Fluid Mechanics PYQs Set 2 (PDF)

Set 2 of 10 · Questions 31-60 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 2 (Q31-60)
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31. $The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = 0.03 N m^{- 1}) [NEET 2023]$ (1) $5.06 \times 10^{- 4} J$ (2) $3.01 \times 10^{- 4} J$ (3) $50.1 \times 10^{- 4} J$ (4) $30.16 \times 10^{- 4} J$ 32. $A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 \times 10^{- 2} N / m . The pressure inside the bubble equals at a point Z_{0} below the free surface of water in a container. Taking g = 10 m / s^{2}, density of water = 10^{3} kg / m^{3}, the value of Z_{0} is [NEET 2019]$ (1) $10 cm$ (2) $1 cm$ (3) $0.5 cm$ (4) $100 cm$ 33. $Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipe$ (1) $velocity is max and pressure is min$ (2) $pressure is max and velocity is min$ (3) $both pressure and velocity are max$ (4) $both velocity an pressure are min$ 34. $A raindrop with radius R=0.2mm falls from a cloud at a height h=2000m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is: [Density of water f_{w} = 1000 k g m^{- 3} and Density of air f_{a} = 1.2 k g m^{- 3}, g = 10 m / s^{2} Coefficient of viscosity of air 1.8 \times 1 0^{- 5} N s m^{- 2}]$ (1) $250. 6 m s^{- 1}$ (2) $43.56 m s^{- 1}$ (3) $4.94 m s^{- 1}$ (4) $14.4 m s^{- 1}$ 35. $A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become:$ (1) $100 times$ (2) $10 times$ (3) $\frac{1}{100} th$ (4) $\frac{1}{10} th$ 36. $A capillary tube of radius r is immersed in water and water rises in it to a height h . The mass of the water in the capillary tube is 5 g. Another capillary tube of radius 2 r is immersed in water. The mass of water that will rise in this tube is [NEET 2020]$ (1) $5.0 g$ (2) $10.0 g$ (3) $20.0 g$ (4) $2.5 g$ 37. $Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization.$ (1) $ρL/T$ (2) $T / ρL$ (3) $T/ρL$ (4) $2T/ρL$ 38. $Two small spherical metal balls, having equal masses, are made from materials of densities ρ_{1} and ρ_{2} (ρ_{1} = 8 ρ_{2}) and have radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals η and whose density is 0.1 ρ_{2} . The ratio of their terminal velocities would be [NEET 2019]$ (1) $\frac{79}{72}$ (2) $\frac{19}{36}$ (3) $\frac{39}{72}$ (4) $\frac{79}{36}$ 39. $A rectangular film of liquid is extended from (4 cm \times 2 cm) to (5 cm \times 4 cm) . If the work done is 3 \times 10^{- 4} J, the value of the surface tension of the liquid is [NEET 2016]$ (1) $0.250 Nm^{- 1}$ (2) $0.125 Nm^{- 1}$ (3) $0.2 Nm^{- 1}$ (4) $8.0 Nm^{- 1}$ 40. $The surface tension and vapour pressure of a liquid at 25^{\circ} C are 8 \times 10^{- 2} Nm^{- 1} and 2.5 \times 10^{3} Pa respectively. The radius of the smallest spherical water droplet which can from without evaporating at 25^{\circ} C is$ (1) $64 μm$ (2) $30 μm$ (3) $60 μm$ (4) $32 μm$ 41. $Spheres of iron and lead having same mass are completely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is W_{1} for iron sphere and W_{2} for lead sphere. Then \frac{W _{1}}{W _{2}} is$ (1) $= 1$ (2) $between 0 and 1$ (3) $= 0$ (4) $> 1$ 42. $An ideal liquid flows through a horizontal tube of variable diameter. The pressure is lowest where the$ (1) $velocity is highest$ (2) $velocity is lowest$ (3) $diameter is largest$ (4) $velocity is intermediate$ 43. $A body weighs 50 grams in air and 40 grams in water. How much would it weigh in a liquid of specific gravity 1.5?