JEE Physics Mechanical Properties Of Fluids MCQs Set 05

Multiple Choice Questions (MCQs) for JEE Physics: Mechanical Properties Of Fluids

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Practice Mechanical Properties Of Fluids MCQs for JEE Physics

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Multiple Choice Questions

Question 1: Poisson's ratio cannot have the value:
(a) 0.1
(b) 0.7
(c) 0.2
(d) 0.5
Show Answer & Explanation

Answer: (b) 0.7

Explanation:
1. For a stable isotropic material Poisson's ratio lies between -1 and 0.5, so 0.7 is not possible

Teacher's Note:
1. Apply the standard formula and check the units.

Question 2: Two wires of the same length and material but different radii r1 and r2 carry the same load at the lower end. The ratio of the stress in the second wire to that in the first is:
(a) \( r_1/r_2 \)
(b) \( r_1^2/r_2^2 \)
(c) \( (r_1/r_2)^{5/2} \)
(d) \( (r_1/r_2)^{1/2} \)
Show Answer & Explanation

Answer: (b) \( r_1^2/r_2^2 \)

Explanation:
1. Stress = F/(pi r^2)
2. The ratio stress2/stress1 = r1^2/r2^2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 3: The pressure increase required to decrease the volume of 200 litres of a liquid by 0.004% is (bulk modulus of the liquid = 2100 MPa):
(a) 188 kPa
(b) 8.4 kPa
(c) 18.8 kPa
(d) 84 kPa
Show Answer & Explanation

Answer: (d) 84 kPa

Explanation:
1. Change in P = B x (dV/V) = 2100e6 x 4e-5 = 8.4e4 Pa = 84 kPa

Teacher's Note:
1. Apply the standard formula and check the units.

Question 4: If S is the stress and Y the Young's modulus of the material of a wire, the energy stored in the wire per unit volume is:
(a) \( S/2Y \)
(b) \( 2Y/S^2 \)
(c) \( S^2/2Y \)
(d) \( 2S^2Y \)
Show Answer & Explanation

Answer: (c) \( S^2/2Y \)

Explanation:
1. Energy density = (1/2) stress x strain = (1/2) S (S/Y) = S^2/(2Y)

Teacher's Note:
1. Apply the standard formula and check the units.

Question 5:
Assertion (A): Stress is the internal force per unit area of a body.
Reason (R): Rubber is more elastic than steel.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. Stress is the restoring force per unit area, so A is true
2. Steel has the greater Young's modulus, so it is more elastic than rubber and R is false

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 6: For a constant hydraulic stress on an object, the fractional change in the object's volume and its bulk modulus B are related as:
(a) \( \Delta V/V\propto B \)
(b) \( \Delta V/V\propto 1/B \)
(c) \( \Delta V/V\propto B^2 \)
(d) \( \Delta V/V\propto B^{-2} \)
Show Answer & Explanation

Answer: (b) \( \Delta V/V\propto 1/B \)

Explanation:
1. B = P/(dV/V), so for constant P the strain is proportional to 1/B

Teacher's Note:
1. Apply the standard formula and check the units.

Question 7: A wire of length L and cross-sectional area A is made of material of Young's modulus Y. The work done in stretching the wire by an amount x is:
(a) \( YAx^2/L \)
(b) \( YAx^2/2L \)
(c) \( YAL^2/x \)
(d) \( YAL^2/2x \)
Show Answer & Explanation

Answer: (b) \( YAx^2/2L \)

Explanation:
1. Force = (YA/L) x, so work = (1/2)(YA/L) x^2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 8: Two vessels A and B have the same base area and contain water to the same height, but the mass of water in A is four times that in B. The ratio of the liquid thrust at the base of A to that at the base of B is:
(a) 4 : 1
(b) 2 : 1
(c) 1 : 1
(d) 16 : 1
Show Answer & Explanation

Answer: (c) 1 : 1

Explanation:
1. Thrust at the base = rho g h x base area, independent of the shape of the vessel
2. Both are equal, so the ratio is 1 : 1

Teacher's Note:
1. Apply the standard formula and check the units.

Question 9: A cylinder is filled with a liquid of density d up to a height h. If the beaker is at rest, the mean pressure on the wall is:
(a) zero
(b) hdg
(c) (h/2) dg
(d) 2hdg
Show Answer & Explanation

Answer: (c) (h/2) dg

Explanation:
1. Pressure on the wall rises linearly from 0 at the top to hdg at the bottom
2. The mean is hdg/2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 10:
Assertion (A): The density of a hollow body is always less than the density of the substance of equal mass.
Reason (R): The volume of a hollow body is greater than that of the substance of the body, while the masses are equal.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Density = mass/volume
2. The same mass in a larger volume gives lower density, so R explains A

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 11: A spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on its pan. The balances are now arranged so that the hanging mass is inside the liquid in the beaker. Then:
(a) balance A will read more than 2 kg
(b) balance B will read more than 5 kg only
(c) A will read less than 2 kg and B more than 5 kg
(d) A and B will read 2 kg and 5 kg respectively
Show Answer & Explanation

Answer: (c) A will read less than 2 kg and B more than 5 kg

Explanation:
1. Buoyancy reduces the tension in the spring, so A reads less
2. By Newton's third law the block pushes down on the liquid with the buoyant force, so B reads more

Teacher's Note:
1. Apply the standard formula and check the units.

