Fluid Mechanics PYQs Set 3 (PDF)

Set 3 of 10 · Questions 61-90 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 3 (Q61-90)
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61. $A small metallic sphere of diameter 2 mm and density 10.5 g / cm^{3} is dropped in glycerine having viscosity 10 Poise and density 1.5 g / cm^{3} respectively. The terminal velocity attained by the sphere is____cm / s . (π = \frac{22}{7}) and g = 10 m / s^{2})$ (1) $3.0$ (2) $1.0$ (3) $2.0$ (4) $1.5$ 62. $Water from a tap emerges vertically downwards with an initial downwards with an initial speed of 1.0 ms^{- 1} . The cross-sectional area of the tap is 10^{- 4} m^{2} . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15m below the tap is: [Take g= 10 ms^{- 2}].$ (1) $2 \times 10^{- 5} m^{2}$ (2) $5 \times 10^{- 5} m^{2}$ (3) $5 \times 10^{- 4} m^{2}$ (4) $1 \times 10^{- 5} m^{2}$ 63. $A soap bubble of initial radius R is to be blown up. The surface tension of the soap film is T. The surface energy needed to double the diameter of the bubble is$ (1) $12 π R^{2} T$ (2) $4 π R^{2} T$ (3) $16 π R^{2} T$ (4) $24 π R^{2} T$ 64. $Three liquids of densities ρ_{1}, ρ_{2} and ρ_{3} (with ρ_{1} > ρ_{2} > ρ_{3}), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ_{1}, θ_{2} and θ_{3} obey [NEET 2016]$ (1) $\frac{π}{2} > θ_{1} > θ_{2} > θ_{3} \geq 0$ (2) $0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2}$ (3) $\frac{π}{2} < θ_{1} < θ_{2} < θ_{3} < π$ (4) $π > θ_{1} > θ_{2} > θ_{3} > \frac{π}{2}$ 65. $A vessel having small hole in the bottom has to hold water without leakage, if water is poured to a height of 7 cm . Then the radius of the hole is [surface tension of water is 0.07 Nm^{- 1}, angle of contact is 0^{\circ} and g = 10 ms^{- 2}]$ (1) $1 mm$ (2) $2 mm$ (3) $4 mm$ (4) $0.2 mm$ 66. $Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly. (Surface tension of soap solution = 0.03 N m^{-1})$ (1) $4π mJ$ (2) $0.2π mJ$ (3) $2π mJ$ (4) $0.4π mJ$ 67. $A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms^{- 1} at a point where the pressure is P pascal. At another point where pressure is \frac{P}{2} pascal its speed is Vms^{- 1} . If the density of the fluid is ρ kgm^{- 3} and the flow is streamline, then V is equal to:$ (1) $\frac{P}{ρ} + v^{2}$ (2) $\frac{2 P}{ρ} + v^{2}$ (3) $\frac{P}{ρ} + v$ (4) $\frac{P}{2 ρ} + v^{2}$ 68. $A swimming pool has depth of 3 meters. The pressure at the bottom of the pool due to water alone is (Density of water is 1000 kg m^{- 3}, Acceleration due to gravity = 10 ms^{- 2})$ (1) $10^{4} Pa$ (2) $3 \times 10^{3} Pa$ (3) $29 \times 10^{3} Pa$ (4) $30 \times 10^{3} Pa$ 69. $A solid sphere, of radius R acquires a terminal velocity v_{1} when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v_{2} , when falling through the same fluid. the ratio (v_{1} / v_{2}) equals:$ (1) $9$ (2) $1/27$ (3) $1/9$ (4) $27$ 70. $A flow of liquid is streamline if the Reynold number is$ (1) $between 2000 to 3000$ (2) $less than 1000$ (3) $between 4000 to 5000$ (4) $greater than 1000$ 71. $A calorimeter of water equivalent 20 g contains 180 g of water at 25^{\circ} C . ’ m ’ grams of steam at 100^{\circ} C is mixed in it till the temperature of the mixture is 31^{\circ} C . The value of ’ m^{’} is close to (Latent heat of water = 540 cal g^{- 1} specific heat of water = 1 cal g^{- 1 \circ} C^{- 1})$ (1) $2$ (2) $3.2$ (3) $2.6$ (4) $4$ 72. $Three identical vessels are filled with three liquids A, B, and C with equal masses but having densities ρ_{A}, ρ_{B} and ρ_{C} respectively. If ρ_{A} > ρ_{B} > ρ_{C} then the pressure at the bottom of the vessels will be$ (1) $Equal in all vessels$ (2) $Maximum in vessel containing liquid A$ (3) $Maximum in vessel containing liquid B$ (4) $Maximum in vessel containing liquid C$ 73. $Assume that a drop of liquid evaporates by decreasing in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization.$ (1) $ρL/T$ (2) $T / ρL$ (3) $T/ρL$ (4) $2T/ρL$ 74. $Two solid pieces, one of steel and the other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air$ (1) $the weight of aluminium is half the weight of steel$ (2) $steel piece will weigh more$ (3) $they have the same weight$ (4) $aluminium piece will weigh more.