NEET Physics Fluid Mechanics Revision Notes

Question. A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink, should be: 
(density of wood = 600 Kg/m³)
a. 80 Kg
b. 50 Kg
c. 60 Kg
d. 30 Kg
Answer : A

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

a. 1/2
b. 3/8
c. 2/3
d. 3/4
Answer : A

Question. 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 spring:
a. Increases
b. Decreases
c. Remains unchanged
d. None of these
Answer : B

Question. The value of g at a place decreases by 2%. The barometric height of mercury:
a. Increases by 2%
b. Decreases by 2%
c. Remains unchanged
d. Sometimes increases and sometimes decreases
Answer : A

Question. 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:
a. Increases
b. Decreases
c. Remain constant
d. First decrease and then increase
Answer : B

Question. Three liquids of densities d, 2d and 3d are mixed in equal proportions of weights. The relative density of the mixture is:
a. 11d/7
b. 18d/11
c. 13d/9
d. 23d/18
Answer : B

Question. A thin metal disc of radius r floats on water surface and bends the surface downwards along the perimeter making an angle θ with vertical edge of disc. If the disc displaces a weight of water W and surface tension of water is T, then the weight of metal disc is:
a. 2π rT + W
b. 2πrT cosθ – W
c. 2π r T cos θ + W
d. W – 2π rT cosθ
Answer : C

Question. There is a horizontal film of soap Solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius R. If the surface tension of the loop be T, then what will be the tension in the thread?
a. πR² / T
b. πR²T
c. 2πRT
d. 2RT
Answer : D

Question. A liquid is filled into a tube with semi-elliptical crosssection as shown in the figure. The ratio of the surface tension forces on the curved part and the plane part of the tube in vertical position will be: 

a. π (a + b) / 4b
b. 2πa / b
c. πa/4b
d. π (a − b) / 2b
Answer : A

Question. A hollow sphere of volume V is floating on 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?
a.V/2
b. V/3
c. V/4
d. V
Answer : A

Question. Two solids A and B float in water. It is observed that A floats with 1/2 of its body immersed in water and B floats with 1/4 of its volume above the water level. The ratio of the density of A to that of B is:
a. 4 : 3
b. 2 : 3
c. 3 : 4
d. 1 : 2
Answer : B

Question. A wooden cylinder floats vertically in water with half of its length immersed. The density of wood is:
a. Equal of that of water
b. Half the density of water
c. Double the density of water
d. The question is incomplete
Answer : B

Question. The pressure inside a small air bubble of radius 0.1mm situated just below the surface of water will be equal to: (Take surface tension of water 70 v 10^-3 Nm^-1 and atmospheric pressure 5 .013 x 10⁵ Nm^-2)
a. 2.054 ×10³ Pa
b. 1.027 ×10³ Pa
c. 1.027 ×10⁵ Pa
d. 2.054 ×10⁵ Pa
Answer : C

Question. The excess pressure inside an air bubble of radius r just below the surface of water is P₁. The excess pressure inside a drop of the same radius just outside the surface is P₂. If T is surface tension then:
a. P₁ = 2P₂
b. P₁ = P₂
c. P₂ = 2P₁
d. P₂ = 0, P₁ ≠ 0
Answer : B

Question. Two capillary tubes of same diameter are kept vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and 50 dyne/cm respectively. Ratio of heights of liquids in the two tubes h_1/h₂ is:
a. 10/9
b. 3/10
c. 10/3
d. 9/10
Answer : D

Question. The work done in increasing the size of a soap film from 10cm × 6cm to 10cm × 11cm is 3 x 10⁻⁴ J. The surface tension of the film is:
a. 1.5 10⁻² Nm⁻¹
b. 3.0 10⁻² Nm⁻¹
c. 6.0 10⁻² Nm⁻¹
d. 11.0 10⁻² Nm⁻¹
Answer : B

Question. A film of water is formed between two straight parallel wires of length 10cm each separated by 0.5cm. If their separation is increased by 1 mm while still maintaining their parallelism, how much work will have to be done: (Surface tension of water 7.2 10^-2 N /m)
a. 7.22 x 10⁻⁶ J
b. 1.44 x 10⁻⁵ J
c. 2.88 x 10⁻⁵ J
d. 5.76 x 10⁻⁵ J
Answer : B

