Fluid Mechanics PYQs Set 6 (PDF)

Set 6 of 10 · Questions 151-180 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 6 (Q151-180)
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151. $Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:$ (1) $1 : 2$ (2) $1 : 2$ (3) $2 : 1$ (4) $2 : 1$ 152. $A rain drop of radius r is falling through air, starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to$ (1) $r^{3}$ (2) $r^{7}$ (3) $r^{5}$ (4) $r^{4}$ 153. $An aluminium sphere is dipped into water. Which of the following is true?$ (1) $Buoyancy in water at 0^{\circ} C will be same as that in water at 4^{\circ} C .$ (2) $Buoyancy will be less in water at 0^{\circ} C than that in water at 4^{\circ} C .$ (3) $Buoyancy may be more or less in water at 4^{\circ} C depending on the radius of the sphere.$ (4) $Buoyancy will be more in water at 0^{\circ} C than that in water at 4^{\circ} C .$ 154. $A liquid does not wet the solid surface if angle of contact is [NEET 2020]$ (1) $equal to 45^{\circ}$ (2) $equal to 60^{\circ}$ (3) $grater than 90^{\circ}$ (4) $zero$ 155. $Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 \times 1 0^{3} k g, The inner and outer radii of each column are 50cm and 100cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 \times 1 0^{11} P a, g = 9.8 m / s^{2}]$ (1) $3.60 \times 1 0^{- 8}$ (2) $2.60 \times 1 0^{- 7}$ (3) $1.87 \times 1 0^{- 3}$ (4) $7.07 \times 1 0^{- 4}$ 156. $Consider a water droplet of diameter 0.2 mm where the outside pressure is 1.5 N / cm^{2} at 25^{\circ} C . The pressure inside the droplet, when the surface tension at 25^{\circ} C is 0.08 N / m is$ (1) $0.32 N / cm^{2}$ (2) $1.18 N / cm^{2}$ (3) $1.82 N / cm^{2}$ (4) $1.66 N / cm^{2}$ 157. $A pure number which determines the types of flow of a liquid through a pipe is known as$ (1) $Reynold's number$ (2) $Bernoulli's number$ (3) $Pascal's number$ (4) $Torricelli's number$ 158. $Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm^{2} and 3 cm^{2} respectively. The rate of flow will be____cm^{3} / s . (take g = 10 m / s^{2})$ (1) $\frac{200}{3}$ (2) $2006$ (3) $1003$ (4) $2003$ 159. $A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible, find at what height from the bottom of the vessel a small hole should be made for the water jet coming out of it to hit the surface of the table at the maximum horizontal distance from the vessel.$ (1) $15 cm$ (2) $35 cm$ (3) $25 cm$ (4) $10 cm$ 160. $Water is flowing continuously from a tap having an internal diameter 8 \times 1 0^{-3} m. The water velocity as it leaves the tap is 0.4 m s^{-1} . The diameter of the water stream at a distance 2 \times 1 0^{-1} m below the tap is close to:$ (1) $5.0 \times 1 0^{-3} m$ (2) $7.5 \times 1 0^{-3} m$ (3) $9.6 \times 1 0^{-3} m$ (4) $3.6 \times 1 0^{-3} m$ 161. $A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0^{\circ} C such that its height above the water surface is 20 cm . When thetemperature of water is increased to 4^{o} C, the height of the cylinder above the water surface becomes 21 cm . The density of water at T = 4^{\circ} C, relative to the density at T = 0^{\circ} C is close to:$ (1) $1.01$ (2) $1.03$ (3) $2.01$ (4) $1.04$ 162. $A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is:$ (1) $650 kg m^{-3}$ (2) $425 kg m^{-3}$ (3) $800 kg m^{-3}$ (4) $928 kg m^{-3}$ 163. $Fully filled open water tank has two holes on either sides of its walls. One is a square hole of side x cm at a depth of 2 m from the top, and the other hole is equilateral triangle of side 4 cm at a depth of 6 m from the top. If the rate of flow of water is same from both the holes, then ' x' is$ (1) $1.73 cm$ (2) $12 cm$ (3) $6.92 cm$ (4) $3.46 cm$ 164. $Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:$ (1) $\frac{8}{3}$ (2) $\frac{3}{8}$ (3) $\frac{3}{4}$ (4) $\frac{4}{3}$ 165. $A