JEE Physics Mechanical Properties Of Fluids MCQs Set 35

Answer: (d) A-4, B-2, C-3, D-1

Explanation:
1. Water-proofing agents increase the angle of contact (A-4).
2. A sphygmomanometer measures gauge pressure (B-2).
3. Pressure more than the gauge pressure is the actual (absolute) pressure (C-3).
4. Merging drops gives larger drops with larger terminal velocity (D-1).

Teacher's Note:
1. Link each term to its meaning.

Answer: (b) capillary action

Explanation:
1. The fine pores of the wick act as capillaries.
2. The oil rises against gravity due to surface tension.

Teacher's Note:
1. Capillary action.

Answer: (d) all of these

Explanation:
1. 1 atm = 1.013 × 10⁵ Pa and 1 bar = 10⁵ Pa.
2. The pascal is the SI unit.

Teacher's Note:
1. All three measure pressure.

Answer: (a) zero

Explanation:
1. At the critical temperature the distinction between liquid and vapour vanishes.
2. So the surface tension is zero.

Teacher's Note:
1. Surface tension vanishes at T_c.

Answer: (d) 6

Explanation:
1. P_A = 8 + 4(0.04)/0.02 = 16 N/m² and P_B = 8 + 4(0.04)/0.04 = 12 N/m².
2. n ∝ PV ∝ Pr³.
3. n_B/n_A = (12 × 64)/(16 × 8) = 6.

Teacher's Note:
1. Use PV = nRT for each bubble.

Answer: (c) Bernoulli's theorem

Explanation:
1. A spinning ball drags air faster on one side, giving a pressure difference.
2. This follows Bernoulli's theorem.

Teacher's Note:
1. Spin creates a pressure difference.

Answer: (b) Mercury

Explanation:
1. For mercury the cohesive force is greater than the adhesive force, so the angle of contact is obtuse.
2. The meniscus is convex.

Teacher's Note:
1. Mercury does not wet glass.

Answer: (a) \( 2\times10^5\ \text{N/m}^2 \)

Explanation:
1. Force = 400 N and total area = 2 × 10 cm² = 2 × 10⁻³ m².
2. P = 400/(2 × 10⁻³) = 2 × 10⁵ N/m².

Teacher's Note:
1. Two bones double the area.

Answer: (c) \( 1.9\times10^5\ \text{Pa} \)

Explanation:
1. Pressure = load/area of the large piston = 13500/(π × 0.15²).
2. = 13500/0.0707 = 1.9 × 10⁵ Pa.

Teacher's Note:
1. P = F/A on the large piston.

Answer: (b) rises

Explanation:
1. The ice displaces liquid of mass equal to its own mass, volume M/1.2.
2. The melted water has volume M/1, which is larger, so the level rises.

Teacher's Note:
1. Water is less dense than the liquid.

Answer: (a) buoyant force

Explanation:
1. The upward force exerted by the fluid is the buoyant force.
2. It equals the weight of the displaced fluid.

Teacher's Note:
1. Upthrust.

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

Explanation:
1. For small drops, surface tension dominates over gravity, so they stay spherical; the assertion is true.
2. The two forces are not equal and opposite in general, so the reason is false.

Teacher's Note:
1. Surface tension wins at small sizes.

Answer: (c) III only

Explanation:
1. Viscous force depends on the area of the layers and on the velocity gradient, so I and II are false.
2. Friction ∝ N, while viscous force does not depend on the normal reaction, so III is true.

Teacher's Note:
1. Contrast solid friction and viscosity.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A hydraulic lift transmits pressure through the fluid, so the assertion is true.
2. The reason is a true definition, but it does not explain the working principle.

Teacher's Note:
1. Both true, no explanation.

Answer: (c) 0.98 m

Explanation:
1. The bowl displaces a volume (2/3)πR³ (R = 0.5 m).
2. Weight = buoyancy: 2 × 10⁴ × (2/3)π(R³ − r³) = 1.2 × 10³ × (2/3)πR³, so r³ = R³(1 − 0.06) = 0.94R³.
3. r = 0.9798R, so the inner diameter ≈ 0.98 m.

Teacher's Note:
1. Equate the weight of the shell to the buoyancy.

Answer: (b) II only

Explanation:
1. Surface tension decreases with temperature, so II is false.
2. I and III are correct.

Teacher's Note:
1. S falls with temperature.

Answer: (c) Both I and II

Explanation:
1. The spinning ball creates different air speeds on its two sides, so a pressure difference appears, as Bernoulli's principle predicts.
2. A spinning cricket ball swerves due to this effect.

Teacher's Note:
1. Spin makes the ball swerve.

Answer: (d) \( 2.25\times10^{-2}\ \text{N} \)

Explanation:
1. F = T × length = 0.075 × (2 × 0.15).
2. = 2.25 × 10⁻² N.

Teacher's Note:
1. Length of the diameter is 30 cm.

Answer: (a) the weight of the liquid displaced

Explanation:
1. The buoyant force equals the weight of the displaced fluid.
2. The apparent loss of weight is this upthrust.

Teacher's Note:
1. Upthrust equals the weight of displaced liquid.

Answer: (a) energy is liberated

Explanation:
1. The total surface area decreases, so the surface energy decreases.
2. The difference is released as energy.

Teacher's Note:
1. Smaller area, lower energy.

Answer: (b) 2.44 cm

Explanation:
1. h = 2T cos θ/(rρg) with r = 0.5 mm.
2. = 2 × 0.06/(5 × 10⁻⁴ × 1000 × 9.8) = 0.0245 m = 2.44 cm.

Teacher's Note:
1. Use h = 2T/rρg.

Answer: (d) 9 mm

Explanation:
1. h ∝ 1/r.
2. A radius one-third as large gives three times the height, 9 mm.

Teacher's Note:
1. Capillary rise is inversely proportional to r.

Answer: (c) \( 3\times10^{-2}\ \text{N/m} \)

Explanation:
1. The increase in area on one side = 10 × 5 = 50 cm², so both sides = 100 cm² = 10⁻² m².
2. T = W/ΔA = 3 × 10⁻⁴/10⁻² = 3 × 10⁻² N/m.

Teacher's Note:
1. Two surfaces.

Answer: (c) Sphere

Explanation:
1. The sphere has the least surface area for a given volume.
2. So its surface energy is the minimum.

Teacher's Note:
1. Sphere minimises area.

Answer: (d) transmitted unchanged to every portion of the fluid and the wall of the containing vessel

Explanation:
1. This is Pascal's law.
2. The pressure change is transmitted undiminished everywhere.

Teacher's Note:
1. Undiminished transmission.