NEET Physics Class 11 Chapter 5 Fluid Mechanics Multiple Choice Questions And Answers

Fluid Mechanics Multiple Choice Questions And Answers

Question 1. The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. The ratio of the density of mercury to that of air is 104. The height of the hill is

1. 250 m
2. 2.5 km
3. 1.25 km
4. 750 m

Answer: 2. 2.5 km

Question 2. If pressure at half the depth of a lake is equal to 2/3 of pressure at the bottom of the lake then what is the depth of the lake

1. 10m
2. 20m
3. 60m
4. 30m

Answer: 2. 20m

Question 3. A uniform tapering vessel is filled with a liquid of density 900 kg/m³. The force that acts on the base of the vessel due to the liquid is (g = 10 ms^-2 )

1. 3.6 N
2. 7.2 N
3. 9.0 N
4. 14.4 N

Answer: 2. 7.2 N

Question 4. The pressure at the bottom of a tank containing a liquid does not depend on

1. Acceleration due to gravity
2. Height of the liquid column
3. Area of the bottom surface
4. Nature of the liquid

Answer: 3. Area of the bottom surface

Question 5. When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of a column of water height H, then the depth of the lake is

1. H
2. 2H
3. 7H
4. 8H

Answer: 3. 7H

Question 6. The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is

1. 5m
2. 10m
3. 15m
4. 20m

Answer: 3. 15m

Question 7. The value of g at a place decreases by 2%.The barometric height of mercury

1. Increases by 2%
2. Decreases by 2%
3. Remains unchanged
4. Sometimes increases and sometimes decreases

Answer: 1. Increases by 2%

Question 8. A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating the reading will be

1. Zero
2. Equal to 76 cm
3. More than 76 cm
4. Less than 76 cm

Answer: 4. Less than 76 cm

Question 9. A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will

1. Increases
2. Decreases
3. Remain constant
4. First decrease and then increase

Answer: 2. Decreases

Question 10. A vertical U-tube of the uniform inner cross-section contains mercury on both sides of its arms. A glycerin (density =1.3g/cm³)column of length 10cm is introduced into one of its arms. Oil of density 0.8 gm/cm³ is poured into the other arm until the upper surfaces of the oil and glycerin are at the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm³

1. 10.4cm
2. 8.2 cm
3. 7.2cm
4. 9.6cm

Answer: 4. 9.6cm

Question 11. From the adjacent figure, the correct observation is

1. The pressure on the bottom of the tank is greater than at the bottom of (2).
2. The pressure on the bottom of the tank is smaller than at the bottom of
3. The pressure depends on the shape of the container
4. The pressure on the bottom of and is the same

Answer: 4. The pressure on the bottom of and is the same

Question 12. Air is blown through a hole in a closed pipe containing liquid. Then the pressure will

1. Increase on sides
2. Increase downwards
3. Increase in all direction
4. Never increases

Answer: 4. Never increases

Question 13. The radius of an air bubble at the bottom of the lake is r and it becomes 2r when the air bubbles rise to the top surface of the lake. If P cm water is the atmospheric pressure, then the depth of the lake is

1. 2p
2. 8p
3. 4p
4. 7p

Answer: 4. 7p

Question 14. A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration towards the right. Pressure is

1. Maximum at, and
2. Minimum at

1. (1)B (2)D
2. (1)C (2)D
3. (1)B (2)C
4. (1)B (2)A

Answer: 1. (1)B (2)D

Question 15. A given-shaped glass tube having a uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity ω then

1. Water levels in both sections A and B go up
2. The water level in Section A goes up and that in B comes down
3. The water level in Section A comes down and in B it goes up
4. Water levels remain the same in both sections

Answer: 1. Water levels in both sections A and B go up

Question 16. A siphon in use is demonstrated in the following figure. The density of the liquid flowing in the siphon is 1.5 gm/cc. The pressure difference between the points P and S will be

1. 10⁵ N/m
2. 2 × 10⁵ N/m
3. Zero
4. Infinity

Answer: 3. Zero

Question 17. Figure here shows the vertical cross-section of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at point. P, as shown, will be

1. h ρ g
2. H ρ g
3. (H – h) ρ g
4. (H – h) ρ g cosθ

Answer: 3. (H – h) ρ g

Question 18. A tank with a length of 10 m, breadth of 8m, and depth of 6m is filled with water to the top. If g = 10 m s^-2 and the density of water is 1000 kg m^-3, then the thrust on the bottom is

1. 6 × 1000 × 10 × 80 N
2. 3 × 1000 × 10 × 48 N
3. 3 × 1000 × 10 × 60 N
4. 3 × 1000 × 10 × 80 N

Answer: 1. 6 × 1000 × 10 × 80 N

Question 19. In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of 20:1. What weight placed on the small piston will be sufficient to lift a car of mass 1500 kg?

1. 3.75 kg
2. 37.5 kg
3. 7.5 kg
4. 75 kg.

