Fluid Mechanics PYQs Set 8 (PDF)

Set 8 of 10 · Questions 211-240 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 8 (Q211-240)
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211. $A water drop of radius 1 μ m falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is 1.8 x 1 0^{- 5} N s m^{- 2} and its density is negligible as compared to that of water 1 0^{6} g m^{- 3} . Terminal velocity of the water drop is: (Take acceleration due to gravity =10 m s^{- 2})$ (1) $145.4 x 1 0^{- 6} m s^{- 1}$ (2) $118.0 x 1 0^{- 6} m s^{- 1}$ (3) $132.6 x 1 0^{- 6} m s^{- 1}$ (4) $123.4 x 1 0^{- 6} m s^{- 1}$ 212. $Water flows into a large tank with flat bottom at the rate of 10^{- 4} m^{3} s^{- 1} . Water is also leaking out of a hole of area 1 c m^{2} at its bottom. If the height of the water in the tank remains steady, then this height is:$ (1) $5.1 cm$ (2) $7 cm$ (3) $4 cm$ (4) $9 cm$ 213. $An ideal fluid flows through a pipe of circular cross section with diameters 5 cm and 10 cm as shown. The ratio of velocities of fluid at A and B is$ (1) $4 : 1$ (2) $1 : 4$ (3) $2 : 1$ (4) $1 : 2$ 214. $A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed ν and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:$ (1) $\frac{1}{2} ρ ν^{2}$ (2) $\frac{1}{4} ρ ν^{2}$ (3) $\frac{3}{4} ρ ν^{2}$ (4) $ρ ν^{2}$ 215. $Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y_{1} and Y_{2} . The combination behaves as a single wire then its Young's modulus is:$ (1) $Y = \frac{2 Y _{1} Y _{2}}{3 ( Y _{1} + Y _{2} )}$ (2) $Y = \frac{2 Y _{1} Y _{2}}{Y _{1} + Y _{2}}$ (3) $Y = \frac{Y _{1} Y _{2}}{2 ( Y _{1} + Y _{2} )}$ (4) $Y = \frac{Y _{1} Y _{2}}{Y _{1} + Y _{2}}$ 216. $Two narrow bores of diameter 5.0mm and 8.0mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 \times 1 0^{- 2} N m^{- 1}, angle of contact =0, g = 10 m s^{- 2} and density of water = 1.0 \times 1 0^{3} k g m^{- 3}]$ (1) $3.62 mm$ (2) $2.19 mm$ (3) $5.34 mm$ (4) $4.97 mm$ 217. $A block of iron contains a hollow cavity as shown below. The block weighs 6000 N in air and 4000 N in water. If the density of iron and water are 6 g / cm^{3} and 1 g / cm^{3}, then the volume of the cavity is (assume, g = 10 m / s^{2})$ (1) $0.05 m^{3}$ (2) $0.5 m^{3}$ (3) $0.25 m^{3}$ (4) $0.1 m^{3}$ 218. $Surface tension of a soap bubble is 2.0 x 1 0^{- 2} M m^{- 1} . Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be: [Take π = \frac{22}{7}]$ (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) $9. 24 x 1 0^{- 4} J$ 219. $Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N . For a streamline flow of liquid the rate of liquid flow is$ (1) $continuously changes with time$ (2) $greater at M than at N$ (3) $greater at N than at M$ (4) $same at M and N .$ 220. $A cylindrical container containing water has a small hole at height of H = 8 cm from the bottom and at depth of 2 cm from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground (x) is$ (1) $4 cm$ (2) $8 cm$ (3) $6 cm$ (4) $42 cm$ 221. $Consider two liquids A and B in a U -shaped tube in static equilibrium as shown in the figure. If the density of the liquid A is twice the density of liquid B; then the relation between h_{A} and h_{B} is$ (1) $h_{A} = \frac{h _{B}}{2}$ (2) $h_{A} = \frac{h _{B}}{2}$ (3) $h_{A} = \frac{h _{B}}{3}$ (4) $h_{A} = \frac{h _{B}}{3}$ 222. $There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2} are filled in the tube. Each liquid subtends 90° angle at center. Radius joining their interface makes an angle α with vertical. Ratio \frac{d _{1}}{d _{2}} is:$ (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) $\frac{1 + s in α}{1 - cos α}$ 223. $A glass tumbler having inner depth of 17.5cm is kept on a table. A student starts pouring water into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?$ (1) $11.7cm$ (2) $10cm$ (3) $7.5cm$ (4) $8.75cm$ 224. $A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,$ (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) $air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases.