Fluid Mechanics PYQs Set 2 (PDF)

Set 2 of 8 · Questions 31-60 of 236

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Mere Teacher · Previous Year Questions NEET Physics · Fluid Mechanics · Set 2 (Q31-60)
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31. $Two small spherical metal balls, having equal masses, are made from materials of densities ρ_{1} and ρ_{2} (ρ_{1} = 8 ρ_{2}) and have radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals η and whose density is 0.1 ρ_{2} . The ratio of their terminal velocities would be [NEET 2019]$ (1) $\frac{79}{72}$ (2) $\frac{19}{36}$ (3) $\frac{39}{72}$ (4) $\frac{79}{36}$ 32. $A rectangular film of liquid is extended from (4 cm \times 2 cm) to (5 cm \times 4 cm) . If the work done is 3 \times 10^{- 4} J, the value of the surface tension of the liquid is [NEET 2016]$ (1) $0.250 Nm^{- 1}$ (2) $0.125 Nm^{- 1}$ (3) $0.2 Nm^{- 1}$ (4) $8.0 Nm^{- 1}$ 33. $The surface tension and vapour pressure of a liquid at 25^{\circ} C are 8 \times 10^{- 2} Nm^{- 1} and 2.5 \times 10^{3} Pa respectively. The radius of the smallest spherical water droplet which can from without evaporating at 25^{\circ} C is$ (1) $64 μm$ (2) $30 μm$ (3) $60 μm$ (4) $32 μm$ 34. $Spheres of iron and lead having same mass are completely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is W_{1} for iron sphere and W_{2} for lead sphere. Then \frac{W _{1}}{W _{2}} is$ (1) $= 1$ (2) $between 0 and 1$ (3) $= 0$ (4) $> 1$ 35. $An ideal liquid flows through a horizontal tube of variable diameter. The pressure is lowest where the$ (1) $velocity is highest$ (2) $velocity is lowest$ (3) $diameter is largest$ (4) $velocity is intermediate$ 36. $A body weighs 50 grams in air and 40 grams in water. How much would it weigh in a liquid of specific gravity 1.5?$ (1) $65 grams$ (2) $45 grams$ (3) $30 grams$ (4) $35 grams$ 37. $A glass flask weighting 390 g, having internal volume 500 cc just floats when half of it is filled with water. Specific gravity of the glass is$ (1) $2.8$ (2) $1.8$ (3) $1.0$ (4) $2.5$ 38. $Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is$ (1) $02 : 01$ (2) $0.8 : 1$ (3) $04 : 01$ (4) $08 : 01$ 39. $A air bubble of radius 1 cm in water has an upward acceleration 9.8 cms^{- 2} . The density of water is 1 gmcm^{- 3} and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm / s^{2})$ (1) $1.52 gm$ (2) $4.51 gm$ (3) $3.15 gm$ (4) $4.15 gm$ 40. $The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d /2, then the viscous force acting on the ball will be [NEET 2021]$ (1) $\frac{M g}{2}$ (2) $Mg$ (3) $\frac{3}{2} M g$ (4) $2 Mg$ 41. $A solid sphere of density ρ = ρ_{0} (1 - \frac{r ^{2}}{R ^{2}}), 0 < r \leq R just floats in a liquid. The density of liquid is (r is distance from centre of sphere)$ (1) $\frac{2}{5} ρ_{0}$ (2) $\frac{5}{2} ρ_{0}$ (3) $\frac{3}{5} ρ_{0}$ (4) $ρ_{0} s$ 42. $A cylindrical vessel, open at the top, contains 15 liters of water. Water drains out through a small opening at the bottom. 5 liter of water comes out in time t_{1}, the next 5 litre in further time t_{2}, and the last 5 litre in further time t_{3}, Then$ (1) $t_{1} < t_{2} < t_{3}$ (2) $t_{1} > t_{2} > t_{3}$ (3) $t_{1} = t_{2} = t_{3}$ (4) $t_{2} > t_{1} = t_{3}$ 43. $The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be______m.$ (1) $0.20$ (2) $0.5$ (3) $0.05$ (4) $0.10$ 44. $A liquid flow steadily through a cylindrical pipe having a radius 2 R at a point A and radius R at point B farther along the flow direction. If the velocity at point B is 4 v, what will be the velocity at point A?