Fluid Mechanics PYQs Set 9 (PDF)

Set 9 of 10 · Questions 241-270 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 9 (Q241-270)
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241. $A metal sheet 4 cm on a side and of negligible thickness is attached to a balance and inserted into container fluid. The balance to which metal sheet is attached read 0.50 N and the contact angle is found to be zero. A small amount of oil is then spread over the metal sheet. The contact angle now becomes 180^{\circ} and the balance now reads 0.49 N . The surface tension of the fluid is$ (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) $0.1 N / m$ 242. $A liquid drop of density ρ is floating half immersed in a liquid of surface tension S and density \frac{ρ}{2} . If the surface tension S of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:$ (1) $\frac{20}{ρ}$ (2) $\frac{80}{ρ}$ (3) $\frac{60}{ρ}$ (4) $\frac{40}{ρ}$ 243. $AU-shaped tube is partially filled with an incompressible liquid of density 1.2 g / cm^{3} . Oil which does not mix with the liquid is next poured into left side of the U-tube until the liquid rises by 15 cm on the right side of U-tube. If the density of the oil is 0.9 g / cm^{3}, the oil level will stand higher than the liquid level of right side of U-tube by$ (1) $15 cm$ (2) $10 cm$ (3) $12 cm$ (4) $9 cm$ 244. $A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r . If the specific gravity of the shell material is \frac{27}{8} w.r.t water, the value of r is$ (1) $\frac{2}{3} R$ (2) $\frac{4}{9} R$ (3) $\frac{1}{3} R$ (4) $\frac{8}{9} R$ 245. $A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross- sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a<<A)$ (1) $\frac{A}{2 a}$ (2) $None of these$ (3) $\frac{2 a}{A}$ (4) $\frac{a}{A}$ 246. $A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be:$ (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) $9. 4 x 1 0^{- 5} J$ 247. $Eight equal drops of water are falling through air with a steady speed of 10 cm s^{- 1} . If the drops coalesce, the new velocity is$ (1) $16 cm s^{- 1}$ (2) $40 cm s^{- 1}$ (3) $5 cm s^{- 1}$ (4) $10 cm s^{- 1}$ 248. $There are identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will have to be applied on the tank to keep it in equilibrium is -$ (1) $ghρa$ (2) $\frac{2 g h}{ρ a}$ (3) $2ρagh$ (4) $\frac{ρ g h}{a}$ 249. $A steel ball of radius 0.05 cm and density 7.8 g c m^{- 3} is dropped into a tank of water. The terminal velocity of the steel ball is (Density of water = 1 g c m^{- 3} and viscosity of water = 0.001 P a s)$ (1) $3.42 ms^{- 1}$ (2) $1.81 ms^{- 1}$ (3) $5.11 ms^{- 1}$ (4) $3.77 ms^{- 1}$ 250. $Two mercury drops (each of radius ‘r’) merge to from bigger drop. The surface energy of the bigger drop, if T is the surface tension, is:$ (1) $4 π r^{2} T$ (2) $2 π r^{2} T$ (3) $2^{8/3} π r^{2} T$ (4) $2^{5/3} π r^{2} T$ 251. $The terminal velocity (v_{t}) of the spherical rain drop depends on the radius (r) of the spherical rain drop as:-$ (1) $r^{172}$ (2) $r$ (3) $r^{2}$ (4) $r^{3}$ 252. $A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid then:$ (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) $Energy is neither released nor absorbed.$ 253. $The cylindrical tube of a spray pump has a cross-section of 8 c m^{2}, one end of which has 40 fine holes each of area 1 0^{- 8} m^{2} . If the liquid flows inside the tube with a speed of 0.15 m mi n^{- 1}, the speed with which the liquid is ejected through the holes is$ (1) $50 m s^{- 1}$ (2) $5 m s^{- 1}$ (3) $0.05 m s^{- 1}$ (4) $0.5 m s^{- 1}$ 254. $Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x_{1} and in the other, x_{2} . When both cylinders are connected through a pipe of negligible volume very close to the bottom, theliquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is$ (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) $gdS (x_{2}^{2} + x_{1}^{2})$ 255. $An air bubble of volume 2.9 cm^{3} rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17^{\circ} C . The volume of the bubble when it reaches the surface, where the water temperature is 27^{\circ} C, is____cm^{3} . (g = 10 m / s^{2}, density of water = 10^{3} kg / m^{3}, and 1 atm pressure is 10^{5} Pa)$ (1) $4.5$ (2) $2.0$ (3) $4.2$ (4) $3.0$ 256. $A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm^{- 1}, density = 667 kgm^{- 