Answer: 1. 3.75 kg

Question 20. Two vessels A and B of different shapes have the same base area and are filled with water up to the same height h (see figure). The force exerted by water on the base is F_A for vessel A and F_B for vessel B. The respective weights of the water-filled vessels are W_A and W_B. Then

1. F_A> F_B ; W_A> W_B
2. F_A= F_B ; W_A> W_B
3. F_A= F_B ; W_A< W_B
4. F_A> F_B ; W_A= W_B

Answer: 2. F_A= FB ; W_A> W_B

Question 21. A hydrogen balloon released on the moon would:

1. Climb up with an acceleration of 9.8 m/s²
2. Climb up with an acceleration of 9.8 × 6 m/s²
3. Neither climb nor fall
4. Fall with an acceleration of 9.8/6 m/s²

Answer: 4. Fall with an acceleration of 9.8/6 m/s²

Question 22. Reason for weightlessness in satellite :

1. Zero gravity
2. Centre of gravity
3. Zero reaction force on a plane of the satellite
4. None of these

Answer: 3. Zero reaction force on a plane of the satellite

Question 22. A hemispherical bowl just floats without sinking in a liquid of density 1.2 × 10³ kg/m³. If the outer diameter and the density of the bowl are 1 m and 2 × 10⁴ kgm³ respectively, then the inner diameter of the bowl will be

1. 0.94 m
2. 0.97 m
3. 0.98 m
4. 0.99 m

Answer: 3. 0.98 m

Question 23. In making an alloy, a substance of specific gravity s₁ and mass m₁ is mixed with another substance of specific gravity s₂ and mass m₂; then the specific gravity of the alloy is

1. \(\left(\frac{m_1+m_2}{s_1+s_2}\right)\)
2. \(\left(\frac{\mathrm{s}_1 \mathrm{~s}_2}{\mathrm{~m}_1+\mathrm{m}_2}\right)\)
3. \(\frac{m_1+m_2}{\left(\frac{m_1}{s_1}+\frac{m_2}{s_2}\right)}\)
4. \(\frac{\left(\frac{m_1}{s_1}+\frac{m_2}{s_2}\right)}{m_1+m_2}\)

Answer: 3. \(\frac{m_1+m_2}{\left(\frac{m_1}{s_1}+\frac{m_2}{s_2}\right)}\)

Question 24. Two solids A and B float in water. It is observed that A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

1. 4 :3
2. 2 :3
3. 3:4
4. 1 :3

Answer: 4. 1 :3

Question 25. A body is just floating on the surface of a liquid. The density of the body is the same as that of the liquid. The body is slightly pushed down. What will happen to the body?

1. It will slowly come back to its earlier position position
2. It will remain submerged, where it is left
3. It will sink
4. It will come out violently

Answer: 2. It will remain submerged, where it is left

Question 26. A rectangular block is 5 cm × 5 cm × 10 cm in size. The block is floating in water with a 5 cm side vertical. If it floats with a 10 cm side vertical, what change will occur in the level of water?

1. No change
2. It will rise
3. It will fall
4. It may rise or fall depending on the density of a block

Answer: 1. No change

Question 27. A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one how will it affect the level of water

1. It will remain unchanged
2. It will rise
3. It will fall
4. First, it will first rise and then fall

Answer: 3. It will fall

Question 28. Two pieces of metal when immersed in a liquid have equal upthrust on them; then

1. Both pieces must have equal weights
2. Both pieces must have equal densities
3. Both pieces must have equal volumes
4. Both are floating to the same depth

Answer: 3. Both pieces must have equal volumes

Question 29. A wooden cylinder floats vertically in water with half of its length immersed. The density of wood is

1. Equal to that of water
2. Half the density of water
3. Double the density of water
4. The question is incomplete

Answer: 2. Half the density of water

Question 30. An ice block contains a glass ball when the ice melts within the water, the level of water

1. Rises
2. Falls
3. Unchanged
4. First rises and then falls

Answer: 2. Falls

Question 31. The construction of submarines is based on

1. Archimedes’ principle
2. Bernoulli’s theorem
3. Pascal’s law
4. Newton’s laws

Answer: 1. Archimedes’ principle

Question 32. A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. The ratio of the mass of concrete to the mass of sawdust will be

1. 8
2. 4
3. 3
4. Zero

Answer: 2. 4

Question 33. A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with an acceleration of g/3, the fraction of volume immersed in the liquid will be

1. \(\frac{1}{2}\)
2. \(\frac{3}{8}\)
3. \(\frac{2}{3}\)
4. \(\frac{3}{4}\)

Answer: 1. \(\frac{1}{2}\)

Question 34. A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

1. 1.6
2. 1.94
3. 3.1
4. 5.25

Answer: 2. 1.94

Question 35. A solid sphere of density η ( > times lighter than water is suspended in a water tank by a string. If the mass of the sphere is m then the tension in the string is given by

1. \(\left(\frac{\eta-1}{\eta}\right) \mathrm{mg}\)
2. ηmg
3. \(\frac{\mathrm{mg}}{\eta-1}\)
4. (η−1)mg

Answer: 4. (η−1)mg

Question 36. A hollow sphere of volume V is floating on a water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

1. V/2
2. V/3
3. V/4
4. V

Answer: 1. V/2

Question 37. Two solids A and B float in water. It is observed that A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

1. 4 : 3
2. 2 : 3
3. 3: 4
4. 1 : 3

Answer: 3. 3: 4

Question 38. The fraction of a floating object of volume V₀ and density d₀ above the surface of a liquid of density d will be

1. \(\frac{d_0}{d}\)
2. \(\frac{\mathrm{dd}_0}{\mathrm{~d}+\mathrm{d}_0}\)
3. \(\frac{d-d_0}{d}\)
4. \(\frac{\mathrm{dd}_0}{\mathrm{~d}-\mathrm{d}_0}\)

Answer: 3. \(\frac{d-d_0}{d}\)

Question 39. The density of the ice is ρ and that of water is σ. What will be the decrease in volume when a mass M of ice melts?

