Fluid Mechanics PYQs Set 4 (PDF)

Set 4 of 8 · Questions 91-120 of 236

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Mere Teacher · Previous Year Questions NEET Physics · Fluid Mechanics · Set 4 (Q91-120)
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91. $A wind with speed 40 m / s blows parallel to the roof of a house. The area of the roof is 250 m^{2} . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (p_{air} = 1.2 kg / m^{3})$ (1) $4.8 \times 10^{5} N, downwards$ (2) $4.8 \times 10^{5} N, upwards$ (3) $2.4 \times 10^{5} N, upwards$ (4) $2.4 \times 10^{5} N, downwards$ 92. $Two water drops each of radius ' r' coalesce to from a bigger drop. If' T' is the surface tension, the surface energy released in this process is:$ (1) $4 π r^{2} T (2 - 2^{\frac{2}{3}})$ (2) $4 π r^{2} T (2 - 2^{\frac{1}{3}})$ (3) $4 π r^{2} T [1 + 2]$ (4) $4 π r^{2} T [2 - 1]$ 93. $A sphere of material of relative density 8 has a concentric spherical cavity and just sinks in water. If the radius of the sphere is 2 cm, then the volume of the cavity is$ (1) $\frac{76}{3} cm^{3}$ (2) $\frac{79}{3} cm^{3}$ (3) $\frac{82}{3} cm^{3}$ (4) $\frac{88}{3} cm^{3}$ 94. $Two mercury drops of radii r and 2 r merge to form a bigger drop. The surface energy released in the process is nearly (Surface tension mercury is S and take 9^{2/3} = 4.326)$ (1) $1.6 π r^{2} S$ (2) $3.2 π r^{2} S$ (3) $17.1 π r^{2} S$ (4) $2.7 π r^{2} S$ 95. $The tension in a massless cable connected to an iron ball of 100 kg when it is submerged in sea water is (ρ_{iron} = 8 \times 10^{3} kg / m^{3}) and (ρ_{sea water} = 1000 kg / m^{3}, g = 10 m / s^{2})$ (1) $950 N$ (2) $846 N$ (3) $875 N$ (4) $933 N$ 96. $A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is 3.08 \times 10^{- 5} m^{3} / s, then the diameter of the hole is (Take g = 10 m / s^{2}]$ (1) $1.0 mm$ (2) $1.2 mm$ (3) $1.4 mm$ (4) $1.6 mm$ 97. $In a U-shaped tube the radius of one limb is 2 mm and that of other limb is 4 mm . A liquid of surface tension 0.03 Nm^{- 1}, density 1500 kgm^{- 3} and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is (Acceleration due to gravity = 10 ms^{- 2})$ (1) $3 mm$ (2) $2.5 mm$ (3) $1 mm$ (4) $1.5 mm$ 98. $The angle of contact between pure water and pure glass, is$ (1) $0^{\circ}$ (2) $45^{\circ}$ (3) $90^{\circ}$ (4) $135^{\circ}$ 99. $A wooden block floating in a bucket of water has \frac{4}{5} of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:$ (1) $0.5$ (2) $0.8$ (3) $0.6$ (4) $0.7$ 100. $A long cylindrical glass vessel has a pinhole of diameter 0.2 mm at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, T = 0.07 Nm^{- 1}, acceleration due to gravity, g = 10 ms^{- 2})$ (1) $14 cm$ (2) $7 cm$ (3) $21 cm$ (4) $28 cm$ 101. $A submarine experiences a pressure of 5.05 \times 10^{6} Pa depth of d_{1} in a sea. When it goes further to a depth of d_{2} , it experiences a pressure of 8.08 \times 10^{6} Pa., Then d_{2} - d_{1} is approximately (density of water = 10³kg/m³ and acceleration due to gravity = 10 ms^{- 2}):$ (1) $300 m$ (2) $400 m$ (3) $600 m$ (4) $500 m$ 102. $Two liquids A and B have θ_{A} and θ_{B} as contact angles in a capillary tube. If K = cos θ_{A} / cos θ_{B} . then identify the correct statement:$ (1) $K is negative, then liquid A and liquid B have convex meniscus.$ (2) $K is negative, then liquid A and liquid B have concave meniscus.$ (3) $K is negative, then liquid A has concave meniscus and liquid B has convex meniscus$ (4) $K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.$ 103. $When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h . If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 % each, then the height of the liquid in the tube will change by % .$ (1) $+1$ (2) $-3$ (3) $+3$ (4) $-1$ 104. $Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water =1000 kg/m³, coefficient of viscosity of water =1 mPa s).$ (1) $10^{3}$ (2) $10^{4}$ (3) $10^{2}$ (4) $10^{6}$ 105. $Water rises to height h in a capillary tube. If the length of capillary tube above the surface of water is made less than h, then$ (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) $water rises upto the tip of capillary tube and then starts overflowing like fountain.