$ (1) $65 grams$ (2) $45 grams$ (3) $30 grams$ (4) $35 grams$ 44. $A glass flask weighting 390 g, having internal volume 500 cc just floats when half of it is filled with water. Specific gravity of the glass is$ (1) $2.8$ (2) $1.8$ (3) $1.0$ (4) $2.5$ 45. $Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is$ (1) $02 : 01$ (2) $0.8 : 1$ (3) $04 : 01$ (4) $08 : 01$ 46. $A air bubble of radius 1 cm in water has an upward acceleration 9.8 cms^{- 2} . The density of water is 1 gmcm^{- 3} and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm / s^{2})$ (1) $1.52 gm$ (2) $4.51 gm$ (3) $3.15 gm$ (4) $4.15 gm$ 47. $The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d /2, then the viscous force acting on the ball will be [NEET 2021]$ (1) $\frac{M g}{2}$ (2) $Mg$ (3) $\frac{3}{2} M g$ (4) $2 Mg$ 48. $A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is σ. The angle of contact between water and the wall of the capillary tube is θ. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?$ (1) $For a given material of the capillary tube, h decreases with increase in r$ (2) $For a given material of the capillary tube, h is independent of σ$ (3) $If this experiment is performed in a lift going up with a constant acceleration, then h decreases$ (4) $h is proportional to contact angle θ$ 49. $A solid sphere of density ρ = ρ_{0} (1 - \frac{r ^{2}}{R ^{2}}), 0 < r \leq R just floats in a liquid. The density of liquid is (r is distance from centre of sphere)$ (1) $\frac{2}{5} ρ_{0}$ (2) $\frac{5}{2} ρ_{0}$ (3) $\frac{3}{5} ρ_{0}$ (4) $ρ_{0} s$ 50. $A cylindrical vessel, open at the top, contains 15 liters of water. Water drains out through a small opening at the bottom. 5 liter of water comes out in time t_{1}, the next 5 litre in further time t_{2}, and the last 5 litre in further time t_{3}, Then$ (1) $t_{1} < t_{2} < t_{3}$ (2) $t_{1} > t_{2} > t_{3}$ (3) $t_{1} = t_{2} = t_{3}$ (4) $t_{2} > t_{1} = t_{3}$ 51. $The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be______m.$ (1) $0.20$ (2) $0.5$ (3) $0.05$ (4) $0.10$ 52. $A liquid flow steadily through a cylindrical pipe having a radius 2 R at a point A and radius R at point B farther along the flow direction. If the velocity at point B is 4 v, what will be the velocity at point A?$ (1) $1 2 v$ (2) $v$ (3) $2 v$ (4) $3 v$ 53. $The velocity of a small ball of mass 'm' and density di, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d_{2}, then the viscous force acting on the ball, will be:$ (1) $mg (1 - \frac{d _{1}}{d _{2}})$ (2) $mg (1 - \frac{d _{2}}{d _{1}})$ (3) $mg (\frac{d _{1}}{d _{2}} - 1)$ (4) $mg (\frac{d _{2}}{d _{1}} - 1)$ 54. $When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is:$ (1) $19.6m$ (2) $29.4m$ (3) $39.2m$ (4) $73.5m$ 55. $Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below$ (1) $Statement I is false but Statement II is true$ (2) $Statement I is true but Statement II is false$ (3) $Both Statement I and Statement II are false$ (4) $Both Statement I and Statement II are true$ 56. $A cubical block side 0.5 m floats on water floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take density of water = 10³kg/m³]$ (1) $46.3 kg$ (2) $87.5 kg$ (3) $65.4 kg$ (4) $30.1 kg$ 57. $A soap bubble is blown to a diameter of 7 cm . 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne / cm then the new radius is_____cm Take (π = \frac{22}{7})$ 58. $In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms^{- 1} and 65 ms^{- 1} respectively. If the wing area is 2 m^{2} the lift of the wing is______N . (Given density of air = 1.2 kg m^{- 3})$ 59. $Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm / s . Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be______cm / s .$ 60. $The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is .$