1. \(\frac{M}{\sigma-\rho}\)
2. \(\frac{\sigma-\rho}{M}\)
3. \(M\left[\frac{1}{\rho}-\frac{1}{\sigma}\right]\)
4. \(\frac{1}{\mathrm{M}}\left[\frac{1}{\rho}-\frac{1}{\sigma}\right]\)

Answer: 3. \(M\left[\frac{1}{\rho}-\frac{1}{\sigma}\right]\)

Question 40. The reading of a spring balance when a block is suspended from it in the air is 60 newton. This reading is changed to 40 newtons when the block is submerged in water. The specific gravity of the block must be therefore :

1. 3
2. 2
3. 6
4. 3/2

Answer: 1. 3

Question 41. A block of steel of size 5 cm × 5 cm × 5 cm is weighed in water. If the relative density of steel is 7. Its apparent weight is :

1. 6 × 5 × 5 × 5 gf
2. 4 × 4 × 4 × 7 gf
3. 5 × 5 × 5 × 7 gf
4. 4 × 4 × 4 × 6 gf

Answer: 1. 6 × 5 × 5 × 5 gf

Question 42. Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g/cc. If the mass of the other is 48 g, its density in g/cc is :

1. 4/3
2. 3/2
3. 3
4. 5

Answer: 3. 3

Question 43. In order for a floating object to be in a stable rotation at equilibrium, its center of buoyancy should be

1. Vertically above its center of gravity
2. Vertically below its center of gravity
3. Horizontally in line with its center of gravity
4. May be anywhere

Answer: 1. Vertically above its center of gravity

Question 44. A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of the spring

1. Increases
2. Decreases
3. Remains unchanged
4. None of these

Answer: 2. Decreases

Question 45. A hollow sphere of volume V is floating on a water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

1. V/2
2. V/3
3. V/4
4. V

Answer: 1. V / 2

Question 46. An ice block contains a glass ball when the ice melts within the water-containing vessel, the level of water

1. Rises
2. Falls
3. Unchanged
4. First rises and then falls

Answer: 2. Falls

Question 47. A large ship can float but a steel needle sinks because of

1. Viscosity
2. Surface tension
3. Density
4. None of these

Answer: 4. None of these

Question 48. An iceberg of density 900 kg/m³ is floating in water of density 1000 Kg/m³. The percentage of the volume of ice-cube outside the water is

1. 20%
2. 35%
3. 10%
4. 25%

Answer: 3. 10%

Question 49. A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass M. It is suspended by a string in a liquid of density ρ where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is:

1. Mg
2. Mg – Vρg
3. Mg + πR²hρg
4. ρg(V + πR²h)

Answer: 4. ρg(V + πR²h)

Question 50. A wooden block with a coin placed on its top floats in water as shown in the figure. The distance and h are shown here. After some time the coin falls into the water. Then

1. l decreases and h increase
2. l increases and h decreases
3. Both l and h increases
4. Both l and h decrease

Answer: 4. Both l and h decrease

Question 51. If a sphere is inserted in water, then it flows with \(\frac{1}{3}\) rd of it outside the water, When it is inserted in an unknown liquid then it flows with \(\frac{3}{4}\) th of it outside, then the density of the unknown liquid is:

1. 4.9 gm/c.c
2. \(\frac{9}{4}\) gm/c.c
3. \(\frac{8}{3}\) gm/c.c
4. \(\frac{3}{8}\) gm/c.c

Answer: 3. \(\frac{8}{3}\) gm/c.c

Question 52. A body of uniform cross-sectional area floats in a liquid of density thrice its value. The fraction of exposed height will be:

1. \(\frac{2}{3}\)
2. \(\frac{5}{6}\)
3. \(\frac{1}{6}\)
4. \(\frac{1}{3}\)

Answer: 1. \(\frac{2}{3}\)

Question 53. A raft of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sing, should be : (draft = 600 kg/m³)

1. 80 kg
2. 50 kg
3. 60 kg
4. 30 kg

Answer: 1. 80 kg

Question 54. A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Them :

1. \(\mathrm{T} \propto \sqrt{\rho}\)
2. \(\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{A}}}\)
3. \(T \propto \frac{1}{\rho}\)
4. \(\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{m}}}\)

Answer: 2. \(\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{A}}}\)

Question 55. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t₀ in air. Neglecting the frictional force of water and given that the density of the bob is (4/3)× 1000 kg/m³. What relationship between t and t₀ is true?

1. t = t₀
2. t = t₀/2
3. t = 2t₀
4. t = 4t₀

Answer: 3. t = 2t₀

Question 56. A jar is filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂, respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.

Which of the following is true for ρ₁, ρ₂ and ρ₃?