3}) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60^{\circ} with one another. Then h is close to (g = 10 ms^{- 2})$ (1) $0.049 m$ (2) $0.087 m$ (3) $0.137 m$ (4) $0.172 m$ 257. $The venturi meter works on [NEET 2023]$ (1) $Bernoulli's principle$ (2) $the principle of parallel axes$ (3) $the principle of perpendicular axes$ (4) $Huygen's principle$ 258. $Hydraulic lift works on the basis of$ (1) $Stoke's law$ (2) $Bernoulli's law$ (3) $Toricelli's law$ (4) $Pascal's law$ 259. $Surface tension of two liquids (having same densities), T_{1} and T_{2}, are measured using capillary rise method utilizing two tubes with inner radii of r_{1} and r_{2} where r_{1} > r_{2} . The measured liquid heights in these tubes are h_{1} and h_{2} respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h_{1} and h_{2} and surfaces tensions T_{1} and T_{2} satisfy the relation:$ (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) $h_{1} < h_{2} and T_{1} = T_{2}$ 260. $In the experiment for measurement of viscosity ' η ' of given liquid with a ball having radius R, consider following statements. (A) Graph between terminal velocity V and R will be a parabola. (B) The terminal velocities of different diameter balls are constant for a given liquid. (C) Measurement of terminal velocity is dependent on the temperature. (D) This experiment can be utilized to assess the density of a given liquid. (E) If balls are dropped with some initial speed, the value of η will change. Choose the correct answer from the options given below:$ (1) $A, B and E Only$ (2) $B, D and E Only$ (3) $A, C and D Only$ (4) $C, D and E Only$ 261. $Consider following statements: (A) Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. (B) As the temperature of liquid rises, the coefficient of viscosity increases. (C) As the temperature of gas increases, the coefficient of viscosity increases (D) The onset of turbulence is determined by Reynold's number. (E) In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:$ (1) $C, D, E Only$ (2) $A, D, E Only$ (3) $B, C, D Only$ (4) $A, B, C Only$ 262. $A uniform heavy rod of weight 10 kg m s^{- 2}, cross-sectional area 100 cm^{2} and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \times 1 0^{11} Nm^{- 2} . Neglecting the lateral contraction, find the elongation of rod due to its own weight.$ (1) $2 \times 1 0^{- 9} m$ (2) $5 \times 1 0^{8} m$ (3) $4 \times 1 0^{- 8} m$ (4) $5 \times 1 0^{- 10} m$ 263. $Water rises to a height 'h' in capillary tube. If the length of capillary tube above the surface of water is made less than 'h' then:$ (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) $Water rises upto the tip of capillary tube and then starts overflowing like fountain.$ 264. $The wettability of a surface by a liquid depends primarily on:$ (1) $surface tension$ (2) $density$ (3) $angle of contact between the surface and the liquid$ (4) $viscosity$ 265. $An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J / m^{2} and density 10^{3} kg / m^{3} . The difference between pressure inside the bubble and atmospheric pressure is N / m^{2} . (Take (g = 10 m / s^{2})$ 266. $A tube of length 1 m is filled completely with an ideal liquid of mass 2 M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is \frac{F}{αM} in SI unit. The value of α is .$ 267. $A metal block of base area 0.20 m^{2} is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is 5.0 x 1 0^{- 3} Pl, the speed of block is_______x 1 0^{- 3} m/s,$ 268. $A bakelite beaker has volume capacity of 500 cc at 30^{\circ} C . When it is partially filled with V_{m} volume (at 30^{\circ} C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ_{(beaker)} = 6 \times 10^{- 6 \circ} C^{- 1} and γ_{(mercury)} = 1.5 \times 10^{- 4 \circ} C^{- 1} where γ is the coefficient of volume expansion, then V_{m} (in cc) is close to$ 269. $A liquid of density 750 k g m^{- 3} flows smoothly through a horizontal pipe that tapers in cross-sectional area from A_{1} = 1.2 x 1 0^{- 2} m^{2} to A_{2} = \frac{A _{1}}{2} . The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is_______\times 1 0^{- 3} m^{3} s^{- 1} .$ 270. $A spherical drop of liquid splits into 1000 identical spherical drops. If u_{i} is the surface energy of the original drop and u_{f} is the total surface energy of the resulting drops, the (ignoring evaporation). \frac{u _{f}}{u _{i}} = (\frac{10}{x}) . Then value of x is______:$