U-tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is [NEET 2017]$ (1) $650 kg m^{- 3}$ (2) $425 kg m^{- 3}$ (3) $800 kg m^{- 3}$ (4) $928 kg m^{- 3}$ 166. $A steady flow of a liquid of density ρ is shown in figure. At point 1, the area of cross-section is 2 A and the speed of flow of liquid is 2 ms^{- 1} . At point 2, the area of crosssection is A. Between the points 1 and 2, the pressure difference is 100 Nm^{- 2} and the height difference is 10 cm . The value of ρ is (Acceleration due to gravity = 10 ms^{- 2})$ (1) $25 kg m^{- 3}$ (2) $30 kg m^{- 3}$ (3) $50 kg m^{- 3}$ (4) $70 kg m^{- 3}$ 167. $Water flows in a horizontal tube (see figure). The pressure of water changes by 700 N m^{- 2} between A and B where the area of cross section are 40 cm^{2} and 20 cm^{2}, respectively. Find the rate of flow ofwater through the tube. (density of water = 1000 kgm^{- 3})$ (1) $2732 cm^{3} / s$ (2) $2142 cm^{3} / s$ (3) $1832 cm^{3} / s$ (4) $3218 cm^{3} / s$ 168. $In a U-tube as shown in a figure, water and oil are in the left side and right side of the tube, respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is [take, ρ_{water} = 1000 kg / m^{3}] [NEET 2019]$ (1) $1200 kg / m^{3}$ (2) $750 kg / m^{3}$ (3) $1000 kg / m^{3}$ (4) $1333 kg / m^{3}$ 169. $Two blocks of masses 3kg and 5kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \frac{24}{π} \times 1 0^{2} N m^{- 2} . What is the minimum radius of the wire? (Take g = 10 m s^{- 2})$ (1) $125cm$ (2) $1250cm$ (3) $12.5cm$ (4) $1.25cm$ 170. $In a horizontal tube the water pressure changes by 1500 Nm^{- 2} between A and B as shown in figure below. The ciross-sectional areas at A and B of the tube are 40 cm^{2} and 20 cm^{2}, respectively. Find the rate of flow of water through the tube.$ (1) $1000 cm^{3} s^{- 1}$ (2) $2000 cm^{3} s^{- 1}$ (3) $4000 cm^{3} s^{- 1}$ (4) $6000 cm^{3} s^{- 1}$ 171. $A small hole of area of cross-section 2 m m^{2} present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/ s^{2}, the rate of flow of water through the open hole would be nearly$ (1) $6.4 \times 1 0^{-6} m^{3} /s$ (2) $12.6 \times 1 0^{-6} m^{3} /s$ (3) $8.9 \times 1 0^{-6} m^{3} /s$ (4) $2.23 \times 1 0^{-6} m^{3} /s$ 172. $A body takes 4 min. to cool from 6 1^{0} C to 5 9^{0} C. If the temperature of the surroundings is 3 0^{0} C, the time taken by the body to cool from 5 1^{0} C to 4 9^{0} C is:$ (1) $4min.$ (2) $3min.$ (3) $8min.$ (4) $6min.$ 173. $A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is [NEET 2022]$ (1) $B$ (2) $C$ (3) $D$ (4) $A$ 174. $Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm / s coalesce to form a bigger drop. The terminal velocity of bigger drop is____cm / s .$ 175. $A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is.......$ 176. $In a hydraulic lift, the surface area of the input piston is 6 cm^{2} and that of the output piston is 1500 cm^{2} . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.$ 177. $Glycerin of density 1. 25 x 1 0^{3} kg m^{- 3} is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are 10 c m^{2} and 5 c m^{2} and pressure drop across its length is 3 N m^{- 2} . The rate of flow of glycerine through the pipe is x x 1 0^{- 5} m^{3} s^{- 1} . The value of x is_____.$ 178. $The surface tension of soap solution is 3. 5 x 10-2 N m^{- 1} . The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is _____x 1 0^{- 4} J. (take π = \frac{22}{7})$ 179. $A hydraulic press can lift 100 kg when a mass ’ m ’ is placed on the smaller piston. It can lift kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass ’ m ’ on the smaller piston.$ 180. $A drop of liquid of radius R = 10-2 m having surface tension S = \frac{0.1}{4 π} N m^{- 1} divides itself into K identical drops. In this process the total change in the surface energy ΔU = 10-3 J. If K = 10 α then the value of α is:$