1. ρ₁> ρ₃> ρ₂
2. ρ₁< ρ₂< ρ₃
3. ρ₁< ρ₃< ρ₂
4. ρ₃< ρ₁< ρ₂

Answer: 3. ρ₁< ρ₃< ρ₂

Question 57. A ball is made of a material of density ρ where ρoil < ρ < ρwater with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Answer: 2

Question 58. A block of volume V and of density σb is placed in a liquid of density σ_l (σ_l > σ_b), then the block is moved upward upto a height h and it is still in the liquid. The increase in gravitational potential energy of the system is :

1. σ_b Vgh
2. (σ_b + σ_l)Vgh
3. (σ_b – σ_l)Vgh
4. None of these

Answer: 3. (σ_b – σ_l)Vgh

Question 59. A metallic sphere floats (just sink) in an immiscible mixture of water (_ρw = 103 kg/mand a liquid (_ρL= 13.5 × 10 with (1/5)th portion by volume in the liquid. The density of the metal is :

1. 4.5 × 10³ kg/m³
2. 4.0 × 10³ kg/m³
3. 3.5 × 10³ kg/m³
4. 1.9 × 10³ kg/m³

Answer: 3. 3.5 × 10³ kg/m³

Question 60. Three liquids of densities d, 2d, and 3d are mixed in equal volumes. Then the density of the mixture is

1. d
2. 2d
3. 3d
4. 5d

Answer: 2. 2d

Question 61. Three liquids of densities d, 2d, and 3d are mixed in equal proportions of weights. The relative density of the mixture is

1. \(\frac{11 d}{7}\)
2. \(\frac{18 d}{11}\)
3. \(\frac{13 d}{9}\)
4. \(\frac{23 d}{18}\)

Answer: 2. \(\frac{18 d}{11}\)

Question 62. Figure shows a weigh-bridge, with a beaker P with water on one pan and a balancing weight R on the other. A solid ball Q is hanging with a thread outside the water. It has a volume of 40 cm³ and weighs 80 g. If this solid is lowered to sink fully in water, but not touching the beaker anywhere, the balancing weight R’ will be

1. Same as R
2. 40 g less than R
3. 40 g more than R
4. 80 g more than R

Answer: 3. 40 g more than R

Question 63. In which one of the following cases will the liquid flow in a pipe be most streamlined

1. Liquid of high viscosity and high density flowing through a pipe of small radius
2. Liquid of high viscosity and low density flowing through a pipe of small radius
3. Liquid of low viscosity and low density flowing through a pipe of large radius
4. Liquid of low viscosity and high density flowing through a pipe of large radius

Answer: 2. Liquid of high viscosity and low density flowing through a pipe of small radius

Question 64. Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of the flow of water in the pipe of 2 cm diameter is

1. 4 times that in the other pipe
2. 14 times than in the other pipe
3. 2 times that in the other pipe
4. 12 times than in the other pipe

Answer: 1. 4 times that in the other pipe

Question 65. Water enters through end A with speed υ1 and leaves through end B with speed υ2 of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have υ₁ = υ₂ for

1. Case 1
2. Case 2
3. Case 3
4. Each case

Answer: 4. Each case

Question 66. Water is moving with a speed of 5.18 ms^-1 through a pipe with a cross-sectional area of 4.20 cm². The water gradually descends 9.66 m as the pipe increases in area to 7.60 cm2. The speed of flow at the lower level is

1. 3.0 ms^-1
2. 5.7 ms^-1
3. 3.82 ms^-1
4. 2.86 ms^-1

Answer: 4. 2.86 ms^-1

Question 67. In the following flag. Is shown the flow of liquid through a horizontal pipe. Three tubes A, B, and C are connected to the pipe. The radii of tubes A, B, and c at the junction are respectively 2 cm, 1 cm, and 2cm. It can be said that the

1. The height of the liquid in tube A is the maximum
2. Height of the liquid in the tubes A and B is the same
3. The height of the liquid in all three tubes is the same
4. Height of the liquid in the tubes A and C is the same

Answer: 4. Height of the liquid in the tubes A and C is the same

Question 68. Air is steaming past a horizontal airplane wing such that its speed is 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per metre3 and the wing is 10 m long and has an average width of 2 m, then the difference of the pressure on the two sides of the wing of

1. 4095.0 Pascal
2. 409.50 Pascal
3. 40.950 Pascal
4. 4.0950 Pascal

Answer: 1. 4095.0 Pascal

Question 69. A cylinder of height 20 m is filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is

1. 10
2. 20
3. 25.5
4. 5

Answer: 2. 20

Question 70. There is a hole in the bottom of the tank having water. If the total pressure at the bottom is 3 atm (1 atm = 10⁵ N/mthen the velocity of water flowing from the hole is

1. \(\sqrt{400} \mathrm{~m} / \mathrm{s}\)
2. \(\sqrt{600} \mathrm{~m} / \mathrm{s}\)
3. \(\sqrt{60} \mathrm{~m} / \mathrm{s}\)
4. None of these

Answer: 1. \(\sqrt{400} \mathrm{~m} / \mathrm{s}\)

Question 71. In a turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube is

1. Zero
2. Maximum
3. Equal to critical velocity
4. May have any value

Answer: 4. May have any value

Question 72. Water is flowing through a tube of non-uniform cross-section ratio of the radius at the entry and exit end of the pipe is 3: 2. Then the ratio of velocities at the entry and exit of liquid is

1. 4: 9
2. 9: 4
3. 8: 27
4. 1: 1

Answer: 1. 4: 9

Question 73. Water is flowing through a horizontal pipe of non-uniform cross-section. At the extremely narrow portion of the pipe, the water will have