$ 75. $A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5\times 1 0^{-2} N/m. The pressure inside the bubble equals at a point Z_{0} below the free surface of water in a container. Taking g = 10 m/ s^{2}, density of water = 1 0^{3} kg/ m^{3}, the value of Z_{0} is:$ (1) $0.5 cm$ (2) $100 cm$ (3) $10 cm$ (4) $1 cm$ 76. $Two capillary tubes P and Q are dipped vertically in water. The height of water level in capillary tube P is (\frac{2}{3})^{rd} of the height in capillary tube Q . The ratio of their diameter is$ (1) $2 : 3$ (2) $3 : 2$ (3) $3 : 4$ (4) $4 : 3$ 77. $If a soap bubble expands, the pressure inside the bubble [NEET 2022]$ (1) $increases$ (2) $remains the same$ (3) $is equal to the atmospheric pressure$ (4) $decreases$ 78. $The specific heat of water = 4200 Jkg^{- 1} K^{- 1} and the latent heat of ice = 3.4 \times 10^{5} Jkg^{- 1} 100 grams of ice at 0^{\circ} C is placed in 200 g of water at 25^{\circ} C . The amount of ice that will melt as the temperature of water reaches 0^{\circ} C is close to (in grams)$ (1) $69.3$ (2) $63.8$ (3) $64.6$ (4) $61.7$ 79. $A spherical drop of radium r is divided in to 8 equal droplets. If the surface tension is S, then the work done in the process will be$ (1) $2 π r^{2} S$ (2) $3 π r^{2} S$ (3) $4 π r^{2} S$ (4) $4 π r^{2} S^{2}$ 80. $The angle of contact is 120^{\circ} when a cylindrical rod is vertically placed in a liquid. If the same rod is placed horizontally in the liquid, then the angle of contact is$ (1) $60^{\circ}$ (2) $30^{\circ}$ (3) $90^{\circ}$ (4) $120^{\circ}$ 81. $A rectangular film of liquid is extended from (4 cm \times 2cm) to (5 cm \times 4 cm). If the work done is 3 \times 1 0^{-4} J, the value of the surface tension of the liquid i$ (1) $8.0 N m^{-1}$ (2) $0.250 N m^{-1}$ (3) $0.125 N m^{-1}$ (4) $0.2 N m^{-1}$ 82. $A barometer is constructed using a liquid (density = 760 kg / m^{3}). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (Density of mercury = 13600 kg / m^{3}) [NEET 2020]$ (1) $1.36 m$ (2) $13.6 m$ (3) $136 m$ (4) $0.76 m$ 83. $Correct Bernoulli's equation is (symbols have their usual meaning):$ (1) $P + m g h + \frac{1}{2} m v^{2} = constant$ (2) $P + ρ g h + \frac{1}{2} ρ v^{2} = constant$ (3) $P + ρ g h + ρ v^{2} = constant$ (4) $P + \frac{1}{2} ρ g h + \frac{1}{2} ρ v^{2} = constant$ 84. $A shower head has 25 circular openings, each with radius 1 mm . The shower head is connected to a pipe with radius 2 cm . If the speed of the water in the pipe is 25 cm / s . What is its speed as it exists the shower head openings?$ (1) $1 m / s$ (2) $2 m / s$ (3) $4 m / s$ (4) $5 m / s$ 85. $A body is suspended by a light string. The tensions in the string when the body is in air, when the body is totally immersed in water and when the body is totally immersed in a liquid are respectively 40.2 N, 28.4 N and 16.6 N . The density of the liquid is$ (1) $1200 kg - m^{- 3}$ (2) $1600 kg^{- m^{- 3}}$ (3) $2000 kg - m^{- 3}$ (4) $2400 kg - m^{- 3}$ 86. $The amount of work done to break a big water drop of radius ' R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be$ (1) $15 J$ (2) $5 J$ (3) $20 J$ (4) $10 J$ 87. $Consider an increase of 1 % in each of radius of artery, viscosity of blood and density of blood respectively. The percentage change in flow rate of blood in artery is$ (1) $0.25 %$ (2) $0.50 %$ (3) $1.0 %$ (4) $3.0 %$ 88. $A non-isotropic solid metal cube has coefficients of linear expansion as 5 \times 10^{- 5} /° C along the x -axis and 5 \times 10^{- 6} /° C along y -axis and z -axis. If coefficient of volume expansion of the solid is C \times 10^{- 6} /° C then the value of C is$ 89. $Mercury is filled in a tube of radius 2 cm up to a height of 30 cm . The force exerted by mercury on the bottom of the tube is ______N . (Given, atmospheric pressure = 10^{5} Nm^{- 2}, density of mercury = 1.36 \times 10^{4} kg m^{-} (^{3}, g = 10 m s^{- 2}, π = \frac{22}{7})$ 90. $The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm / s . The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be____cm / s .$