Fluid Mechanics PYQs Set 4 (PDF)

Set 4 of 10 · Questions 91-120 of 289

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 4 (Q91-120)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
91. $The speed of the water in a river is v near the surface. If the coefficient of viscosity of water is η and the depth of the river is H, then the shearing stress between the horizontal layers of water is$ (1) $η \frac{H}{v}$ (2) $η \frac{v}{H}$ (3) $\frac{v}{η H}$ (4) $η ν H$ 92. $1000 spherical drops of water each 10^{- 8} m in diameter coalesce to form one large spherical drop. The amount of energy liberated in this process (in joule) is (surface tension of water is 0.075 N / m).$ (1) $10.75 π \times 10^{- 15}$ (2) $6.75 π \times 10^{- 15}$ (3) $8.65 π \times 10^{- 15}$ (4) $3.88 π \times 10^{- 15}$ 93. $A person of height 1.65 m is standing upright. The additional external force required by 'blood vessel of length 1 cm, diameter 1 mm at feet to balance the pressure compared to similar blood vessel in head is (Density of blood = 1.1 \times 10^{3} kg m^{- 3}, g = 10 ms^{- 2})$ (1) $0.57 N$ (2) $5.7 N$ (3) $1.85 N$ (4) $3.14 N$ 94. $Three liquids of equal masses are taken in three identical cubical vessels A, B and C . Their densities are ρ_{A}, ρ_{B} and ρ_{C} respectively. But ρ_{A} < ρ_{B} < ρ_{C} . The force exerted by the liquid on the base of the cubical vessel is$ (1) $maximum in vessel C$ (2) $minimum in vessel C$ (3) $the same in all the vessels$ (4) $maximum in vessel A .$ 95. $Pressure inside a soap bubble is greater than the pressure outside by an amount: (given: R = Radius of bubble S = Surface tension of bubble)$ (1) $\frac{2 S}{R}$ (2) $\frac{4 R}{S}$ (3) $\frac{S}{R}$ (4) $\frac{4 S}{R}$ 96. $A water drop of radius 1cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be: [Given π = 3.14]$ (1) $8. 5 x 1 0^{- 4} J$ (2) $8. 2 x 1 0^{- 4} J$ (3) $7. 5 x 1 0^{- 4} J$ (4) $5. 3 x 1 0^{- 4} J$ 97. $The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m^{3} water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:$ (1) $6.0 m$ (2) $4.8 m$ (3) $9.6 m$ (4) $2.9$ 98. $A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force and gravitational force acting on it are F_{v}, F_{B} and F_{W} respectively. Then the correct relation between them is$ (1) $F_{B} > F_{V} = F_{W}$ (2) $F_{w} = F_{V} + F_{B}$ (3) $F_{B} = F_{W} + F_{V}$ (4) $F_{V} = F_{B} + F_{W}$ 99. $If there were no gravity, which of the following will not be there for a fluid?$ (1) $Viscosity$ (2) $Surface tension$ (3) $Pressure$ (4) $Archimedes's upward thrust$ 100. $A rectangular vessel when full of water, takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?$ (1) $9 minutes$ (2) $7 minutes$ (3) $5 minutes$ (4) $3 minutes$ 101. $What is the rate at which a trapped bubble of 2 mm diameter rises slightly through a solution of density 13.6 \times 10^{3} kg / m^{3} and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligibility and g = 10 m / s^{2} .$ (1) $20 m / s$ (2) $2 m / s$ (3) $0.2 m / s$ (4) $0.02 m / s$ 102. $A cubical block of density ρ_{b} = 600 kg / m^{3} floats in a liquid of density ρ_{e} = 900 kg / m^{3} . If the height of block is H = 8.0 cm then height of the submerged part is____cm.$ (1) $6.3$ (2) $4.3$ (3) $5.3$ (4) $7.3$ 103. $A cube of metal is subjected to a hydrostatic pressure of 4 GPa . The percentage change in the length of the side of the cube is close to (Given bulk modulus of metal, B = 8 \times 10^{10} Pa)$ (1) $0.6$ (2) $20$ (3) $1.67$ (4) $5$ 104. $A capillary tube of radius 0.1 mm is dipped in water. The water rises to a height of 2 cm in the tube. If the surface tension of water is 0.072 Nm^{- 1}, the contact angle between water and wall of the tube is$ (1) $θ = cos^{- 1} (\frac{1}{3.6})$ (2) $θ = cos^{- 1} (\frac{1}{7.2})$ (3) $θ = cos^{- 1} (\frac{1}{1.8})$ (4) $θ = cos^{- 1} (\frac{1}{6.2})$ 105. $A 0.5 kg block of brass (density = 8 \times 10^{3} kg m^{- 3}) is suspended from a string. What is the tension in the string if the block is completely immersed in water? (g = 10 ms^{- 2})$ (1) $5 N$ (2) $\frac{0.5}{8 \times 10 ^{3}} N$ (3) $\frac{5}{8} N$ (4) $\frac{35}{8} N$ 106. $A wind with speed 40 m / s blows parallel to the roof of a house. The area of the roof is 250 m^{2} . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (p_{air} = 1.2 kg / m^{3})$ (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) $2.4 \times 10^{5} N, downwards$ 107. $Two water drops each of radius ' r' coalesce to from a bigger drop. If' T' is the surface tension, the surface energy released in this process is:$ (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) $4 π r^{2} T [2 - 1]$ 108. $A sphere of material of relative density 8 has a concentric spherical cavity and just sinks in water. If the radius of the sphere is 2 cm, then the volume of the cavity is$ (1) $\frac{76}{3} cm^{3}$ (2) $\frac{79}{3} cm^{3}$ (3) $\frac{82}{3} cm^{3}$ (4) $\frac{88}{3} cm^{3}$ 109. $Two mercury drops of radii r and 2 r merge to form a bigger drop. The surface energy released in the process is nearly (Surface tension mercury is S and take 9^{2/3} = 4.326)$ (1) $1.6 π r^{2} S$ (2) $3.2 π r^{2} S$ (3) $17.1 π r^{2} S$ (4) $2.7 π r^{2} S$ 110. $The tension in a massless cable connected to an iron ball of 100 kg when it is submerged in sea water is (ρ_{iron} = 8 \times 10^{3} kg / m^{3}) and (ρ_{sea water} = 1000 kg / m^{3}, g = 10 m / s^{2})$ (1) $950 N$ (2) $846 N$ (3) $875 N$ (4) $933 N$ 111. $A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is 3.08 \times 10^{- 5} m^{3} / s, then the diameter of the hole is (Take g = 10 m / s^{2}]$ (1) $1.0 mm$ (2) $1.2 mm$ (3) $1.4 mm$ (4) $1.6 mm$ 112. $In a U-shaped tube the radius of one limb is 2 mm and that of other limb is 4 mm . A liquid of surface tension 0.03 Nm^{- 1}, density 1500 kgm^{- 3} and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is (Acceleration due to gravity = 10 ms^{- 2})$ (1) $3 mm$ (2) $2.5 mm$ (3) $1 mm$ (4) $1.5 mm$ 113. $The angle of contact between pure water and pure glass, is$ (1) $0^{\circ}$ (2) $45^{\circ}$ (3) $90^{\circ}$ (4) $135^{\circ}$ 114. $A wooden block floating in a bucket of water has \frac{4}{5} of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:$ (1) $0.5$ (2) $0.8$ (3) $0.6$ (4) $0.7$ 115. $A long cylindrical glass vessel has a pinhole of diameter 0.2 mm at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, T = 0.07 Nm^{- 1}, acceleration due to gravity, g = 10 ms^{- 2})$ (1) $14 cm$ (2) $7 cm$ (3) $21 cm$ (4) $28 cm$ 116. $A submarine experiences a pressure of 5.05 \times 10^{6} Pa depth of d_{1} in a sea. When it goes further to a depth of d_{2} , it experiences a pressure of 8.08 \times 10^{6} Pa., Then d_{2} - d_{1} is approximately (density of water = 10³kg/m³ and acceleration due to gravity = 10 ms^{- 2}):$ (1) $300 m$ (2) $400 m$ (3) $600 m$ (4) $500 m$ 117. $Two liquids A and B have θ_{A} and θ_{B} as contact angles in a capillary tube. If K = cos θ_{A} / cos θ_{B} . then identify the correct statement:$ (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) $K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.$ 118. $The reading of pressure meter attached with a closed pipe is 4.5 \times 10^{4} N / m^{2} . On opening the valve, water starts flowing and the reading of pressure metre falls to 2.0 \times 10^{4} N / m^{2} . The velocity of water is found to be V m / s . The value of V is______$ 119. $There is an air bubble of radius 1. 0 mm in a liquid of surface tension 0. 075 N m^{- 1} and density 1000 kg m^{- 3} at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is_______Pa(g = 10 m s^{- 2}).$ 120. $A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is 3696 x 1 0^{- x} N. The value of x is (Given, g = 9.8 m/ s^{2} and π = \frac{22}{7})$