Fluid Mechanics PYQs Set 7 (PDF)

Set 7 of 10 · Questions 181-210 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 7 (Q181-210)
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181. $The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:$ (1) $1 : 9$ (2) $1 : 3$ (3) $1 : 27$ (4) $1 : 81$ 182. $Two solids P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with \frac{2}{3}^{rd} of its volume is immersed. The ratio of densities of P and Q is$ (1) $\frac{4}{3}$ (2) $\frac{3}{4}$ (3) $\frac{2}{3}$ (4) $\frac{3}{2}$ 183. $Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is ?$ (1) $0.458$ (2) $0$ (3) $0.917$ (4) $1$ 184. $A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively floats half submerged in a liquid of density 2.0 g / cm^{3} . The density of the material of the sphere is$ (1) $1.02 g / cm^{3}$ (2) $1.14 g / cm^{3}$ (3) $1.18 g / cm^{3}$ (4) $1.24 g / cm^{3}$ 185. $A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density σ at equilibrium position. The extension x_{0} of the spring when it is in equilibrium is: (Here k is spring constant)$ (1) $\frac{Mg}{k}$ (2) $\frac{Mg}{k} (1 - \frac{LAσ}{M})$ (3) $\frac{Mg}{k} (1 - \frac{LAσ}{2 M})$ (4) $\frac{Mg}{k} (1 + \frac{LAσ}{M})$ 186. $Two cylindrical vessels of equal cross sectional area of 2 m^{2} contain water up to height 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is: (Density of water is 10^{3} kg / m^{3} and g = 10 m / s^{2})$ (1) $1 \times 10^{5} J$ (2) $4 \times 10^{4} J$ (3) $6 \times 10^{4} J$ (4) $8 \times 10^{4} J$ 187. $A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m^{2} . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the direction of the force will be: (P_{ai r} = 1.2 kg / m^{3})$ (1) $4.8 x 1 0^{5} N, upwards$ (2) $2.4 x 1 0^{5} N, upwards$ (3) $2.4 x 1 0^{5} N, downwards$ (4) $4.8 x 1 0^{5} N, downwards$ 188. $A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is ρ, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity)$ (1) $\frac{2 S}{bρg} cos (θ - α)$ (2) $\frac{2 S}{bρg} cos (θ + α)$ (3) $\frac{2 S}{bρg} cos (θ - α /2)$ (4) $\frac{2 S}{bρg} cos (θ + α /2)$ 189. $An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg / m^{3} . If the pressure inside the bubble is 2100 N / m^{2} greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g = 10 m / s^{2})$ (1) $0.1$ (2) $0.05$ (3) $0.02$ (4) $0.25$ 190. $A small spherical droplet of density d is floating exactly half immerse in a liquid of density ρ and surface tension T . The radius of the droplet is (take note that the surface tension applies an upwardforce on the droplet):$ (1) $r = \frac{T}{( d + ρ ) g}$ (2) $r = \frac{3 T}{( 2 d - ρ ) g}$ (3) $r = \frac{T}{( d - ρ ) g}$ (4) $r = \frac{2 T}{3 ( d + ρ ) g}$ 191. $A long cylindrical vessel is half filled with a liquid filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:$ (1) $2.0$ (2) $0.1$ (3) $0.4$ (4) $1.2$ 192. $A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m / s, then velocity of water leaving the point (2) will be$ (1) $4 m / s$ (2) $2 m / s$ (3) $6 m / s$ (4) $8 m / s$ 193. $Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h . A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to [NEET 2016]$ (1) ${2 + (n + 1) p} ρ$ (2) ${2 + (n - 1) p} ρ$ (3) ${1 + (n - 1) p} ρ$ (4) ${1 + (n + 1) p} ρ$ 194. $Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is P_{0} . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude$ (1) $2 P_{0} R h + π R^{2} ρ g h - 2 R T$ (2) $2 P_{0} R h + R ρ g h^{2} - 2 R T$ (3) $P_{0} π R^{2} + R ρ g h^{2} - 2 R T$ (4) $P_{0} π R^{2} + R ρ g h^{2} + 2 R T$ 195. $A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9)$ (1) $1 : 1$ (2) $5 : 4$ (3) $8 : 9$ (4) $9 : 10$ 196. $The radius of the bore of a capillary tube is r and the angle of contact of the liquid is θ . When the tube is dipped in the liquid, the radius of curvature of the meniscus of liquid rising in the tube is$ (1) $rsin θ$ (2) $\frac{r}{sin θ}$ (3) $rcos θ$ (4) $\frac{r}{cos θ}$ 197. $A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)$ (1) $2 Mg$ (2) $Mg$ (3) $\frac{3}{2} Mg$ (4) $\frac{Mg}{2}$ 198. $An air bubble of radius 1 mm is at a depth of 8 cm below the free surface of a liquid column. If the surface tension and density of the liquid is 0.1 N / m and 2000 Kg / m^{3}, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? [Take g = 10 m / s^{2}]$ (1) $1500 N / m^{2}$ (2) $1800 N / m^{2}$ (3) $1600 N / m^{2}$ (4) $1700 N / m^{2}$ 199. $A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn / cm and glass water contact angle ≃ 0^{\circ}) with 30^{\circ} inclined with vertical. The length of water risen in the capillary is cm. Take (g = 9.8 m / s^{2})$ (1) $\frac{82}{5}$ (2) $\frac{57}{2}$ (3) $\frac{71}{5}$ (4) $\frac{68}{5}$ 200. $A mercury drop of radius 1 0^{- 3} m is broken into 125 equal size droplets. Surface tension of mercury is 0.45 N m^{- 1} . The gain in surface energy is:$ (1) $2.26 x 1 0^{- 5} J$ (2) $28 x 1 0^{- 5} J$ (3) $17.5 x 1 0^{- 5} J$ (4) $5 x 1 0^{- 5} J$ 201. $A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s^{- 1} . Thedifference in the height, h (in cm) of liquid at the centre of vessel and at the side will be$ (1) $\frac{2 ω ^{2}}{25 g}$ (2) $\frac{5 ω ^{2}}{2 g}$ (3) $\frac{2 ω ^{2}}{5 g}$ (4) $\frac{25 ω ^{2}}{2 g}$ 202. $A closed water tank has cross-sectional area A . It has a small hole at a depth of h from the free surface of water. The radius of the hole is r so that r ≪ \frac{A}{π} . If P_{0} is the pressure inside the tank above water level, and P_{a} is the atmospheric pressure, the rate of flow of the water coming out of the hole is [ρ is the density of water]$ (1) $π r^{2} 2 gh$ (2) $π r^{2} 2 gh + \frac{2 ( P _{0} - P _{a} )}{ρ}$ (3) $π r^{2} 2 gH$ (4) $π r^{2} gh + \frac{2 ( P _{0} - P _{a} )}{ρ}$ 203. $Water flows in a horizontal tube (see figure). The pressure of water changes by 700 N m^{-2} between A and B where the area of cross section are 40 c m^{2} and 20 c m^{2}, respectively. Find the rate of flow of water through the tube. (density of water = 1000 k g m^{-3})$ (1) $2720 c m^{3} /s$ (2) $2420 c m^{3} /s$ (3) $3020 c m^{3} /s$ (4) $1810 c m^{3} /s$ 204. $A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 \times 1 0^{-2} N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is:$ (1) $0.0125 N m^{-1}$ (2) $0.1 N m^{-1}$ (3) $0.05 N m^{-1}$ (4) $0.025 N m^{-1}$ 205. $A wooden cube (density of wood ‘d’) of side ‘λ’ floats in a liquid of density ‘ρ’ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period ‘T’. Then, ‘T’ is equal to:$ (1) $2 π \frac{l d}{ρg}$ (2) $2 π \frac{l ρ}{dg}$ (3) $2 π \frac{l d}{( ρ - d ) g}$ (4) $2 π \frac{l ρ}{( ρ - d ) g}$ 206. $A fully loaded being aircraft has a mass of 5.4 x kg. Its total wing area is 500 . It is in level flight with a speed of 1080 km/h. If the density of air is 1.2 kg , the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be (g = 10 m/)$ (1) $16$ (2) $6$ (3) $8$ (4) $10$ 207. $Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/ m^{2} . The radii of bubbles A and B are 2cm and 4cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio n_{B} / n_{A}, where n_{A} and n_{B} are the number of moles of air in bubbles A and B, respectively. [Neglect the effect of gravity.]$ 208. $The velocity of a small ball of mass 0.3g and density 8g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x \times 1 0^{- 4} N, the value of x is____. [use g = 10m/ s^{2}]$ 209. $A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is \frac{10}{x} . The value of x is______$ 210. $A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ____N .$