$ 106. $A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ_{0} . After sometime, the ball falls with constant velocity. The viscous force on the ball is:$ (1) $mg (1 - ρ ρ_{0})$ (2) $mg (1 + \frac{ρ}{ρ _{0}})$ (3) $mg (\frac{ρ _{0}}{ρ} - 1)$ (4) $mg (1 - \frac{ρ _{0}}{ρ})$ 107. $Two capillary tubes of different diameters are dipped in water. The rise of water is$ (1) $the same in both tubes$ (2) $greater in the tube of larger diameter$ (3) $greater in the tube of smaller diameter$ (4) $independent of the diameter of the tube.$ 108. $The heart of man pumps 5 liters of through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 \times 1 0^{3} kg/ m^{3} and g = 10m/ s^{2} then the power of heart in watt is:$ (1) $2.35$ (2) $3.0$ (3) $1.50$ (4) $1.70$ 109. $The lower end of a capillary tube is dipped into water and it is observed that the water in capillary tube rises by 7.5 cm . Find the radius of the capillary tube used, if surface tension of water is 7.5 \times 10^{- 2} Nm^{- 1} . Angle of contact between water and glass is 0^{\circ} and acceleration due to gravity is 10 ms^{- 2} .$ (1) $0.2 cm$ (2) $0.1 cm$ (3) $0.4 mm$ (4) $0.2 mm$ 110. $An air bubble of volume 1 c m^{3} rises from the bottom of a lake 40 m deep to the surface at a temperature of 12 °C. The atmospheric pressure is 1 x 1 0^{5} Pa, the density of water is 1000 kg m^{- 3} and g = 10 m s^{- 2} . There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be$ (1) $2 c m^{3}$ (2) $3 c m^{3}$ (3) $4 c m^{3}$ (4) $5 c m^{3}$ 111. $A cylinder of mass and material density ρ hanging from a string is lowered into a vessel of cross-sectional area A containing a liquid of density σ (< ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is$ (1) $Zero$ (2) $\frac{mg}{A}$ (3) $\frac{mgρ}{σA}$ (4) $\frac{mσg}{ρA}$ 112. $An object of mass m is suspended at the end of a massless wire of length L and area of cross-section, A. Young modulus of the material of the wire is Y . If the mass is pulled down slightly its frequency of oscillation along the vertical direction is$ (1) $f = \frac{1}{2 π} \frac{mL}{YA}$ (2) $f = \frac{1}{2 π} \frac{YA}{mL}$ (3) $f = \frac{1}{2 π} \frac{YL}{mA}$ (4) $f = \frac{1}{2 π} \frac{mA}{YL}$ 113. $Eight equal drops of water are falling through air with a steady velocity of 10 cm s^{- 1} . If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is$ (1) $40 cm s^{- 1}$ (2) $10 cm s^{- 1}$ (3) $30 cm s^{- 1}$ (4) $80 cm s^{- 1}$ 114. $Two different wires having lengths L_{1} and L_{2}, and respective temperature coefficient of linear expansion α_{1} and α_{2} are joined end-to-end. Then the effective temperature coefficient of linear expansion is$ (1) $2 α_{1} α_{2}$ (2) $4 \frac{α _{1} α _{2}}{α _{1} + α _{2}} \frac{L _{2} L _{1}}{( L _{2} + L _{1} ) ^{2}}$ (3) $\frac{α _{1} + α _{2}}{2}$ (4) $\frac{α _{1} L _{1} + α _{2} L _{2}}{L _{1} + L _{2}}$ 115. $A cylindrical metal box whose flat surface has an area of 0.01 m^{2} rests on liquid of 0.3 mm thickness. If upon applying a horizontal force of magnitude \frac{1}{3} N, the box slides with a constant speed of 0.09 ms^{- 1}, the coefficient of viscosity of the liquid is nearly$ (1) $2.5\times 1 0^{- 2} Pa.s$ (2) $1.1\times 1 0^{- 1} Pa.s$ (3) $1.1\times 1 0^{- 2} Pa.s$ (4) $2.5\times 1 0^{- 1} Pa.s$ 116. $When the temperature of a metal wire is increased from 0^{\circ} C to 10^{\circ} C its length increases by 0.02 % The percentage change in its mass density will be closest to$ (1) $2.3$ (2) $0.06$ (3) $0.8$ (4) $0.008$ 117. $Water does not wet an oily glass because$ (1) $cohesive force of oil is greater than adhesive force between oil and glass$ (2) $cohesive force of oil is greater than cohesive force of water$ (3) $oil repels water$ (4) $cohesive force of water is greater than adhesive force between water and oil molecules$ 118. $Energy needed in breaking a liquid drop of radius R, into n smaller drops each of radius r, is [T- Surface tension of the liquid]$ (1) $(4 π r^{2} n - 4 π R^{2}) T$ (2) $(\frac{4}{3} π r^{3} n - \frac{4}{3} π R^{3}) T$ (3) $(4 π R^{2} - 4 π r^{2}) nT$ (4) $(4 π R^{2} - n 4 π r^{2}) / T$ 119. $The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m^{3} / min. water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:$ (1) $2.9 m$ (2) $9.6 m$ (3) $4.8 m$ (4) $6.0 m$ 120. $A metal cube of side 10 cm rests on a film of a liquid of thickness 0.2 mm . If upon applying a horizontal force F of magnitude 0.1 N the cube slides with a constant speed of 0.08 m / s, then the coefficient of viscosity is$ (1) $2.5 \times 1 0^{- 2} Ns m^{- 2}$ (2) $0.25 \times 1 0^{- 2} Ns m^{- 2}$ (3) $5 \times 1 0^{- 2} Ns m^{- 2}$ (4) $0.5 \times 1 0^{- 2} Ns m^{- 2}$