Question. If the work done in blowing a bubble of volume V is W, then the work done in blowing the bubble of volume 2V from the same soap solution will be:
a. W/2
b. √2W
c. ³√2 W
d. ³√4 W
Answer : D

Question. The lower end of a capillary tube is at a depth of 12cm and the water rises 3cm in it. The mouth pressure required to blow an air bubble at the lower end will be X cm of water column where X is:
a. 3
b. 9
c. 12
d. 15
Answer : D

Question. An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm³)
a. 350 cm³
b. 300 cm³
c. 250 cm³
d. 22 cm³
Answer : B

Question. A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density 13.6 g/cm³). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?

a. 1.2 cm
b. 2.35 cm
c. 0.56 cm
d. 0.8 cm
Answer : C

Question. A capillary tube of radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled, mass of water that will rise in the capillary tube will now be:
a. M
b. 2M
c. M/2
d. 4M
Answer : B

Question. Water rises to a height h in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be:
a. 6h
b. (1/6)h 
c. h
d. Zero
Answer : A

Question. Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is 2.2cm and that in the other is 6.6cm. The ratio of their radii is:
a. 9 : 1
b. 1 : 9
c. 3 : 1
d. 1 : 3
Answer : C

Question. 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. Ratio of mass of concrete to mass of sawdust will be:
a. 8
b. 4
c. 3
d. Zero
Answer : B

Question. A vessel contains oil (density = 0.8 gm/cm³) over mercury (density = 13.6 gm/cm³). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm3 is:
a. 3.3
b. 6.4
c. 7.2
d. 12.8
Answer : C

Question. A wooden block of volume 1000 cm³ is suspended from a spring balance. It weighs 12 N in air. It is suspended in water such that half of the block is below the surface of water. The reading of the spring balance is:
a. 10 N
b. 9 N
c. 8 N
d. 7 N
Answer : D

Question. An iceberg is floating in sea water. The density of ice is 0.92 gm/cm³ and that of sea water is 1.03g/cm³. What percentage of the iceberg will be below the surface ofwater?
a. 3%
b. 11%
c. 89%
d. 92%
Answer : C

Question. The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 104. The height of the hill is:
a. 250 m
b. 2.5 km
c. 1.25 km
d.750 m
Answer : B

Question. Two substances of densities ρ₁ and ρ₂ are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of ρ₁ and ρ₂ are:
a. 1 ρ = 6 and 2 ρ = 2
d. 1 ρ = 3 and 2 ρ = 5
c. 1 ρ =12 and 2 ρ = 4
d. None of these
Answer : A

Question. Two capillary tubes of the same length but different radii r₁ and r₂ are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before?
a. r₁ + r₂
b. r₁² + r²₂
c. r₁⁴ + r₂⁴
d. None of these
Answer : D

Question. A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then:

a. l decreases and h increases
b. l increases and h decreases
c. Both l and h increase
d. Both l and h decrease
Answer : D

Question. 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
a. 4 : 3
b. 2 : 3
c. 3 : 4
d. 1 : 3 
Answer : D

Question. A vessel with water is placed on a weighing pan and reads 600 g. Now a ball of 40 g and density 0.80 g/cc is sunk into the water with a pin as shown in fig. keeping it sunk.
The weighing pan will show a reading:

a. 600 g
b. 550 g
c. 650 g
d. 632 g
Answer : C

Question. Two different liquids are flowing in two tubes of equal radius. The ratio of coefficients of viscosity of liquids is 52:49 and the ratio of their densities is 13:1, then the ratio of their critical velocities will be
a. 4 : 49
b. 49 : 4
c. 2 : 7
d. 7 : 2
Answer : A

