Fluid Mechanics PYQs Set 8 (PDF)

Set 8 of 8 · Questions 211-236 of 236

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Mere Teacher · Previous Year Questions NEET Physics · Fluid Mechanics · Set 8 (Q211-236)
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211. $Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x_{1} and in the other, x_{2} . When both cylinders are connected through a pipe of negligible volume very close to the bottom, theliquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is$ (1) $gdS (x_{2} + x_{1})^{2}$ (2) $\frac{1}{4} gdS (x_{2} - x_{1})^{2}$ (3) $\frac{3}{4} gdS (x_{2} - x_{1})^{2}$ (4) $gdS (x_{2}^{2} + x_{1}^{2})$ 212. $An air bubble of volume 2.9 cm^{3} rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17^{\circ} C . The volume of the bubble when it reaches the surface, where the water temperature is 27^{\circ} C, is____cm^{3} . (g = 10 m / s^{2}, density of water = 10^{3} kg / m^{3}, and 1 atm pressure is 10^{5} Pa)$ (1) $4.5$ (2) $2.0$ (3) $4.2$ (4) $3.0$ 213. $A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm^{- 1}, density = 667 kgm^{- 3}) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60^{\circ} with one another. Then h is close to (g = 10 ms^{- 2})$ (1) $0.049 m$ (2) $0.087 m$ (3) $0.137 m$ (4) $0.172 m$ 214. $The venturi meter works on [NEET 2023]$ (1) $Bernoulli's principle$ (2) $the principle of parallel axes$ (3) $the principle of perpendicular axes$ (4) $Huygen's principle$ 215. $Hydraulic lift works on the basis of$ (1) $Stoke's law$ (2) $Bernoulli's law$ (3) $Toricelli's law$ (4) $Pascal's law$ 216. $Surface tension of two liquids (having same densities), T_{1} and T_{2}, are measured using capillary rise method utilizing two tubes with inner radii of r_{1} and r_{2} where r_{1} > r_{2} . The measured liquid heights in these tubes are h_{1} and h_{2} respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h_{1} and h_{2} and surfaces tensions T_{1} and T_{2} satisfy the relation:$ (1) $h_{1} > h_{2} and T_{1} = T_{2}$ (2) $h_{1} = h_{2} and T_{1} = T_{2}$ (3) $h_{1} > h_{2} and T_{1} < T_{2}$ (4) $h_{1} < h_{2} and T_{1} = T_{2}$ 217. $In the experiment for measurement of viscosity ' η ' of given liquid with a ball having radius R, consider following statements. (A) Graph between terminal velocity V and R will be a parabola. (B) The terminal velocities of different diameter balls are constant for a given liquid. (C) Measurement of terminal velocity is dependent on the temperature. (D) This experiment can be utilized to assess the density of a given liquid. (E) If balls are dropped with some initial speed, the value of η will change. Choose the correct answer from the options given below:$ (1) $A, B and E Only$ (2) $B, D and E Only$ (3) $A, C and D Only$ (4) $C, D and E Only$ 218. $Consider following statements: (A) Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. (B) As the temperature of liquid rises, the coefficient of viscosity increases. (C) As the temperature of gas increases, the coefficient of viscosity increases (D) The onset of turbulence is determined by Reynold's number. (E) In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:$ (1) $C, D, E Only$ (2) $A, D, E Only$ (3) $B, C, D Only$ (4) $A, B, C Only$ 219. $A uniform heavy rod of weight 10 kg m s^{- 2}, cross-sectional area 100 cm^{2} and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \times 1 0^{11} Nm^{- 2} . Neglecting the lateral contraction, find the elongation of rod due to its own weight.$ (1) $2 \times 1 0^{- 9} m$ (2) $5 \times 1 0^{8} m$ (3) $4 \times 1 0^{- 8} m$ (4) $5 \times 1 0^{- 10} m$ 220. $Water rises to a height 'h' in capillary tube. If the length of capillary tube above the surface of water is made less than 'h' then:$ (1) $water rises upto the top of capillary tube and stays there without overflowing$ (2) $water rises upto a point a little below the top and stays there$ (3) $water does not rise at all.$ (4) $Water rises upto the tip of capillary tube and then starts overflowing like fountain.