STD 11 - Fluid mechanics PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 115 questions

51. 51. The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross sectional areas at \(A\) is \(1.5\,cm ^2\), and \(B\) is \(25\,mm ^2\), if the speed of liquid at \(B\) is \(60\,cm / s\) then \(\left( P _{ A }- P _{ B }\right)\) is :(Given \(P _{ A }\) and \(P _{ B }\) are liquid pressures at \(A\) and \(B\) points.Density \(\rho=1000\,kg\,m ^{-3}\) \(A\) and \(B\) are on the axis of tube \(............\,Pa\)
    2023 Hard
52. 52. The surface of water in a water tank of cross section area \(750\,cm ^2\) on the top of a house is \(h m\). above the tap level. The speed of water coming out through the tap of cross section area \(500\,mm ^2\) is \(30\,cm / s\). At that instant, \(\frac{d h}{d t}\) is \(x \times 10^{-3} m / s\). The value of \(x\) will be \(.............\). 2023 Medium
53. 53. A liquid of density \(750\,kgm ^{-3}\) flows smoothly through a horizontal pipe that tapers in crosssectional area from \(A _{1}=1.2 \times 10^{-2}\,m ^{2}\) to \(A_{2}=\frac{A_{1}}{2}\). The pressure difference between the wide and narrow sections of the pipe is \(4500\,Pa\). The rate of flow of liquid is________\(\times 10^{-3}\,m ^{3} s ^{-1}\) 2022 Hard
54. 54. A pressure-pump has a horizontal tube of cross-sectional area \(10\,cm ^{2}\) for the outflow of water at a speed of \(20\,m / s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is \(...N\) [given : density of water \(=1000\,kg / m ^{3}\) ] 2022 Medium
55. 55. A small spherical ball of radius \(0.1 \,mm\) and density \(10^{4} \,kg m ^{-3}\) falls freely under gravity through a a distance \(h\) 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 \(h\) wil be \(m\). (Given \(g =10 \,ms ^{-2}\), viscosity of water \(=1.0 \times 10^{-5} \,N - sm ^{-2}\) ) 2022 Hard
56. 56. A water drop of radius \(1\,\mu m\) falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is \(1.8 \times 10^{-5}\,Nsm ^{-2}\) and its density is negligible as compared to that of water \(10^{6}\,gm ^{-3}\). Terminal velocity of the water drop is________ \(\times 10^{-6}\,ms ^{-1}\) (Take acceleration due to gravity \(=10\,ms ^{-2}\) ) 2022 Medium
57. 57. An ideal fluid of density \(800 \; kgm ^{-3}\), flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from \(a\) to \(\frac{ a }{2}\). The pressure difference between the wide and narrow sections of pipe is \(4100 \; Pa\). At wider section, the velocity of fluid is \(\frac{\sqrt{x}}{6} \; ms ^{-1}\) for \(x = \dots\) \(\left(\right.\) Given \(g =10 \; m ^{-2}\) )
    2022 Hard
58. 58. Consider a cylindrical tank of radius \(1 m\) is filled with water. The top surface of water is at \(15\,m\) from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of \(5\,m\) from the bottom. A force of \(5 \times 10^{5} N\) is applied an the top surface of water using a piston. The speed of efflux from the hole will be. (given atmospheric pressure \(P_{A}=1.01 \times 10^{5}\,Pa\), density of water \(\rho_{ w }=1000\,kg / m ^{3}\) and gravitational acceleration \(g=10\,m / s ^{2}\) )
    2022 Hard
59. 59. If \(\rho\) is the density and \(\eta\) is coefficient of viscosity of fluid which flows with a speed \(v\) in the pipe of diameter \(d\), the correct formula for Reynolds number \(R _{ e }\) is .............. 2022 Easy
60. 60. The area of cross-section of a large tank is \(0.5 \; m ^{2}\). It has a narrow opening near the bottom having area of cross-section \(1 \; cm ^{2}\). A load of \(25 \; kg\) 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 \(40 \; cm\) above the bottom, will be \(\dots \; cms ^{-1}\). \(\left[\right.\) Take \(\left.g =10 \; ms ^{-2}\right]\) 2022 Medium
61. 61. The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is  ........ \(\times 10^{8}\; Nm ^{-2}\) 2022 Medium
62. 62. The diameter of an air bubble which was initially \(2\,mm\), rises steadily through a solution of density \(1750\,kg\,m\,m ^{-3}\) at the rate of \(0.35\,cms ^{-1}\). The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible). 2022 Medium
63. 63. The terminal velocity \(\left( v _{ t }\right)\) of the spherical rain drop depends on the radius ( \(r\) ) of the spherical rain drop as 2022 Easy