Question. An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

a. 3.0 m/s
b.1.5 m/s
c. 1.0 m/s
d. 2.25 m/s
Answer : C

Question. A manometer connected to a closed tap reads 3.5 × 105 N/m². When the valve is opened, the reading of manometer falls to 3.0 × 105 N/m², then velocity of flow of water is
a. 100 m/s
b. 10 m/s
c. 1 m/s
d. 10 √10 m/s
Answer : B

Question. A cylinder of height 20 m is completely 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
a. 10
b. 20
c. 25.5
d. 5
Answer : B

Question. There is a hole of area A at the bottom of cylindrical vessel. Water is filled up to a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time equal to
a. t
b. 4t
c. 2 t
d. t/4
Answer : C

Question. n drops of a liquid, each with surface energy E, join to form a single drop:
a. Some energy will be released in the process
b. Some energy will be absorbed in the process
c. the energy releases or absorbed will be E(n − n^2/3)
d. the energy released or absorbed will be nE(2^2/3 - 1)
Answer : A, C

Question. A body of density ρ is dropped from rest from a height h into a lake of density σ, where σ > ρ. Which of the following statements for the body are correct if all dissipative effects are neglected?
a. The speed of the body just entering the lake is 2gh
b. The body in the lake experiences upward acceleration equal to g (σ/ρ) – g
c. The maximum depth to which the body sinks in the lake is hρ (σ – ρ)
d. The body does not come back to the surface of the lake
Answer : A, B, C

Question. Which of the following are correct?
a. When a liquid flows through aw horizontal pipe of varying cross-section, pressure is lowest where velocity is highest
b. When a gale blows over a hut, the force on the roof due to the gale is directed outward
c. When a small solid sphere is dropped in a viscous medium the net force on the sphere goes on decreasing till it becomes zero
d. Viscous force is a velocity dependent force
Answer : ALL

Question. A steel cube weighs 1 kg in air and 0.88 kg in water. The density of the steel is 7.71×10³ kg/m³ and of water is 103kg/m³. The cube:
a. must be solid
b. must be hollow
c. consists of pure steel
d. consists of impure steel
Answer : A, D

Question. A body totally immersed in water is raised in the water by a height h. The density of the body is d and the density of water is d₀ while the volume of the body is V and d > d_0. Which of the following statements will be true?
a. The net work done on raising the body is Vdgh
b. The increase in the potential energy of the body is Vgh (d – d₀)
c. The potential energy of water is not changed by raising the body
d. The work done on the body by the gravitational force is equal and opposite to the work done by the hydrostatic force so that net work done is zero
Answer : B, C

Question. A sample of metal weighs 210 gm in air, 180 gm in water and 120 gm in liquid. Then relative density (RD) of
a. Metal is 3
b. Metal is 7
c. Liquid is 3
d. Liquid is 1/3
Answer : B, C

Question. An air bubble in a water tank rises from the bottom to the top. Which of the following statements are true
a. Bubble rises upwards because pressure at the bottom is
less than that at the top.
b. Bubble rises upwards because pressure at the bottom is greater than that at the top.
c. As the bubble rises, its size increases
d. As the bubble rises, its size decreases
Answer : B, C

Question. Which of the following correct?
a. A streamline is a line, tangent at every point of which gives the magnitude, and direction of velocity at that instant
b. The working principle of pressure gauges for measuring static pressure of a fluid flowing in a pipe is based on Bernoulli’s theorem
c. When a ball moves with constant velocity in a viscous liquid, then the sum of viscous force and buoyant force equals the weight of the ball
d. Strokes’ law is applicable if Reynolds number is greater than 4000
Answer : A, B, C

Question. Two spheres P and Q of equal radii have densities ρ₁ and ρ₁ respectively. The spheres are connected by a mass less string and placed in liquids L₁ and L₂ of densities σ₁ and σ₂ and viscosities 1 η and 2 η , respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure). If sphere P alone in L₂ has terminal velocity V_P and Q alone in L₁ has terminal velocity, V_Q then

Answer : A, D

Assertion and Reason

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Assertion: A large soap bubble expands while a small bubble shrinks when they are connected to each other by a capillary tube
Reason: The excess pressure inside a bubble (or drop) is inversely proportional to the radius.
Answer : A

