Fluid Mechanics PYQs Set 10 (PDF)

Set 10 of 10 · Questions 271-289 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 10 (Q271-289)
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271. $A hydrophilic surface is characterized by the contact angle at the water solid interface. The value of contact angle should be$ (1) $> 90^{\circ}$ (2) $< 90^{\circ}$ (3) $= 90^{\circ}$ (4) $= 180^{\circ}$ 272. $Which of the following works on Pascal's law?$ (1) $Aneroid barometer$ (2) $Hydraulic lift$ (3) $Sprayer$ (4) $Venturimeter$ 273. $Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m^{2} . It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: (g = 10 m / s^{2})$ (1) $3 m / s$ (2) $5 m / s$ (3) $2 m / s$ (4) $4 m / s$ 274. $If p is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is:$ (1) $R_{e} = \frac{η d}{ρv}$ (2) $R_{e} = \frac{ρv}{η d}$ (3) $R_{e} = \frac{ρvd}{η}$ (4) $R_{e} = \frac{η}{ρvd}$ 275. $Consider a cylindrical tank of radius 1m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5m from the bottom. A force of 5 x 1 0^{5} N is applied an the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure P_{A} = 1.01 x 1 0^{5} Pa, density of water ρ_{w} = 1000 kg/ m^{3} and gravitational acceleration g = 10 m/ s^{2})$ (1) $11.6 m/s$ (2) $10.8 m/s$ (3) $17.8 m/s$ (4) $14.4 m/s$ 276. $A pressure-pump has a horizontal tube of cross-sectional area 10 c m^{2} for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given: density of water = 1000 kg/ m^{3}]$ (1) $300N$ (2) $500N$ (3) $250 N$ (4) $400 N$ 277. $Two liquid columns of same height 5 m and densities ρ and 2 ρ are filled in a container of uniform cross-sectional area. Then ratio of force exerted by the liquid on upper half of the wall to lower half of the wall is.$ (1) $\frac{1}{4}$ (2) $\frac{1}{2}$ (3) $\frac{1}{3}$ (4) $\frac{2}{3}$ 278. $In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 \times 1 0^{- 5} m and density 1.2 \times 1 0^{3} k g m^{- 3} ? Take viscosity of liquid = 1.8 \times 1 0^{- 5} N s m^{- 2} . (Neglect buoyancy due to air).$ (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) $5.8 \times 1 0^{- 10} N$ 279. $Two cylindrical vessels of equal cross-sectional area 16 c m^{2} contain water up to heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal The work done by the force of gravity during the process, is [Take density of water = 1 0^{3} kg/ m^{3} and g = 10 m s^{- 2}]$ (1) $0.25 J$ (2) $1 J$ (3) $8J$ (4) $12 J$ 280. $A drop of liquid of density p is floating half immersed in a liquid of density a and surface tension 7.5 x 1 0^{- 4} N c m^{- 1} . The radius of drop in cm will be: (Take: g = 10 m/ s^{2})$ (1) $\frac{15}{2 ρ - σ}$ (2) $\frac{15}{ρ - σ}$ (3) $\frac{3}{2 ρ - σ}$ (4) $\frac{3}{20 2 ρ - σ}$ 281. $Water rises in plant fibres due to$ (1) $capillarity$ (2) $viscosity$ (3) $fluid pressure$ (4) $osmosis.$ 282. $Consider a solid sphere of radius R and mass density ρ (r) = ρ_{0} (1 - \frac{r ^{2}}{R ^{2}}), 0 < r \leq R . The minimum density of a liquid in which it will float is:$ (1) $\frac{ρ _{0}}{3}$ (2) $\frac{2 ρ _{0}}{3}$ (3) $\frac{ρ _{0}}{5}$ (4) $\frac{2 ρ _{0}}{5}$ 283. $A circular film of a liquid has an area of 10 cm^{2} . If the work done in making its radius two times the initial radius is 8 \times 10^{- 3} J, the surface tension of the liquid is (1 + \frac{1}{a}) Nm^{- 1} . The value of α is$ (1) $5$ (2) $4$ (3) $3$ (4) $2$ 284. $A cylindrical tank having large diameter is filled with water to a height H . A hole of cross-sectional area 5 cm^{2} in the tank allows water to drain out. If the water drains out at the rate of 2 \times 10^{- 3} m^{3} s^{- 1}, then the value of H is (acceleration due to gravity = 10 ms^{- 2})$ (1) $80 cm$ (2) $120 cm$ (3) $60 cm$ (4) $90 cm$ 285. $Two liquids of densities ρ_{1} and ρ_{2} (ρ_{2} = 2 ρ_{1}) are filled up behind a square wall of side 10m as shown in figure. Each liquid has a height of 5m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):$ (1) $\frac{1}{2}$ (2) $\frac{1}{3}$ (3) $\frac{1}{4}$ (4) $\frac{2}{3}$ 286. $Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is .$ 287. $A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm^{2} with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 \times 10^{3} kg / m^{3} . What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m / s^{2})$ 288. $The lower end of a capillary of radius r = 0.2 mm and length λ = 8 cm is immersed in water whose temperature is constant and equal to T_{l o w} = 0ºC. The temperature of the upper end of the capillary is T_{u p} = 100ºC. Determine the height h to which the water in the capillary rises, assuming that the thermal conductivity of the capillary is much higher than the thermal conductivity of water in it. The heat exchange with the ambient should be neglected. Use the following temperature dependence of the surface tension of water: T, ºC 0 20 50 90 σ, mN/m 76 73 67 60$ 289. $Wires W_{1} and W_{2} are made of same material having the breaking stress of 1.25 \times 1 0^{9} N / m^{2} W_{1} and W_{2} have cross-sectional area of 8 \times 1 0^{- 7} m^{2} and 4 \times 1 0^{- 7} m^{2}, respectively. Masses of 20kg and 10kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is kg. (Use g = 10 m / s^{2})$