1. Maximum speed and least pressure
2. Maximum pressure and least speed
3. Both pressure and speed maximum
4. Both pressure and speed least

Answer: 1. Maximum speed and least pressure

Question 74. A liquid flows in a tube from left to right as shown in the figure. A₁ and A₂ are the cross-sections of the portions of the tube as shown. Then the ratio of speeds ν₁/ ν₂ will be

1. A₁/ A₂
2. A₂/ A₁
3. \(\sqrt{A_2} / \sqrt{A_1}\)
4. \(\sqrt{A_1} / \sqrt{A_2}\)

Answer: 2. A₂/ A₁

Question 75. A large tank filled with water to a height of ‘h’ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to \(\frac{h}{2}\) and from \(\frac{h}{2}\) to zero is

1. \(\sqrt{2}\)
2. \(\frac{1}{\sqrt{2}}\)
3. \(\sqrt{2}-1\)
4. \(\frac{1}{\sqrt{2}-1}\)

Answer: 3. \(\sqrt{2}-1\)

Question 76. There is a hole in area A at the bottom of the cylindrical vessel. Water is filled up to a height of h and water flows out in t second. If water is filled to a height of 4h, it will flow out in time equal to

1. t
2. 4t
3. 2 t
4. t/4

Answer: 3. 2 t

Question 77. In this figure, an ideal liquid flows through the tube, which is of uniform cross-section. The liquid has velocities v_A and v_B, and pressure P_A and P_B at points A and B respectively

1. v_A = v_B
2. v_B > v_A
3. P_A = P_B
4. P_B > P_A

Answer: (1,4)

Question 78. A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section A₁ and A₂, are v₁ and v₂ respectively. The difference in the levels of the liquid in the two vertical tubes is h

1. The volume of the liquid flowing through the tube in unit time is A₁v₁
2. \(v_2-v_1=\sqrt{2 g h}\)
3. \(v_2^2-v_1^2=2 g h\)
4. The energy per unit mass of the liquid is the same in both sections of the tube

Answer: (1,3,4)

Question 79. An L-shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of the water current is v, then

1. The water in the tube rises to height \(\frac{v^2}{2 \mathrm{~g}}\)
2. The water in the tube rises to height \(\frac{\mathrm{g}}{2 \mathrm{v}^2}\)
3. The water in the tube does not rise at all
4. None of these

Answer: 1. The water in the tube rises to height \(\frac{v^2}{2 \mathrm{~g}}\)

Question 80. A streamlined body falls through the air from a height of h on the surface of a liquid. If d and D(D > d) represent the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest is

1. \(\sqrt{\frac{2 h}{g}}\)
2. \(\sqrt{\frac{2 h}{g} \cdot \frac{D}{d}}\)
3. \(\sqrt{\frac{2 h}{g} \cdot \frac{d}{D}}\)
4. \(\sqrt{\frac{2 h}{g}}\left(\frac{d}{D-d}\right)\)

Answer: 4. \(\sqrt{\frac{2 h}{g}}\left(\frac{d}{D-d}\right)\)

Question 81. A large tank is filled with water to a height of H. A small hole is made at the base of the tank. It takes T₁ time to decrease the height of water to \(\frac{H}{\eta}(\eta>1)\), and it takes T₂ time to take out the rest of the water. T₁ = T₂ then the value of η is

1. 2
2. 3
3. 4
4. \(2 \sqrt{2}\)

Answer: 3. 4

Question 82. Bernoulli’s principle is based on the law of conservation:

1. Mass
2. Momentum
3. Energy
4. None of these

Answer: 3. Energy

Question 83. The action of the paint gun is based on:

1. Bernoulli’s principle
2. Boyle’s law
3. Faraday’s law
4. Archimedes principle

Answer: 1. Bernoulli’s principle

Question 84. Bernoulli’s equation is applicable to points:

1. In a steadily flowing liquid
2. In a streamlined
3. In a straight line perpendicular to a streamline
4. For ideal liquid streamline flow on a streamline

Answer: 4. For ideal liquid streamline flow on a streamline

Question 85. Bernoulli’s equation is based upon:

1. Isochoric process
2. Isobaric process
3. Isothermal process
4. Adiabatic process

Answer: 3. Isothermal process

Question 86. The horizontal flow of fluid depends upon

1. Pressure difference
2. Amount of fluid
3. Density of fluid
4. All the above

Answer: 1. Pressure difference

Question 87. In steady horizontal flow:

1. The pressure is greatest where the speed is least
2. The pressure is independent of speed
3. The pressure is the least where the speed is the least
4. (1) and (3) are correct

Answer: 1. The pressure is greatest where the speed is least

Question 88. In a laminar flow, the velocity of the liquid in contact with the walls of the tube is

1. Zero
2. Maximum
3. In between zero and maximum
4. Equal to critical velocity

Answer: 1. Zero

Question 89. In a turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube is –

1. Zero
2. Maximum
3. Equal to critical velocity
4. May have any value

Answer: 4. May have any value

Question 90. The Reynolds number of a flow is the ratio of

1. Gravity to viscous force
2. Gravity force to pressure force
3. Inertia forces to viscous force
4. Viscous forces to pressure forces

Answer: 3. Inertia forces to viscous force

Question 91. A tank is filled with water up to height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of the water. Express the horizontal distance x in terms of H and D :