$ 221. $The wettability of a surface by a liquid depends primarily on:$ (1) $surface tension$ (2) $density$ (3) $angle of contact between the surface and the liquid$ (4) $viscosity$ 222. $A hydrophilic surface is characterized by the contact angle at the water solid interface. The value of contact angle should be$ (1) $> 90^{\circ}$ (2) $< 90^{\circ}$ (3) $= 90^{\circ}$ (4) $= 180^{\circ}$ 223. $Which of the following works on Pascal's law?$ (1) $Aneroid barometer$ (2) $Hydraulic lift$ (3) $Sprayer$ (4) $Venturimeter$ 224. $Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m^{2} . It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: (g = 10 m / s^{2})$ (1) $3 m / s$ (2) $5 m / s$ (3) $2 m / s$ (4) $4 m / s$ 225. $If p is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is:$ (1) $R_{e} = \frac{η d}{ρv}$ (2) $R_{e} = \frac{ρv}{η d}$ (3) $R_{e} = \frac{ρvd}{η}$ (4) $R_{e} = \frac{η}{ρvd}$ 226. $Consider a cylindrical tank of radius 1m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5m from the bottom. A force of 5 x 1 0^{5} N is applied an the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure P_{A} = 1.01 x 1 0^{5} Pa, density of water ρ_{w} = 1000 kg/ m^{3} and gravitational acceleration g = 10 m/ s^{2})$ (1) $11.6 m/s$ (2) $10.8 m/s$ (3) $17.8 m/s$ (4) $14.4 m/s$ 227. $A pressure-pump has a horizontal tube of cross-sectional area 10 c m^{2} for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given: density of water = 1000 kg/ m^{3}]$ (1) $300N$ (2) $500N$ (3) $250 N$ (4) $400 N$ 228. $Two liquid columns of same height 5 m and densities ρ and 2 ρ are filled in a container of uniform cross-sectional area. Then ratio of force exerted by the liquid on upper half of the wall to lower half of the wall is.$ (1) $\frac{1}{4}$ (2) $\frac{1}{2}$ (3) $\frac{1}{3}$ (4) $\frac{2}{3}$ 229. $In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 \times 1 0^{- 5} m and density 1.2 \times 1 0^{3} k g m^{- 3} ? Take viscosity of liquid = 1.8 \times 1 0^{- 5} N s m^{- 2} . (Neglect buoyancy due to air).$ (1) $3.8 \times 1 0^{- 11} N$ (2) $3.9 \times 1 0^{- 10} N$ (3) $1.8 \times 1 0^{- 10} N$ (4) $5.8 \times 1 0^{- 10} N$ 230. $Two cylindrical vessels of equal cross-sectional area 16 c m^{2} contain water up to heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal The work done by the force of gravity during the process, is [Take density of water = 1 0^{3} kg/ m^{3} and g = 10 m s^{- 2}]$ (1) $0.25 J$ (2) $1 J$ (3) $8J$ (4) $12 J$ 231. $A drop of liquid of density p is floating half immersed in a liquid of density a and surface tension 7.5 x 1 0^{- 4} N c m^{- 1} . The radius of drop in cm will be: (Take: g = 10 m/ s^{2})$ (1) $\frac{15}{2 ρ - σ}$ (2) $\frac{15}{ρ - σ}$ (3) $\frac{3}{2 ρ - σ}$ (4) $\frac{3}{20 2 ρ - σ}$ 232. $Water rises in plant fibres due to$ (1) $capillarity$ (2) $viscosity$ (3) $fluid pressure$ (4) $osmosis.$ 233. $Consider a solid sphere of radius R and mass density ρ (r) = ρ_{0} (1 - \frac{r ^{2}}{R ^{2}}), 0 < r \leq R . The minimum density of a liquid in which it will float is:$ (1) $\frac{ρ _{0}}{3}$ (2) $\frac{2 ρ _{0}}{3}$ (3) $\frac{ρ _{0}}{5}$ (4) $\frac{2 ρ _{0}}{5}$ 234. $A circular film of a liquid has an area of 10 cm^{2} . If the work done in making its radius two times the initial radius is 8 \times 10^{- 3} J, the surface tension of the liquid is (1 + \frac{1}{a}) Nm^{- 1} . The value of α is$ (1) $5$ (2) $4$ (3) $3$ (4) $2$ 235. $A cylindrical tank having large diameter is filled with water to a height H . A hole of cross-sectional area 5 cm^{2} in the tank allows water to drain out. If the water drains out at the rate of 2 \times 10^{- 3} m^{3} s^{- 1}, then the value of H is (acceleration due to gravity = 10 ms^{- 2})$ (1) $80 cm$ (2) $120 cm$ (3) $60 cm$ (4) $90 cm$ 236. $Two liquids of densities ρ_{1} and ρ_{2} (ρ_{2} = 2 ρ_{1}) are filled up behind a square wall of side 10m as shown in figure. Each liquid has a height of 5m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):$ (1) $\frac{1}{2}$ (2) $\frac{1}{3}$ (3) $\frac{1}{4}$ (4) $\frac{2}{3}$