Fluid Mechanics PYQs Set 1 (PDF)

Set 1 of 10 · Questions 1-30 of 289

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Mere Teacher · Previous Year Questions JEE Main Physics · Fluid Mechanics · Set 1 (Q1-30)
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1. $The gauge pressure at a depth of 50 m in a sea is (Density of sea water is 1025 kg m^{- 3} and g = 10 ms^{- 2})$ (1) $1025 Pa$ (2) $512500 Pa$ (3) $20000 Pa$ (4) $15000 Pa$ 2. $A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to [NEET 2018]$ (1) $r^{5}$ (2) $r^{2}$ (3) $r^{3}$ (4) $r^{4}$ 3. $An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:$ (1) $\frac{81}{256}$ (2) $\frac{9}{16}$ (3) $\frac{3}{4}$ (4) $\frac{3}{16}$ 4. $What is the terminal velocity of a rain drop of radius 0.02 mm ? [Note that the coefficient of viscosity of air is 1.8 \times 10^{- 5} N / m^{2}, density of water is 1000 kg / m^{3} . Use g = 10 m / s^{2} and density of air can be neglected in comparison with density of water]$ (1) $4.9 cm / s$ (2) $9.8 cm / s$ (3) $0.49 cm / s$ (4) $49 cm / s$ 5. $If 1000 droplets of water of surface tension 0.07 N/m. having same radius 1 mm each, combine to from a single drop. In the process the released surface energy is- (Take π = \frac{22}{7})$ (1) $7. 92 x 1 0^{- 6} J$ (2) $7. 92 x 1 0^{- 4} J$ (3) $9. 68 x 1 0^{- 4} J$ (4) $8. 8 x 1 0^{- 5} J$ 6. $The value of tension in a long thin metal wire has been changed from T1 to T_{2} . The lengths of the metal wire at two different values of tension T1 and T1 are l_{1} and l_{2} respectively. The actual length of the metal wire is:$ (1) $\frac{T _{1} l _{2} - T _{2} l _{1}}{T _{1} - T _{2}}$ (2) $\frac{T _{1} l _{1} - T _{2} l _{2}}{T _{1} - T _{2}}$ (3) $\frac{l _{1} + l _{2}}{2}$ (4) $T_{1} T_{2} l_{1} l_{2}$ 7. $A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:$ (1) $8 π R^{2} T$ (2) $3 π R^{2} T$ (3) $1 8 π R^{2} T$ (4) $4 π R^{2} T$ 8. $A sphere of relative density σ and diameter D has concentric cavity of diameter d . The ratio of \frac{D}{d}, if it just floats on water in a tank is:$ (1) $(\frac{σ - 2}{σ + 2})^{1/3}$ (2) $(\frac{σ}{σ - 1})^{1/3}$ (3) $(\frac{σ - 1}{σ})^{1/3}$ (4) $(\frac{σ + 1}{σ - 1})^{1/3}$ 9. $A tank of oil has height of 4 m and density of 850 kg m^{- 3} . The gauge pressure at the bottom of the tank is (1 atm = 10^{5} Pa), Acceleration due to gravity = 10 ms^{- 2})$ (1) $34 kPa$ (2) $384 kPa$ (3) $284 kPa$ (4) $200 kPa$ 10. $A small hole of area of cross-section 2 mm^{2} is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m / s^{2}, the rate of flow of water through the open hole would be nearly [NEET 2019]$ (1) $8.9 \times 10^{- 6} m^{3} / s$ (2) $2.23 \times 10^{- 6} m^{3} / s$ (3) $6.4 \times 10^{- 6} m^{3} / s$ (4) $12.6 \times 10^{- 6} m^{3} / s$ 11. $A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m^{- 3})$ (1) $1400 cm^{3}$ (2) $600 cm^{3}$ (3) $4000 cm^{3}$ (4) $400 cm^{3}$ 12. $A bullet of mass 5 g, travelling with a speed of 210 m / s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal / (g - ° C) (1 cal = 4.2 \times 10^{7} ergs) close to$ (1) $83.3^{\circ} C$ (2) $87.5^{\circ} C$ (3) $38.4^{\circ} C$ (4) $119.2^{\circ} C$ 13. $A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v_{0} . Estimated maximum error in the quantity η is : (Ignore errors associated with σ, ρ and g, gravitational acceleration)$ (1) $\frac{2Δ r}{r} + \frac{Δ v _{o}}{v _{o}}$ (2) $2 \frac{Δ r}{r} - \frac{Δ v _{o}}{v _{o}}$ (3) $2 (\frac{Δ r}{r} - \frac{Δ v _{o}}{v _{o}})$ (4) $2 (\frac{Δ r}{r} + \frac{Δ v _{o}}{v _{o}})$ 14. $The pressure at the bottom of a liquid tank is not proportional to the$ (1) $acceleration due to gravity$ (2) $density of the liquid$ (3) $height of the liquid$ (4) $area of the liquid surface$ 15. $A meniscus drop of radius 1 cm is sprayed into 10^{6} droplets of equal size. Calculate the energy expended if surface tension of mercury is 435 \times 10^{- 3} N / m .