64. 64. The velocity of a small ball of mass \(0.3\,g\) and density \(8\,g / cc\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(1.3\,g / cc\), then the value of viscous force acting on the ball will be \(x \times 10^{-4}\,N\), the value of \(x\) is [use \(g=10\,m / s ^{2}\) ]  2022 Medium
65. 65. The velocity of a small ball of mass ' \(m\) ' and density \(d _{1}\), when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is \(d _{2}\), then the viscous force acting on the ball, will be 2022 Medium
66. 66. The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) ) 2022 Medium
67. 67. Two cylindrical vessels of equal cross-sectional area \(16\,cm ^{2}\) contain water upto herghts \(100\,cm\) and \(150\,cm\) 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 \(......J\) [Take density of water \(=10^{3}\,kg / m ^{3}\) and \(g =10\,ms ^{-2}\) ] 2022 Hard
68. 68. A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston. 2021 Hard
69. 69. A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) 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 \((a\,<\,<\,A)\)
    2021 Hard
70. 70. A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ] 2021 Hard
71. 71. An object is located at \(2\, km\) beneath the surface of the water. If the fractional compression \(\frac{\Delta V }{ V }\) is \(1.36\, \%,\) the ratio of hydraulic stress to the corresponding hydraulic strain will be ......... . [Given : density of water is \(1000\, kg m ^{-3}\) and \(\left. g =9.8 \,ms ^{-2} .\right]\) 2021 Medium
72. 72. 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 \(10 \,ms ^{-2}\) ]
    2021 Hard
73. 73. In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius \(2.0 \times 10^{-5}\, {m}\) and density \(1.2 \times 10^{3} \,{kgm}^{-3}\) ? Take viscosity of liquid \(=1.8 \times 10^{-5}\, {Nsm}^{-2} .\) (Neglect buoyancy due to air). 2021 Medium
74. 74. Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \(0.01 \,cm ^{3}\) of oleic acid per \(cm ^{3}\) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \(4\, cm ^{2}\) by considering \(100\) spherical drops of radius \(\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\, cm .\) Then the thickness of oleic acid layer will be \(x \times 10^{-14} \,m\). Where \(x\) is ...... . 2021 Hard
75. 75. The pressure acting on a submarine is \(3 \times 10^{5}\;Pa\) 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 \(1 \times 10^{5} \;Pa\) density of water is \(10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}\) ) 2021 Medium
76. 76. The water is filled upto height of \(12\, {m}\) in a tank having vertical sidewalls. A hole is made in one of the walls at a depth \('{h}'\) below the water level. The value of \('h'\) for which the emerging stream of water strikes the ground at the maximum range is \(.....\,{m}\). 2021 Medium
77. 77. What will be the nature of flow of water from a circular tap, when its flow rate increased from \(0.18\, L / min\) to \(0.48\, L / min\) ? The radius of the tap and viscosity of water are \(0.5\, cm\) and \(10^{-3}\, Pa s\), respectively. (Density of water : \(10^{3}\, kg / m ^{3}\) ) 2021 Medium
78. 78. When a rubber ball is taken to a depth of \(......\,{m}\) in deep sea, its volume decreases by \(0.5\, \%\) (The bulk modulus of rubber \(=9.8 \times 10^{8}\, {Nm}^{-2}\) Density of sea water \(=10^{3} {kgm}^{-3}\) \(\left.{g}=9.8\, {m} / {s}^{2}\right)\) 2021 Medium
79. 79. A air bubble of radius \(1\,cm\) in water has an upward acceleration \(9.8\, cm\, s ^{-2}\). The density of water is \(1\, gm\, cm ^{-3}\) and water offers negligible drag force on the bubble. The mass of the bubble is\(.......gm\) \(\left( g =980 \,cm / s ^{2}\right)\) 2020 Hard
80. 80. A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is \(5\, cm\) and the angular speed of rotation is  \(\omega\; rad \,s^{-1}\). The difference in the height, \(h(\) in \(cm )\) of liquid at the centre of vessel and at the side will be
    2020 Hard
81. 81. A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to 2020 Medium
82. 82. A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\) 2020 Hard