1. \(x=\sqrt{D(H-D)}\)
2. \(x=\sqrt{\frac{D(H-D)}{2}}\)
3. \(x=2 \sqrt{D(H-D)}\)
4. \(x=4 \sqrt{D(H-D)}\)

Answer: 3. \(x=2 \sqrt{D(H-D)}\)

Question 92. A fixed cylindrical vessel is filled with water up to height H. A hole is bored in the wall at a depth of h from the free surface of the water. For maximum horizontal range, h is equal to :

1. H
2. 3H/4
3. H/2
4. H/4

Answer: 3. H/2

Question 93. An incompressible liquid flows through a horizontal tube as shown in the figure. Then the velocity ‘ v ‘ of the fluid is :

1. 3.0 m/s
2. 1.5 m/s
3. 1.0 m/s
4. 2.25 m/s

Answer: 3. 1.0 m/s

Question 94. For a fluid that is flowing steadily, the level in the vertical tubes is best represented by

Answer: 1

Question 95. Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure p at points along the axis is represented by

Answer: 1

Question 96. Air is blown through a hole in a closed pipe containing liquid. Then the pressure will :

1. Increase on sides
2. Increase downwards
3. Increase in all directions
4. Never increases

Answer: 3. Increase in all directions

Question 97. The Working of an atomizer depends upon

1. Bernoulli’s theorem
2. Boyle’s law
3. Archimedes principle
4. Newton’s law of motion

Answer: 1. Bernoulli’s theorem

Question 98. A cylinder of height 20m is completely filled with water. The velocity of efflux of water (in ms–through a small hole on the side wall of the cylinder near its bottom, is :

1. 10
2. 20
3. 25.5
4. 5

Answer: 2. 20

Question 99. An application of Bernoulli’s equation for fluid flow is found in

1. Dynamic lift of an aeroplane
2. Viscosity meter
3. Capillary rise
4. Hydraulic press

Answer: 1. Dynamic lift of an aeroplane

Question 100. A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then radius R, is equal to :

1. \(\frac{\mathrm{L}}{\sqrt{2 \pi}}\)
2. 2 π L
3. L
4. \(\frac{L}{2 \pi}\)

Answer: 1. \(\frac{\mathrm{L}}{\sqrt{2 \pi}}\)

Question 101. Water is filled in a container upto height 3m. A small hole of area ‘a’ is punched in the wall of the container at a height of 52.5 cm from the bottom. The cross-sectional area of the container is A. If a/A = 0.1 then v² is : (where v is the velocity of water coming out of the hole) (g = 10 m/s²)

1. 50
2. 51
3. 48
4. 51.5

Answer: 1. 50

Question 102. Statement -1 

The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up but tends to narrow down when held vertically down.

Statement -2

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

1. Statement -1 is True, Statement -2 is True; Statement -2 is a correct explanation for Statement -1
2. Statement -1 is True, Statement -2 is True; Statement -2 is NOT a correct explanation for Statement -1
3. Statement -1 is True, Statement -2 is False
4. Statement -1 is False, Statement -2 is True.

Answer: 1. Statement -1 is True, Statement -2 is True; Statement -2 is a correct explanation for Statement -1

Question 103. Water is flowing inside a tube of a uniform radius ratio of the radius of entry and exit terminals of the tube is 3: 2. Then the ratio of velocities at entry and exit terminals will be :

1. 4: 9
2. 9: 4
3. 8: 27
4. 1: 1

Answer: 1. 4: 9

Question 104. At what speed, the velocity head of water is equal to the pressure head of 40 cm of hg?

1. 10.3 m/s
2. 2.8 m/s
3. 5.6 m/s
4. 8.4 m/s

Answer: 1. 10.3 m/s

Question 105. A hole in the bottom of the tank has water. If the total pressure at the bottom is 3 atm (1 atm = 10⁵ Nm^-2), then the velocity of water flowing from the hole is :

1. \(\sqrt{400} \mathrm{~ms}^{-1}\)
2. \(\sqrt{600} \mathrm{~ms}^{-1}\)
3. \(\sqrt{60} \mathrm{~ms}^{-1}\)
4. None of these

Answer: 1. \(\sqrt{400} \mathrm{~ms}^{-1}\)

Question 106. The velocity of water flowing in a non-uniform tube is 20 cm/s at a point where the tube radius is 0.2 cm. The velocity at another point, where the radius is 0.1 cm is:

1. 80 cm/s
2. 40 cm/s
3. 20 cm/s
4. 5 cm/s

Answer: 1. 80 cm/s

Question 107. Water is poured into a vessel at a constant rate β m³/s. There is a small hole of area α at the bottom of the vessel. The maximum level of water in the vessel is proportional to

1. β/α
2. β²/α
3. β²/ α²
4. α²/ β²

Answer: 3. β²/ α²

Question 108. A manometer connected to a closed tap reads 3.5 × 10⁵ N/m², When the value is opened, the reading of the manometer falls to 3.0 × 10⁵ N/m², then the velocity of the flow of water is

1. 100 m/s
2. 10 m/s
3. 1 m/s
4. 1010m/s

Answer: 2. 10 m/s

Question 109. According to Bernoulli’s equation \(\frac{P}{p g}+h \frac{1}{2} \frac{v}{g}\)= Constant

The terms A, B, and C are generally called respectively :