$ (1) $1 2 v$ (2) $v$ (3) $2 v$ (4) $3 v$ 45. $The velocity of a small ball of mass 'm' and density di, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d_{2}, then the viscous force acting on the ball, will be:$ (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) $mg (\frac{d _{2}}{d _{1}} - 1)$ 46. $When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is:$ (1) $19.6m$ (2) $29.4m$ (3) $39.2m$ (4) $73.5m$ 47. $Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below$ (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) $Both Statement I and Statement II are true$ 48. $A cubical block side 0.5 m floats on water floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take density of water = 10³kg/m³]$ (1) $46.3 kg$ (2) $87.5 kg$ (3) $65.4 kg$ (4) $30.1 kg$ 49. $A small metallic sphere of diameter 2 mm and density 10.5 g / cm^{3} is dropped in glycerine having viscosity 10 Poise and density 1.5 g / cm^{3} respectively. The terminal velocity attained by the sphere is____cm / s . (π = \frac{22}{7}) and g = 10 m / s^{2})$ (1) $3.0$ (2) $1.0$ (3) $2.0$ (4) $1.5$ 50. $Water from a tap emerges vertically downwards with an initial downwards with an initial speed of 1.0 ms^{- 1} . The cross-sectional area of the tap is 10^{- 4} m^{2} . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15m below the tap is: [Take g= 10 ms^{- 2}].$ (1) $2 \times 10^{- 5} m^{2}$ (2) $5 \times 10^{- 5} m^{2}$ (3) $5 \times 10^{- 4} m^{2}$ (4) $1 \times 10^{- 5} m^{2}$ 51. $A soap bubble of initial radius R is to be blown up. The surface tension of the soap film is T. The surface energy needed to double the diameter of the bubble is$ (1) $12 π R^{2} T$ (2) $4 π R^{2} T$ (3) $16 π R^{2} T$ (4) $24 π R^{2} T$ 52. $Three liquids of densities ρ_{1}, ρ_{2} and ρ_{3} (with ρ_{1} > ρ_{2} > ρ_{3}), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ_{1}, θ_{2} and θ_{3} obey [NEET 2016]$ (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) $π > θ_{1} > θ_{2} > θ_{3} > \frac{π}{2}$ 53. $A vessel having small hole in the bottom has to hold water without leakage, if water is poured to a height of 7 cm . Then the radius of the hole is [surface tension of water is 0.07 Nm^{- 1}, angle of contact is 0^{\circ} and g = 10 ms^{- 2}]$ (1) $1 mm$ (2) $2 mm$ (3) $4 mm$ (4) $0.2 mm$ 54. $Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly. (Surface tension of soap solution = 0.03 N m^{-1})$ (1) $4π mJ$ (2) $0.2π mJ$ (3) $2π mJ$ (4) $0.4π mJ$ 55. $A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms^{- 1} at a point where the pressure is P pascal. At another point where pressure is \frac{P}{2} pascal its speed is Vms^{- 1} . If the density of the fluid is ρ kgm^{- 3} and the flow is streamline, then V is equal to:$ (1) $\frac{P}{ρ} + v^{2}$ (2) $\frac{2 P}{ρ} + v^{2}$ (3) $\frac{P}{ρ} + v$ (4) $\frac{P}{2 ρ} + v^{2}$ 56. $A swimming pool has depth of 3 meters. The pressure at the bottom of the pool due to water alone is (Density of water is 1000 kg m^{- 3}, Acceleration due to gravity = 10 ms^{- 2})$ (1) $10^{4} Pa$ (2) $3 \times 10^{3} Pa$ (3) $29 \times 10^{3} Pa$ (4) $30 \times 10^{3} Pa$ 57. $A solid sphere, of radius R acquires a terminal velocity v_{1} when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v_{2} , when falling through the same fluid. the ratio (v_{1} / v_{2}) equals:$ (1) $9$ (2) $1/27$ (3) $1/9$ (4) $27$ 58. $A flow of liquid is streamline if the Reynold number is$ (1) $between 2000 to 3000$ (2) $less than 1000$ (3) $between 4000 to 5000$ (4) $greater than 1000$ 59. $A calorimeter of water equivalent 20 g contains 180 g of water at 25^{\circ} C . ’ m ’ grams of steam at 100^{\circ} C is mixed in it till the temperature of the mixture is 31^{\circ} C . The value of ’ m^{’} is close to (Latent heat of water = 540 cal g^{- 1} specific heat of water = 1 cal g^{- 1 \circ} C^{- 1})$ (1) $2$ (2) $3.2$ (3) $2.6$ (4) $4$ 60. $Three identical vessels are filled with three liquids A, B, and C with equal masses but having densities ρ_{A}, ρ_{B} and ρ_{C} respectively. If ρ_{A} > ρ_{B} > ρ_{C} then the pressure at the bottom of the vessels will be$ (1) $Equal in all vessels$ (2) $Maximum in vessel containing liquid A$ (3) $Maximum in vessel containing liquid B$ (4) $Maximum in vessel containing liquid C$