Question. Assertion: At critical temperature surface tension of a liquid becomes zero.
Reason: At this temperature, intermolecular forces for liquids and gases become equal. Liquids can expand without any restriction.
Answer : A

Question. Assertion: A rain drop after falling through some height attains a constant velocity.
Reason: At constant velocity, the viscous drag is just equal to weight.
Answer : A

Question. Assertion: Mosquitos are killed (which are present in water) when kerosene is sprayed on water surface in tanks ponds.
Reason: Kerosene is very harmful for mosquitoes.
Answer : E

Question. Assertion: More is the cohesive force, more is the surface tension.
Reason: More cohesive force leads to more shrinking of liquid surface.
Answer : A

Question. Assertion: The stretching of an elastic spring is determined by the shear modulus of the force constant of the spring.
Reason: For a given stretching force, the amount of stretching depends on the force constant of the spring.
Answer : B

Question. Assertion: When height of a tube is less then liquid rise in the capillary tube, the liquid does not overflow.
Reason: Product of radius of meniscus and height of liquid in capillary tube always remains constant.
Answer : A

Question. Assertion: Hydrostatic pressure is a vector quantity.
Reason: Pressure is force divides by area and force is a vector quantity.
Answer : E

Question. Assertion: A man is sitting in a boat which is floating on a pond. If the man drinks some water from the pond, the level of water in the pond decreases.
Reason: According to Archimedes’ principle, the weight displaced by body is equal to the weight of the body.
Answer : E

Question. Assertion: In the diagram shown, a cube is floating in water in tilted position. In shown situation, the cube is in stable position, i.e., cube won’t sink.

Reason: The point of application of gravitational force and buoyancy force are passing through the same line in the above described case.
Answer : C

Question. Assertion: Two wires A and B have the same crosssectional area and are made of the same material but the length of wire A is the twice that B. For a given load, the strain in wire A is twice that in B.
Reason: For a given load the extension in a wire is proportional to its length.
Answer : D

Question. Assertion: The viscosity of liquid increases rapidly with rise of temperature.
Reason: Viscosity of a liquid is the property of the liquid by virtue of which is opposes the relative motion amongst its different layers.
Answer : E

Question. Assertion: Aeroplanes are made to run on the runway before take off, so that the acquire the necessary lift.
Reason: According to Bernoulli’s theorem, as velocity increases, pressure decreases and vice-versa.
Answer : A

Question. Assertion: Two wires A and B are made of the same material. The length of wire A is twice that of B but the diameter of A is half that of B. For a given load, the strain produced in B will be twice that in A.
Reason: For a given load, the extension produced in a wire is directly proportional to its length and inversely proportional to the area of cross-section.
Answer : D

Question. Assertion: A very light spinning ball can be held hanging in air by blowing air as shown in fig.

Reason: The weight of the ball can be balanced by upthrust due to viscosity of air.
Answer : C

Comprehension Based

Paragraph –I

A student performs an experiment to find surface tension of water/liquid by capillary rise method. He sets up his apparatus with different capillary tubes dipped form same stand in water in petri dish.

Question. He has capillary tube of different shapes as shown in figure. The level of liquid in capillary tubes:
a. A, B, C and D is same
b. A and D is same, higher in B, lower in C
c. A and D is same, higher in C, lower in B
d. A and C is same, lower in D and lowest in B
Answer : A

Question. The capillary tube A used by him showed rise of liquid upto certain height. During experimentation the tube breaks form a point below the level of liquid in tube and is shown as tube B as shown in figure:

a. the liquid will continue over flowing the tube B
b. the liquid will not rise in the tube
c. the tube will be filled with liquid upto to making top surface plane and stop
d. liquid will reach top and will have to shape concave and will not rise due to more pressure on concave side of free surface
Answer : C

Question. The student is performing this experiments in lift with a long capillary tube and measures capillary rise as h. The lift starts falling due to breaking of its supporting cable.
The level of liquid in capillary will be:
a. remain the same
b. liquid will rise upto to top of tube and stopo
c. the liquid will fall down and will show not rise
d. the liquid will go on falling till its velocity is equal to critical velocity
Answer : B

Paragraph –II

The behavior of liquid relative to solid container depends on forces of adhesion and cohesion, which produces a particular shape of free surface when filled in a narrow tube. The forces of cohesion are denoted as Fc, that of adhesion as Fa and the angle f contact as θ. From your study of surface tension answer the following questions.