1. Gravitational head, pressure head, and velocity head
2. Gravity, gravitational head, and velocity head
3. Pressure head, gravitational head, and velocity head
4. Gravity, Pressure, and velocity head

Answer: 3. Pressure head, gravitational head, and velocity head

Question 110. The weight of the sphere in the air is 50g. Its weight is 40 g in a liquid, at a temperature of 20°C. When the temperature increases to 70°C, it weight becomes 45 g. Find

1. The ratio of densities of liquid at given two temperatures,

Answer: \(\frac{\rho_1}{\rho_2}=\frac{2}{1}\) the ratio of densities of liquid at given two temperatures,

2. The coefficient of cubical expansion of liquid assumes that there is no expansion of the volume of a sphere.

Answer: \(\frac{1}{(70-20)}=0.02 /{ }^{\circ} \mathrm{C}\)

Question 111. The cubical container ABCDEFGH which is completely filled with an ideal (nonviscous and incompressible) fluid, moves in a gravity-free space with an acceleration of a = \(a_0(\hat{i}-\hat{j}+\hat{k})\) where a₀ is a positive constant. Then the only point in the container where pressure is maximum is

1. B
2. C
3. E
4. F

Answer: 1. B

Question 112. In the previous question pressure will be minimal at point –

1. A
2. B
3. H
4. F

Answer: 4. F

Question 113. A cylindrical tank of height 0.4 m is open at the top and has a diameter of 0.16 m. Water is filled in it up to a height of 0.16 m. how long it will take to empty the tank through a hole of radius 5×10^-3 m in its bottom?

1. 46.26 sec.
2. 4.6 sec.
3. 462.6 sec.
4. 4.46 sec.

Answer: 1. 46.26 sec.

Question 114. A narrow tube completely filled with a liquid is lying on a series of cylinders as shown in the figure. Assuming no sliding between any surfaces, the value of the acceleration of the cylinders for which liquid will not come out of the tube from anywhere is given by opening to the atmosphere

1. \(\frac{\mathrm{gH}}{2 \mathrm{~L}}\)
2. \(\frac{\mathrm{gH}}{\mathrm{L}}\)
3. \(\frac{2 \mathrm{gH}}{\mathrm{L}}\)
4. \(\frac{\mathrm{gH}}{\sqrt{2 \mathrm{~L}}}\)

Answer: 1. \(\frac{\mathrm{gH}}{2 \mathrm{~L}}\)

Question 115. A liquid is kept in a cylindrical vessel that is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/s, The difference in the height of the liquid at the center of the vessel and its sides will be (π² = 10) :

1. 3 cm
2. 2 cm
3. 3/2 cm
4. 2/3 cm

Answer: 2. 2 cm

Question 116. A container of liquid is released from the rest, on a smooth inclined plane as shown in the figure. The length of the inclined plane is sufficient, and assume liquid is finally in equilibrium. Finally liquid surface makes an angle horizontal.

1. 60º
2. 45º
3. 30º
4. None of these

Answer: 3. 30º

Question 117. A U-tube of base length “l” filled with the same volume of two liquids of densities ρ and 2ρ is moving with an acceleration “a” on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by:

1. \(\frac{\mathrm{a}}{2 \mathrm{~g}} \ell\)
2. \(\frac{3 \mathrm{a}}{2 \mathrm{~g}} \ell\)
3. \(\frac{\mathrm{a}}{\mathrm{g}} \ell\)
4. \(\frac{2 \mathrm{a}}{3 \mathrm{~g}} \ell\)

Answer: 2. \(\frac{3 \mathrm{a}}{2 \mathrm{~g}} \ell\)

Question 118. A given-shaped glass tube having a uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity ω then:

1. Water levels in both sections A and B go up
2. The water level in Section A goes up and that in B comes down
3. The water level in Section A comes down and in B it goes up
4. Water levels remain the same in both sections

Answer: 1. Water levels in both sections A and B go up

Question 119. A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D > > d) as shown in the figure. If it is burning at the rate of 2cm/hour then the top of the candle will

1. Remain at the same height
2. Fall at the rate of 1 cm/hour
3. Fall at the rate of 2 cm/hour
4. Go up the rate of 1 cm/hour

Answer: 2. Fall at the rate of 1 cm/hour

Question 120. There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to:

1. h^1/2
2. h
3. h^3/2
4. h²

Answer: 2. h

Question 121. The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed υ with which the liquid is crossing points at a distance X from O along a radius XO would look like

Answer: 4

Question 122. A wind with a speed of 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m². Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the direction of the force will be : (Pair = 1.2 kg / m³)

1. 4.8 x 10⁵ N, upwards
2. 2.4 x 10⁵ N, upwards
3. 2.4 x 10⁵ N, downwards
4. 4.8 x 10⁵ N, downwards

Answer: 2. 2.4 x 10⁵ N, upwards

Question 123. The heart of a 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 ×103 kg/m³ and g = 10m/s² then the power of heart in watt is:

1. 2.35
2. 3.0
3. 1.50
4. 1.70

Answer: 4. 1.70

Question 124. 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. \(\frac{\mathrm{VR}^2}{\mathrm{nr}^2}\)
2. \(\frac{V R^2}{n^3 r^2}\)
3. \(\frac{\mathrm{V}^2 \mathrm{R}}{\mathrm{nr}}\)
4. \(\frac{V R^2}{n^2 r^2}\)

