Fluid Mechanics PYQs Set 7 (PDF)

Set 7 of 8 · Questions 181-210 of 236

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Mere Teacher · Previous Year Questions NEET Physics · Fluid Mechanics · Set 7 (Q181-210)
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181. $Two narrow bores of diameter 5.0mm and 8.0mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 \times 1 0^{- 2} N m^{- 1}, angle of contact =0, g = 10 m s^{- 2} and density of water = 1.0 \times 1 0^{3} k g m^{- 3}]$ (1) $3.62 mm$ (2) $2.19 mm$ (3) $5.34 mm$ (4) $4.97 mm$ 182. $A block of iron contains a hollow cavity as shown below. The block weighs 6000 N in air and 4000 N in water. If the density of iron and water are 6 g / cm^{3} and 1 g / cm^{3}, then the volume of the cavity is (assume, g = 10 m / s^{2})$ (1) $0.05 m^{3}$ (2) $0.5 m^{3}$ (3) $0.25 m^{3}$ (4) $0.1 m^{3}$ 183. $Surface tension of a soap bubble is 2.0 x 1 0^{- 2} M m^{- 1} . Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be: [Take π = \frac{22}{7}]$ (1) $0. 72 x 1 0^{- 4} J$ (2) $5. 76 x 1 0^{- 4} J$ (3) $18. 48 x 1 0^{- 4} J$ (4) $9. 24 x 1 0^{- 4} J$ 184. $Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N . For a streamline flow of liquid the rate of liquid flow is$ (1) $continuously changes with time$ (2) $greater at M than at N$ (3) $greater at N than at M$ (4) $same at M and N .$ 185. $A cylindrical container containing water has a small hole at height of H = 8 cm from the bottom and at depth of 2 cm from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground (x) is$ (1) $4 cm$ (2) $8 cm$ (3) $6 cm$ (4) $42 cm$ 186. $Consider two liquids A and B in a U -shaped tube in static equilibrium as shown in the figure. If the density of the liquid A is twice the density of liquid B; then the relation between h_{A} and h_{B} is$ (1) $h_{A} = \frac{h _{B}}{2}$ (2) $h_{A} = \frac{h _{B}}{2}$ (3) $h_{A} = \frac{h _{B}}{3}$ (4) $h_{A} = \frac{h _{B}}{3}$ 187. $There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2} are filled in the tube. Each liquid subtends 90° angle at center. Radius joining their interface makes an angle α with vertical. Ratio \frac{d _{1}}{d _{2}} is:$ (1) $\frac{1 + s in α}{1 - s in α}$ (2) $\frac{1 + cos α}{1 - cos α}$ (3) $\frac{1 + t an α}{1 - t an α}$ (4) $\frac{1 + s in α}{1 - cos α}$ 188. $A glass tumbler having inner depth of 17.5cm is kept on a table. A student starts pouring water into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?$ (1) $11.7cm$ (2) $10cm$ (3) $7.5cm$ (4) $8.75cm$ 189. $A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,$ (1) $air from end 1 flows towards end 2. No change in the volume of the soap bubbles$ (2) $air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases$ (3) $no change occurs$ (4) $air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases.$ 190. $Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P_{1} . The reading of the pressure gauge falls to P_{2} when the valve is opened. The speed of water flowing in the pipe is proportional to$ (1) $P_{1} - P_{2}$ (2) $(P_{1} - P_{2})^{4}$ (3) $(P_{1} - P_{2})^{2}$ (4) $P_{1} - P_{2}$ 191. $Two non-mixing liquids of densities ρ and nρ (n > 1) are put in container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal t$ (1) ${1 + (n - 1) p}ρ$ (2) ${1 + (n + 1) p}ρ$ (3) ${2+(n + 1) p}ρ$ (4) ${2 + (n - 1) p}ρ$ 192. $A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in the figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is 10 rad s^{- 1}, then the height difference between the liquid at the centre of the vessel and its sides is (g = 10 ms^{- 2})$ (1) $125\times 1 0^{- 4} m$ (2) $100 \times 10^{- 4} m$ (3) $50 \times 10^{- 4} m$ (4) $25 \times 10^{- 4} m$ 193. $A small ball of mass M and density p is dropped in a viscous liquid of density ρ_{0} . After some time, the ball falls with a constant velocity. What is the viscous force on the ball?