Question. For liquids having forces of cohesion F_c < √2F_a the forces of adhesion, the angle of contact will be:
a. 0
b. 90
c. obtuse
d. acute
Answer : D

Question. For liquids having forces of adhesion F_c < √2F_a
a. the liquid will stick to wall and get depressed in capillary tube
b. the liquid will stick to wall and rise in capillary tube
c. the liquid will not stick to wall and get depressed in capillary tube
d. the liquid will not stick to wall and will rise in capillary tube
Answer : C

Question. For the liquids where forces of adhesion F_a = F_c forces of cohesion as for water in silver container, which of the following statements is not correct:
a. There will be no rise in capillary tube
b. The angle of contact will be zero
c. The angle of contact will be 90º
d. The free surface will be plane
Answer : D

Paragraph –III

Liquids exert pressure obeying Pascal’s law. Knowledge of Pascal’s law has helped the scientist and engineers to know roughly the height of atmosphere, the height of water tanks, the height of buildings upto which water can be supplied with or without water pump. How will you help a construction company with your knowledge of Pascal’s law to overcome the following problems?

Question. The height of building to which water can be raised without force up, is:
a. 5 m
b. 10 m
c. 15 m
d. 20 m
Answer : B

Question. Height of air column above surface of earth assuming uniform density of air as 1.3 kg/m³, is:
a. 80 m
b. 800 m
c. 8000 m
d. 80 km
Answer : C

Question. Which of the following statements is not correct?
a. Pressure is a scalar quantity
b. Pressure exerted at the bottom of container containing liquid of density ρ, height of column h with atmospheric pressure P0 is P0 + hρg
c. Average pressure on walls of the container containing liquid upto height h having density ρ is 1/2hρg
d. Pressure exerted by liquid at bottom of container depends on shape of its surface
Answer : D

Match the Column

Question. Different instruments work on the different principles of column I mentions the instruments while column II gives the principle on which they work. Match the proper principle with device or instrument.
Column I                            Column II
(A) Ink pen                1. Capillarity principle
(B) Ball point             2. Gravity principle
(C) Helicopter           3. Archimedes’
(D) Aeroplane           4. Bernoulli’s principle
a. A → 1, B → 2, C → 3, D → 4
b. A → 4, B → 3, C → 2, D → 1
c. A → 3, B → 2, C → 1, D → 4
d. A → 2, B → 1, C → 4, D → 3
Answer : A

Question. Study of properties of matter helps the student to know some phenomenon having important applications of the principles learnt by him in his daily life. Can you match
some of the phenomenon you observe with the principles you have studied.

a. A → 1, B → 2, C → 3, D → 4
b. A → 4, B → 3, C → 2, D → 1
c. A → 3, B → 2, C → 1, D → 4
d. A → 3, B → 4, C → 2, D → 1
Answer : D

Integer

Question. A water tank is 20 m deep. If the water barometer reads 10 m at that place, then what is the pressure at the bottom of the tank in atmosphere?
Answer : 3

Question. There is a soap bubble of radius 2.4×10^–4m in air cylinder which is originally at the pressure of 105N/m². The air in the cylinder is now compressed isothermally until the radius of the bubble is halved. The pressure of air in the cylinder now becomes n×105N/m². The surface tension of soap film is 0.08 Nm^–1. Find the integer value of n.
Answer : 8

Question. A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes T₁ time to decrease the height of water to H/η (η > 1) ; and it takes T₂ time to take out the rest of water. If T₁ = T₂ , then the value of η is
Answer : 4

Question. 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 / cm³. If the mass of the other is 48 g, its density in g / cm³ is
Answer : 3

Question. A ball whose density is 0.4 × 10³ kg/m³ falls into water from a height of 9 cm . To what depth does the ball sink?
Answer : 6