity through a distance hh before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of hh is approximately:
    (The coefficient of viscosity of water is     9.8×10−6 N s/m29.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2 )    JEE Main/MCQ/Medium/Viscosity
  171. 171Small water droplets of radius 0.01 mm0.01 \mathrm{~mm} are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s10 \mathrm{~cm} / \mathrm{s}. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____cm/s\mathrm{cm} / \mathrm{s}.JEE Main/Numerical/Medium/Viscosity
  172. 172A small ball of mass mm and density ρ\rho is dropped in a viscous liquid of density ρ0\rho_0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :JEE Main/MCQ/Medium/Viscosity
  173. 173A small spherical ball of radius rr, falling through a viscous medium of negligible density has terminal velocity vv. Another ball of the same mass but of radius 2r2r, falling through the same viscous medium will have terminal velocity:JEE Main/MCQ/Medium/Viscosity
  174. 174Given below are two statements :
    Statement (I) : Viscosity of gases is greater than that of liquids.
    Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Viscosity
  175. 175Given below are two statements: one is labelled as
    Assertion A and the other is labelled as Reason R
    Assertion A : A spherical body of radius     (5±0.1)mm(5\pm 0.1)mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 44%.
    Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below    JEE Main/MCQ/Medium/Viscosity
  176. 176An air bubble of diameter 6mm6mm rises steadily through a solution of density 1750kgm−31750kg{m}^{-3} at the rate of 0.35cms−10.35cm{s}^{-1}. The co-efficient of viscosity of the solution (neglect density of air) is ________ Pas (given, g=10ms−2g=10m{s}^{-2}).JEE Main/Numerical/Medium/Viscosity
  177. 177A metal block of base area 0.20m20.20{m}^{2} is placed on a table, as shown in figure. A liquid film of thickness 0.25mm0.25mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1N0.1N and moves with a constant speed. If the viscosity of the liquid is 5.0×10–3Pl5.0\times {10}^{–3}Pl, the speed of block is ______ ×10−3ms−1\times {10}^{-3}m{s}^{-1}.
    JEE Main/Numerical/Medium/Viscosity/With diagram
  178. 178A spherical ball of radius 1mm1mm and density 10.5gcc−110.5g{cc}^{-1} is dropped in glycerine of coefficient of viscosity 9.89.8 poise and density 1.5gcc−11.5g{cc}^{-1}. Viscous force on the ball when it attains constant velocity is 3696×10−xN3696\times {10}^{-x}N. The value of xx is
    (Given,     g=9.8ms−2andπ=227g=9.8m{s}^{-2}\text{and}\pi =\dfrac{22}{7})    JEE Main/Numerical/Medium/Viscosity
  179. 179The diameter of an air bubble which was initially 2mm2mm, rises steadily through a solution of density 1750 kg/m31750 \mathrm{~kg} / \mathrm{m}^3 at the rate of 0.35 cm/s0.35 \mathrm{~cm} / \mathrm{s}. Coefficient of viscosity of the solution is ______ (Assume mass of the bubble to be negligible) (Answer in Poise to the nearest integer)JEE Main/Numerical/Medium/Viscosity
  180. 180A small spherical ball of radius 0.1mm0.1mm and density 104kgm−3{10}^{4}kg{m}^{-3} falls freely under gravity through a distance hh before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of hh will be ____ mm. (Given g=10ms−2g=10{ms}^{-2}, viscosity of water =1.0×10−5N‐sm−2=1.0\times {10}^{-5}N‐s{m}^{-2} ).JEE Main/Numerical/Medium/Viscosity
  181. 181A water drop of radius 1μm1\mu m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8×10−5Nsm−21.8\times {10}^{-5}Ns{m}^{-2} and its density is negligible as compared to that of water 106gm−3{10}^{6}g{m}^{-3}. Terminal velocity of the water drop is
    (Take acceleration due to gravity     =10ms−2=10{ms}^{-2})    JEE Main/MCQ/Medium/Viscosity
  182. 182The velocity of a small ball of mass mm and density d1{d}_{1}, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2{d}_{2}, then the viscous force acting on the ball, will beJEE Main/MCQ/Medium/Viscosity
  183. 183The velocity of upper layer of water in a river is 36kmh−136km{h}^{-1}. Shearing stress between horizontal layers of water is 10−3Nm−2{10}^{-3}N{m}^{-2}. Depth of the river is _____ mm. (Co-efficient of viscosity of water is 10−2Pas{10}^{-2}Pas)JEE Main/Numerical/Medium/Viscosity
  184. 184The terminal velocity (vt)\left({v}_{t}\right) of the spherical rain drop depends on the radius (r)\left(r\right) of the spherical rain drop asJEE Main/MCQ/Medium/Viscosity
  185. 185In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0×10−5m2.0\times {10}^{-5}m and density 1.2×103kgm−31.2\times {10}^{3}kg{m}^{-3}? Take viscosity of liquid =1.8×10−5Nsm−2.=1.8\times {10}^{-5}Ns{m}^{-2}. (Neglect buoyancy due to air).JEE Main/MCQ/Medium/Viscosity
  186. 186A raindrop with radius R=0.2mmR=0.2mm falls from a cloud at a height h=2000mh=2000m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water fw=1000kgm−3{f}_{w}=1000kg{m}^{-3} and Density of air fa=1.2kgm−3,g=10m/s2{f}_{a}=1.2kg{m}^{-3},g=10m/{s}^{2} Coefficient of viscosity of air =1.8×10−5Nsm−2]\left.=1.8\times {10}^{-5}Ns{m}^{-2}\right]JEE Main/MCQ/Medium/Viscosity
  187. 187In an experiment to verify Stokes law, a small spherical ball of radius rr and density ρ\rho falls under gravity through a distance hh in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of hh is proportional to: (ignore viscosity of air)JEE Main/MCQ/Medium/Viscosity
  188. 188A solid sphere, of radius R acquires a terminal velocity v1{v}_{1} when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η.\eta . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2,{v}_{2}, when falling through the same fluid, the ratio (v1v2)\left(\dfrac{{v}_{1}}{{v}_{2}}\right) equals:JEE Main/MCQ/Medium/Viscosity
  189. 189In an experiment, a small steel ball falls through a liquid at a constant speed of 10 cm/s10 \mathrm{~cm} / \mathrm{s}. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?JEE Main/MCQ/Medium/Viscosity
  190. 190A spherical solid ball of volume VV is made of a material of density ρ1\rho_1. It is falling through a liquid of density ρ2(ρ2<ρ1)\rho_2\left(\rho_2 \lt \rho_1\right). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous =−kv2(k>0)F_{\text {viscous }}=-k v^2(k\gt 0). The terminal speed of the ball isJEE Main/MCQ/Medium/Viscosity
  191. 191If the terminal speed of a sphere of gold (density =19.5 kg/m3=19.5 \mathrm{~kg} / \mathrm{m}^3 ) is 0.2 m/s0.2 \mathrm{~m} / \mathrm{s} in a viscous liquid (density =1.5 kg/m3=1.5 \mathrm{~kg} / \mathrm{m}^3 ) of the same size in the same liquid.JEE Main/MCQ/Medium/Viscosity
  192. 192Spherical balls of radius RR are falling in a viscous fluid of viscosity η\eta with a velocity vv. The retarding viscous force acting on the spherical ball isJEE Main/MCQ/Medium/Viscosity

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