$ (1) $F = Mg (1 + \frac{ρ _{0}}{ρ})$ (2) $F = Mg (1 + \frac{ρ}{ρ _{0}})$ (3) $F = Mg (1 - \frac{ρ _{0}}{ρ})$ (4) $F = Mg (1 \pm ρ ρ_{0})$ 194. $Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10 cm^{2}, the velocity of water is 1 ms^{- 1} and the pressure is 2000 Pa . The pressure at another point where the cross-sectional area is 5 cm^{2} is$ (1) $4000 Pa$ (2) $2000 Pa$ (3) $1000 Pa$ (4) $500 Pa$ 195. $The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross-sectional areas at A is 1.5 c m^{2}, and B is 25 m m^{2}, if the speed of liquid at B is 60 cm s^{- 1} then (P_{A} - P_{B}) is (Given P_{A} and P_{B} are liquid pressures at A and B points. Density ρ = 1000 kg m^{- 3} A and B are on the axis of tube)$ (1) $135 Pa$ (2) $27 Pa$ (3) $175 Pa$ (4) $36 Pa$ 196. $A venturimeter has a pipe diameter of 4 cm and a throat diameter of 2 cm . Velocity of water in the pipe section is 10 m / s . The pressure drop, between pipe section and the throat section is [use density of water = 1000 kg / m^{3}]$ (1) $1.5 \times 10^{5} Pa$ (2) $7.5 \times 10^{5} Pa$ (3) $75 \times 10^{5} Pa$ (4) $4.5 \times 10^{5} Pa$ 197. $An object of mass 10 kg is released from rest in a liquid. If the object moves a distance of 2 m while sinking in time duration of 1 s, then ithe mass of the liquid displaced by the submerged object is (Acceleration due to gravity = 10 m s^{- 2})$ (1) $5 kg$ (2) $6 kg$ (3) $3 kg$ (4) $4 kg$ 198. $A metal sheet 4 cm on a side and of negligible thickness is attached to a balance and inserted into container fluid. The balance to which metal sheet is attached read 0.50 N and the contact angle is found to be zero. A small amount of oil is then spread over the metal sheet. The contact angle now becomes 180^{\circ} and the balance now reads 0.49 N . The surface tension of the fluid is$ (1) $6.25 \times 10^{- 2} N / m$ (2) $1.25 \times 10^{- 1} N / m$ (3) $4.25 \times 10^{- 2} N / m$ (4) $0.1 N / m$ 199. $A liquid drop of density ρ is floating half immersed in a liquid of surface tension S and density \frac{ρ}{2} . If the surface tension S of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:$ (1) $\frac{20}{ρ}$ (2) $\frac{80}{ρ}$ (3) $\frac{60}{ρ}$ (4) $\frac{40}{ρ}$ 200. $AU-shaped tube is partially filled with an incompressible liquid of density 1.2 g / cm^{3} . Oil which does not mix with the liquid is next poured into left side of the U-tube until the liquid rises by 15 cm on the right side of U-tube. If the density of the oil is 0.9 g / cm^{3}, the oil level will stand higher than the liquid level of right side of U-tube by$ (1) $15 cm$ (2) $10 cm$ (3) $12 cm$ (4) $9 cm$ 201. $A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r . If the specific gravity of the shell material is \frac{27}{8} w.r.t water, the value of r is$ (1) $\frac{2}{3} R$ (2) $\frac{4}{9} R$ (3) $\frac{1}{3} R$ (4) $\frac{8}{9} R$ 202. $A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross- sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a<<A)$ (1) $\frac{A}{2 a}$ (2) $None of these$ (3) $\frac{2 a}{A}$ (4) $\frac{a}{A}$ 203. $A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be:$ (1) $2. 8 x 1 0^{- 4} J$ (2) $1. 5 x 1 0^{- 3} J$ (3) $1. 9 x 1 0^{- 4} J$ (4) $9. 4 x 1 0^{- 5} J$ 204. $Eight equal drops of water are falling through air with a steady speed of 10 cm s^{- 1} . If the drops coalesce, the new velocity is$ (1) $16 cm s^{- 1}$ (2) $40 cm s^{- 1}$ (3) $5 cm s^{- 1}$ (4) $10 cm s^{- 1}$ 205. $There are identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will have to be applied on the tank to keep it in equilibrium is -$ (1) $ghρa$ (2) $\frac{2 g h}{ρ a}$ (3) $2ρagh$ (4) $\frac{ρ g h}{a}$ 206. $A steel ball of radius 0.05 cm and density 7.8 g c m^{- 3} is dropped into a tank of water. The terminal velocity of the steel ball is (Density of water = 1 g c m^{- 3} and viscosity of water = 0.001 P a s)$ (1) $3.42 ms^{- 1}$ (2) $1.81 ms^{- 1}$ (3) $5.11 ms^{- 1}$ (4) $3.77 ms^{- 1}$ 207. $Two mercury drops (each of radius ‘r’) merge to from bigger drop. The surface energy of the bigger drop, if T is the surface tension, is:$ (1) $4 π r^{2} T$ (2) $2 π r^{2} T$ (3) $2^{8/3} π r^{2} T$ (4) $2^{5/3} π r^{2} T$ 208. $The terminal velocity (v_{t}) of the spherical rain drop depends on the radius (r) of the spherical rain drop as:-$ (1) $r^{172}$ (2) $r$ (3) $r^{2}$ (4) $r^{3}$ 209. $A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid then:$ (1) $Energy = 4 V T (\frac{1}{r} - \frac{1}{R}) is released.$ (2) $Energy = 3 V T (\frac{1}{r} + \frac{1}{R}) is released.$ (3) $Energy = 3 V T (\frac{1}{r} - \frac{1}{R}) is released.$ (4) $Energy is neither released nor absorbed.$ 210. $The cylindrical tube of a spray pump has a cross-section of 8 c m^{2}, one end of which has 40 fine holes each of area 1 0^{- 8} m^{2} . If the liquid flows inside the tube with a speed of 0.15 m mi n^{- 1}, the speed with which the liquid is ejected through the holes is$ (1) $50 m s^{- 1}$ (2) $5 m s^{- 1}$ (3) $0.05 m s^{- 1}$ (4) $0.5 m s^{- 1}$