Answer: 1. \(\frac{\mathrm{VR}^2}{\mathrm{nr}^2}\)

Question 125. Two non-mixing liquids of densities ρ and nρ (n > are put in a 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 < in the denser liquid. The density d is equal to

1. {1 + (n – 1)p}ρ
2. {1 + (n + 1)p}ρ
3. {2+(n + 1)p}ρ
4. {2 + (n – 1)p}ρ

Answer: 1. {1 + (n – 1)p}ρ

Question 126. 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

Answer: 4. 928 kg m^-3

Question 127. A small hole of area of cross-section 2 mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s², the rate of flow of water through the open hole would be nearly

1. 6.4 × 10^-6 m³/s
2. 12.6 × 10^-6 m³/s
3. 8.9 × 10^-6 m³/s
4. 2.23 × 10^-6 m³/s

Answer: 2. 12.6 × 10^-6 m³/s

Question 128. In a U-tube, as shown in the figure water and oil are on 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/m³]

1. 1200 kg/m³
2. 750 kg/m³
3. 1000 kg/m³
4. 1333 kg/m³

Answer: 2. 750 kg/m³

Question 129. A liquid does not wet the solid surface if the angle of contact is:

1. Equal to 45°
2. Equal to 60°
3. Greater than 90°
4. Zero

Answer: 3. Greater than 90°

Question 130. A barometer is constructed using a liquid (density = 760 kg/m³). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (Density of mercury = 13600 kg/m

1. 1.36 m
2. 13.6 m
3. 136 m
4. 0.76 m

Answer: 2. 13.6 m

Question 131. A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is

1. 20.0 g
2. 2.5 g
3. 5.0 g
4. 10.0g

Answer: 4. 10.0g

Question 132. The velocity of a small ball of mass M and density, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be

1. Mg
2. \(\frac{3}{2} \mathrm{Mg}\)
3. 2Mg
4. \(\frac{\mathrm{Mg}}{2}\)

Answer: 4. \(\frac{\mathrm{Mg}}{2}\)

Question 133. Water is flowing continuously from a tap having an internal diameter 8 × 10^-3 m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close to :

1. 5.0 × 10^-3 m
2. 7.5 × 10^-3 m
3. 9.6 × 10^-3 m
4. 3.6 × 10^-3 m

Answer: 4. 3.6 × 10^-3 m

Question 134. A wooden cube (density of wood ‘d’) of side ‘l’ floats in a liquid of density ‘p’ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs a simple harmonic motion of period ‘T’. Then, ‘T’ is equal to :

1. \(2 \pi \sqrt{\frac{\ell \mathrm{d}}{\rho \mathrm{g}}}\)
2. \(2 \pi \sqrt{\frac{\ell \rho}{d g}}\)
3. \(2 \pi \sqrt{\frac{\ell d}{(\rho-d) g}}\)
4. \(2 \pi \sqrt{\frac{\ell \rho}{(\rho-d) g}}\)

Answer: 1. \(2 \pi \sqrt{\frac{\ell \mathrm{d}}{\rho \mathrm{g}}}\)

Question 135. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density σ at the equilibrium position. The extension x₀ of the spring when it is in equilibrium is : (Here k is spring constant)

1. \(\frac{\mathrm{Mg}}{\mathrm{k}}\)
2. \(\frac{M g}{k}\left(1-\frac{L A \sigma}{M}\right)\)
3. \(\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA} \sigma}{2 \mathrm{M}}\right)\)
4. \(\frac{\mathrm{Mg}}{\mathrm{k}}\left(1+\frac{\mathrm{LA} \sigma}{\mathrm{M}}\right)\)

Answer: 3. \(\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA} \sigma}{2 \mathrm{M}}\right)\)

Question 136. There is a circular tube in a vertical plane. Two liquids that do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends a 90° angle at the center. The radius joining their interface makes an angle α with vertical. Ratio \(\frac{d_1}{d_2}\) is :

1. \(\frac{1+\sin \alpha}{1-\sin \alpha}\)
2. \(\frac{1+\cos \alpha}{1-\cos \alpha}\)
3. \(\frac{1+\tan \alpha}{1-\tan \alpha}\)
4. \(\frac{1+\sin \alpha}{1-\cos \alpha}\)

Answer: 3. \(\frac{1+\tan \alpha}{1-\tan \alpha}\)

Question 137. The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m³/ min. water per minute through a circular opening of a 2 cm radius in its wall. The depth of the center 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

Answer: 3. 4.8 m

Question 138. A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to : (density of water = 10³ kg/m³)

1. 5.00 rad s^-1
2. 3.70 rad s^-1
3. 2.50 rad s^-1
4. 1.25 rad s^-1

Answer: 4. 1.25 rad s^-1

Question 139. A liquid of density is coming out of a hose pipe of radius a with horizontal speed and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% loses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be :

1. \(\frac{1}{2} \rho v^2\)
2. \(\frac{1}{4} \rho v^2\)
3. \(\frac{3}{4} \rho v^2\)
4. \(\rho v^2\)

Answer: 3. \(\frac{3}{4} \rho v^2\)

Question 140. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of the increase in length of the steel wire is :

1. 3.0 mm
2. Zero
3. 5.0 mm
4. 4.0

Answer: 1. 3.0 mm