Question 12: A jar is filled with two non-mixing liquids 1 (upper) and 2 (lower) of densities rho1 and rho2. A solid ball of density rho3 comes to rest at the boundary between the two liquids. Then:
(a) \( \rho_3\lt\rho_1\lt\rho_2 \)
(b) \( \rho_1>\rho_3>\rho_2 \)
(c) \( \rho_1\lt\rho_2\lt\rho_3 \)
(d) \( \rho_1\lt\rho_3\lt\rho_2 \)
Show Answer & Explanation

Answer: (d) \( \rho_1\lt\rho_3\lt\rho_2 \)

Explanation:
1. The upper liquid floats on the lower one, so rho1 is less than rho2
2. A ball resting at the interface is denser than the upper liquid and lighter than the lower one

Teacher's Note:
1. Apply the standard formula and check the units.

Question 13: A boat of length 3 m and breadth 2 m floats on a lake. The boat sinks by one cm when a man gets on it. The mass of the man is:
(a) 60 kg
(b) 62 kg
(c) 72 kg
(d) 128 kg
Show Answer & Explanation

Answer: (a) 60 kg

Explanation:
1. Extra buoyant force = rho g x (area x depth)
2. Mass = 1000 x 3 x 2 x 0.01 = 60 kg

Teacher's Note:
1. Apply the standard formula and check the units.

Question 14: If the density of a block is 981 kg/m3, then it shall:
(a) sink in water
(b) float in water with some part immersed
(c) float completely immersed in water
(d) float completely out of water
Show Answer & Explanation

Answer: (b) float in water with some part immersed

Explanation:
1. The block is less dense than water (1000 kg/m3), so it floats with a part immersed

Teacher's Note:
1. Apply the standard formula and check the units.

Question 15:
Assertion (A): The specific gravity of a fluid is a dimensionless quantity.
Reason (R): It is the ratio of the density of the fluid to the density of water.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A ratio of two densities has no unit, so R explains A

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 16: A piece of ice is floating in a jar containing water. When the ice melts, the level of water:
(a) rises
(b) falls
(c) remains unchanged
(d) changes erratically
Show Answer & Explanation

Answer: (c) remains unchanged

Explanation:
1. Ice displaces water equal to its own weight
2. The melt water has the same volume as the displaced water

Teacher's Note:
1. Apply the standard formula and check the units.

Question 17: A metal sample weighs 210 g in air, 180 g in water and 120 g in an unknown liquid. Then:
(a) the density of the metal is 3 g/cm3
(b) the density of the metal is 7 g/cm3
(c) the density of the metal is 4 times the density of the unknown liquid
(d) the metal will float in water
Show Answer & Explanation

Answer: (b) the density of the metal is 7 g/cm3

Explanation:
1. Loss in water = 30 g, so volume = 30 cm3
2. Density = 210/30 = 7 g/cm3

Teacher's Note:
1. Apply the standard formula and check the units.

Question 18: 'Torr' is the unit of:
(a) pressure
(b) density
(c) volume
(d) flux
Show Answer & Explanation

Answer: (a) pressure

Explanation:
1. 1 torr is the pressure of 1 mm of mercury

Teacher's Note:
1. Apply the standard formula and check the units.

Question 19: A sphere floats in water with 1/3 of its volume outside. When floating in an unknown liquid, 3/4 of its volume is outside. The density of the liquid is:
(a) 4/9 g/cc
(b) 9/4 g/cc
(c) 8/3 g/cc
(d) 3/8 g/cc
Show Answer & Explanation

Answer: (c) 8/3 g/cc

Explanation:
1. In water the sphere has density 2/3 g/cc
2. In the liquid 1/4 is immersed, so density of liquid = 4 x 2/3 = 8/3 g/cc

Teacher's Note:
1. Apply the standard formula and check the units.

Question 20:
Assertion (A): A hydrogen-filled balloon stops rising after it has attained a certain height in the sky.
Reason (R): The atmospheric pressure decreases with height and becomes zero when the maximum height is attained.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. The balloon stops where the air density equals the average density of the balloon, so A is true
2. Atmospheric pressure does not become zero there, so R is false

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 21: Which of the following works on Pascal's law?
(a) sprayer
(b) venturimeter
(c) hydraulic lift
(d) aneroid barometer
Show Answer & Explanation

Answer: (c) hydraulic lift

Explanation:
1. A hydraulic lift transmits pressure equally through an enclosed liquid

Teacher's Note:
1. Apply the standard formula and check the units.

Question 22: An object of weight W and density rho is submerged in a fluid of density rho1. Its apparent weight will be:
(a) \( W(\rho-\rho_1) \)
(b) \( (\rho-\rho_1)/W \)
(c) \( W(1-\rho_1/\rho) \)
(d) \( W(\rho_1-\rho) \)
Show Answer & Explanation

Answer: (c) \( W(1-\rho_1/\rho) \)

Explanation:
1. Apparent weight = W - buoyant force = W - V rho1 g = W(1 - rho1/rho)

Teacher's Note:
1. Apply the standard formula and check the units.

Question 23: Which law states that the magnitude of pressure within a fluid is equal in all parts?
(a) Pascal's law
(b) Gay-Lussac's law
(c) Dalton's law
(d) Boyle's law
Show Answer & Explanation

Answer: (a) Pascal's law

Explanation:
1. Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished everywhere

Teacher's Note:
1. Apply the standard formula and check the units.

Question 24: A body measures 5 N in air and 2 N when put in water. The buoyant force is:
(a) 7 N
(b) 9 N
(c) 3 N
(d) none of these
Show Answer & Explanation

Answer: (c) 3 N

Explanation:
1. Buoyant force = loss of weight = 5 - 2 = 3 N

Teacher's Note:
1. Apply the standard formula and check the units.

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