$ 225. $Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P_{1} . The reading of the pressure gauge falls to P_{2} when the valve is opened. The speed of water flowing in the pipe is proportional to$ (1) $P_{1} - P_{2}$ (2) $(P_{1} - P_{2})^{4}$ (3) $(P_{1} - P_{2})^{2}$ (4) $P_{1} - P_{2}$ 226. $Two non-mixing liquids of densities ρ and nρ (n > 1) are put in container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal t$ (1) ${1 + (n - 1) p}ρ$ (2) ${1 + (n + 1) p}ρ$ (3) ${2+(n + 1) p}ρ$ (4) ${2 + (n - 1) p}ρ$ 227. $A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in the figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is 10 rad s^{- 1}, then the height difference between the liquid at the centre of the vessel and its sides is (g = 10 ms^{- 2})$ (1) $125\times 1 0^{- 4} m$ (2) $100 \times 10^{- 4} m$ (3) $50 \times 10^{- 4} m$ (4) $25 \times 10^{- 4} m$ 228. $A small ball of mass M and density p is dropped in a viscous liquid of density ρ_{0} . After some time, the ball falls with a constant velocity. What is the viscous force on the ball?$ (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) $F = Mg (1 \pm ρ ρ_{0})$ 229. $Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10 cm^{2}, the velocity of water is 1 ms^{- 1} and the pressure is 2000 Pa . The pressure at another point where the cross-sectional area is 5 cm^{2} is$ (1) $4000 Pa$ (2) $2000 Pa$ (3) $1000 Pa$ (4) $500 Pa$ 230. $The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross-sectional areas at A is 1.5 c m^{2}, and B is 25 m m^{2}, if the speed of liquid at B is 60 cm s^{- 1} then (P_{A} - P_{B}) is (Given P_{A} and P_{B} are liquid pressures at A and B points. Density ρ = 1000 kg m^{- 3} A and B are on the axis of tube)$ (1) $135 Pa$ (2) $27 Pa$ (3) $175 Pa$ (4) $36 Pa$ 231. $A venturimeter has a pipe diameter of 4 cm and a throat diameter of 2 cm . Velocity of water in the pipe section is 10 m / s . The pressure drop, between pipe section and the throat section is [use density of water = 1000 kg / m^{3}]$ (1) $1.5 \times 10^{5} Pa$ (2) $7.5 \times 10^{5} Pa$ (3) $75 \times 10^{5} Pa$ (4) $4.5 \times 10^{5} Pa$ 232. $An object of mass 10 kg is released from rest in a liquid. If the object moves a distance of 2 m while sinking in time duration of 1 s, then ithe mass of the liquid displaced by the submerged object is (Acceleration due to gravity = 10 m s^{- 2})$ (1) $5 kg$ (2) $6 kg$ (3) $3 kg$ (4) $4 kg$ 233. $A U-tube is made up of capillaries of bores 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne/cm and zero contact angle. Calculate the density of the liquid if the difference in the levels of the meniscus is 1.25 cm.$ 234. $A soap bubble of radius 3cm is formed inside the another soap bubble of radius 6cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is \dots.cm.$ 235. $The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m~^{3} at the rate of 0.35 c m s^{- 1} . The coefficient of viscosity of the solution is_______ poise (in nearest integer), (the density of air is negligible).$ 236. $In 5 minutes, a body cools from 7 5^{0} C to 6 5^{0} C at room temperature of 2 5^{0} C. The temperature of body at the end of next 5 minutes is ____.$ 237. $The area of cross-section of a large tank is 0.5 m^{2} It has a narrow opening near the bottom having area of cross-section 1 c m^{2} A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be_______c m s^{- 1} .$ 238. $A small spherical ball of radius 0.1 mm and density 1 0^{4} kg m^{3} falls freely under gravity through a a distance h before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be_____m. (Given g = 10 m s^{- 2}, viscosity of water = 1.0 x 1 0^{- 5} N- s m^{- 2}).$ 239. $Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2. 0 c m^{2} . The area of cross section at the outlet is 10 m m^{2} . If the piston is pushed at a speed of 4 cm s^{- 1}, the speed of outgoing fluid is_____cm s^{- 1}$ 240. $A film of soap solution is formed on a loop frame loop of 6.28 cm long thread is gently put on the film and the film is broken with a needle inside the loop. the thread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution = 0.030 N/m.$