$ (1) $54.1 \times 10^{- 3} J$ (2) $64.1 \times 10^{- 3} J$ (3) $74.1 \times 10^{- 3} J$ (4) $84.1 \times 10^{- 3} J$ 16. $Three liquids of densities ρ_{1}, ρ_{2} and ρ_{3} (with ρ_{1} > ρ_{2} > ρ_{3}), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ_{1}, θ_{2} and θ_{3} obey$ (1) $π > θ1 > θ2 > θ3 < \frac{π}{2}$ (2) $\frac{π}{2} > θ_{1} > θ_{2} > θ_{3} \geq 0$ (3) $0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2}$ (4) $\frac{π}{2} < θ1 > θ2 > θ3 < π$ 17. $The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r . If the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is$ (1) $\frac{v R ^{2}}{n ^{2} r ^{2}}$ (2) $\frac{v R ^{2}}{n r ^{2}}$ (3) $\frac{v R ^{2}}{n ^{3} r ^{2}}$ (4) $\frac{v ^{2} R}{nr}$ 18. $A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 N / m, then the excess force required to take it away from the surface is [NEET 2024]$ (1) $19.8 mN$ (2) $198 mN$ (3) $1.98 mN$ (4) $99 mN$ 19. $A large number of water drops, each of radius r, combine to have a drop of radius R . If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be:$ (1) $\frac{2 T}{rJ}$ (2) $\frac{3 T}{rJ}$ (3) $\frac{2 T}{J} (\frac{1}{r} - \frac{1}{R})$ (4) $\frac{3 T}{J} (\frac{1}{r} - \frac{1}{R})$ 20. $A horizontal pipeline carrying gasoline has a cross sectional diameter of 5 mm . If the viscosity and density of the gasoline are 6 \times 10^{- 3} Poise and 720 kg / m^{3} respectively, the velocity after which the flow becomes turbulent is$ (1) $> 1.66 m / s$ (2) $> 3.33 m / s$ (3) $> 1.6 \times 10^{- 3} m / s$ (4) $> 0.33 m / s$ 21. $A body of volume V floats on water with \frac{1}{3} of its volume above the surface. The volume of the object above the surface when floating on a liquid of specific gravity 1.5 is$ (1) $\frac{3 V}{8}$ (2) $\frac{4 V}{9}$ (3) $\frac{5 V}{9}$ (4) $\frac{2 V}{3}$ 22. $A spherical ball of radius 1 \times 10^{- 4} m and density 10^{5} kg / m^{3} falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 \times 10^{- 6} N s / m^{2})$ (1) $2296 m$ (2) $2518 m$ (3) $2249 m$ (4) $2396 m$ 23. $In a well pressure at a point 10 m below the surface of water is (g = 10 ms^{- 2})$ (1) $2 \times 10^{4} Nm^{- 2}$ (2) $10^{5} Nm^{- 2}$ (3) $10^{4} Nm^{- 2}$ (4) $2 \times 10^{5} Nm^{- 2}$ 24. $The area of cross-section of a railway track is 0. 01 m^{2} . The temperature variation is 1 0^{0} C. Coefficient of linear expansion of material of track is 1 0^{- 5} /^{0} C . The energy stored per meter in the track is ____ J/m. (Young's modulus of material of track is 1 0^{11} N m^{- 2})$ 25. $A stone of mass 20g is projected from a rubber catapult of length 0.1m and area of cross section 1 0^{- 6} m^{2} stretched by an amount 0.04m. The velocity of the projected stone is ___m/s (Young's modulus of rubber = 0.5 \times 1 0^{9} N / m^{2})$ 26. $An air bubble of diameter 6 mm rises steadily through a solution of density 1750 kg m^{- 3} at the rate of 0. 35 cm s^{- 1} . The co-efficient of viscosity of the solution (neglect density of air) is________Pas (given, g = 10 m s^{- 2}).$ 27. $64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be_____mV.$ 28. $A plane is in level flight at constant speed and each of its two wings has an area of 40 m^{2} . If the speed of the air is 180 km / h over the lower wing surface and 252 km / h over the upper wing surface, the mass of the plane is _____kg. (Take air density to be 1 kg m^{- 3} and g = 10 ms^{- 2})$ 29. $A soap bubble of surface tension 0.04 N / m is blown to a diameter of 7 cm . If (15000 - x) μJ of work is done in blowing it further to make its diameter 14 cm , then the value of x is____(π = 22/7)$ 30. $The surface of water in a water tank of cross section area 750 c m^{2} on the top of a house is h m. above the tap level. The speed of water coming out through the tap of cross section area 500 m m^{2} is 30 cm/s. At that instant, \frac{d h}{d t} is x x 1 0^{- 3} m/s. The value of x will be _____.$