83. 83. A leak proof cylinder of length \(1 \;\mathrm{m},\) made of a metal which has very low coefficient of expansion is floating vertically in water at \(0^{\circ} \mathrm{C}\) such that its height above the water surface is \(20\; \mathrm{cm} .\) When the temperature of water is increased to \(4^{\circ} \mathrm{C},\) the height of the cylinder above the water surface becomes \(21 \;\mathrm{cm} .\) The density of water at \(\mathrm{T}=4^{\circ} \mathrm{C},\) relative to the density at \(\mathrm{T}=0^{\circ} \mathrm{C}\) is close to 2020 Medium
84. 84. An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are \(6.4 \;\mathrm{cm}\) and \(4.8 \;\mathrm{cm},\) respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is: 2020 Medium
85. 85. Consider a solid sphere of radius \(\mathrm{R}\) and mass density \(\rho(\mathrm{r})=\rho_{0}\left(1-\frac{\mathrm{r}^{2}}{\mathrm{R}^{2}}\right),  0<\mathrm{r} \leq \mathrm{R} .\) The minimum density of a liquid in which it will float is 2020 Hard
86. 86. In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) 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 \(h\) is proportional to : (ignore viscosity of air) 2020 Medium
87. 87. Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d.\) The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_{1}\) and in the other, \(x_{2}\). 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 2020 Hard
88. 88. Two liquids of densities \(\rho_{1}\) and \(\rho_{2}\left(\rho_{2}=2 \rho_{1}\right)\) are filled up behind a square wall of side \(10\; \mathrm{m}\) as shown in figure. Each liquid has a height of \(5 \;\mathrm{m} .\) The ratio of the forces due to these liquids exerted on upper part \(MN\) to that at the lower pait \(NO\) is (Assume that the liquids are not mixing)
    2020 Medium
89. 89. Water flows in a horizontal tube (see figure). The pressure of water changes by \(700\; \mathrm{Nm}^{-2}\) between \(\mathrm{A}\) and \(\mathrm{B}\) where the area of cross section are \(40\; \mathrm{cm}^{2}\) and \(20\; \mathrm{cm}^{2},\) respectively. Find the rate of flow of water through the tube. ........ \(\mathrm{cm}^{3} / \mathrm{s}\) (density of water \(=1000\; \mathrm{kgm}^{-3}\) )
    2020 Hard
90. 90. A cubical block of side \(0.5\,m\) floats on water with \(30\%\) of its volume under water. ....... \(kg\) is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water \(= 10^3\,kg/m^3\) ] 2019 Hard
91. 91. 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 2019 Hard
92. 92. 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 ........ \(mm\) 2019 Hard
93. 93. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is \(5\,cm\) and its rotational speed is \(2\) rotations per second, then the difference in the heights between the centre and the sides, in \(cm,\) will be 2019 Medium
94. 94. A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals 2019 Hard
95. 95. A submarine experiences a pressure of \(5.05\times 10^6\,Pa\) at a depth of \(d_1\) in a sea. When it goes further to a depth of \(d_2,\) it experiences a pressure of \(8.08\times 10^6\,Pa.\) Then \(d_2 -d_1\) is approximately ........ \(m\) (density of water \(= 10^3\,kg/m^3\) and acceleration due to gravity \(= 10\,ms^{-2}\) ) 2019 Medium
96. 96. A wooden block floating in a bucket of water has \(\frac{4}{5}\) 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 2019 Hard
97. 97. The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74\,m^3\) water per minute through a circular opening of \(2\,cm\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ \(m\) 2019 Medium
98. 98. Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\) 2019 Medium
99. 99. Water from a pipe is coming at a rate of \(100\, litres\) per minute. If the radius of the pipe is \(5\, cm\), the Reynolds number for the flow is of the order of : (density of water \(= 1000\, kg/m^3\), coefficient of viscosity of water \(= 1\, mPa\, s\)) 2019 Hard
100. 100. Water from a tap emerges vertically downwards with an initial speed of \(1.0\,ms^{-1}.\) The cross-sectional area of the tap is \(10^{-4}\,m^2.\) Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional area of the stream, \(0.15\,m\) below the tap would be: (take \(g = 10\,ms^{-2}\) ) 2019 Medium

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