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Surface tension by capillary rise and detergent effect: NEET MCQs with answers

49 questions on this topic of Experimental Skills (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. A capillary tube of radius r = 0.2 mm is dipped vertically into a beaker of pure water (density = 1000 kg/m³, contact angle θ = 0°). Water rises to a height of 7.5 cm. Taking g = 10 m/s², the surface tension of water calculated from this experiment is:

  1. 0.015 N/m
  2. 0.0375 N/m
  3. 0.150 N/m
  4. 0.075 N/m
Show answer and explanation

Answer: (D) 0.075 N/m

Surface tension is given by T = (r h ρ g) / (2 cos θ). Substituting r = 0.2 × 10⁻³ m, h = 7.5 × 10⁻² m, ρ = 1000 kg/m³, g = 10 m/s², and cos 0° = 1 gives T = (0.2 × 10⁻³ × 7.5 × 10⁻² × 1000 × 10) / 2 = 0.15 / 2 = 0.075 N/m.

medium

2. An experimenter measures the capillary rise of water as h = (4.00 ± 0.02) cm in a tube of radius r = (0.50 ± 0.01) mm using g = 9.8 m/s² and ρ = 1000 kg/m³ (both assumed exact). The maximum percentage error in the calculated value of surface tension T is:

  1. 1.5%
  2. 2.0%
  3. 2.5%
  4. 3.0%
Show answer and explanation

Answer: (C) 2.5%

Surface tension is calculated by T = (r h ρ g) / 2. The relative error is ΔT/T = Δr/r + Δh/h. Here, Δr/r = 0.01 / 0.50 = 0.02 (2.0%) and Δh/h = 0.02 / 4.00 = 0.005 (0.5%). The maximum percentage error is 2.0% + 0.5% = 2.5%.

hard

3. A capillary tube has two unequal open ends: the upper part has an internal radius r₁ = 0.5 mm and the lower part immersed in water has an internal radius r₂ = 0.2 mm. If the water column reaches into the upper wider section, what is the capillary rise h measured up to the meniscus? (Take T = 0.070 N/m, ρ = 1000 kg/m³, g = 10 m/s², θ = 0°)

  1. 2.8 cm
  2. 1.4 cm
  3. 3.5 cm
  4. 7.0 cm
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Answer: (A) 2.8 cm

The pressure difference across the curved meniscus depends on the radius at the meniscus location itself. Since the meniscus forms in the upper section of radius r₁, the balancing condition gives h = (2 T cos θ)/(r₁ ρ g) = (2 × 0.070 × 1)/(0.5 × 10⁻³ × 1000 × 10) = 0.14 / 5 = 0.028 m = 2.8 cm.

medium

4. In a capillary rise experiment, the measured height h is 5.00 cm with a permissible error of ±0.05 cm, and the measured radius r of the tube is 0.100 mm with a permissible error of ±0.002 mm. Assuming the values of g and ρ are known with negligible error and contact angle θ = 0°, what is the maximum percentage error in the calculated value of surface tension T?

  1. 1.0%
  2. 3.0%
  3. 2.0%
  4. 4.0%
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Answer: (B) 3.0%

Surface tension is T = (r h ρ g) / 2. The relative error is ΔT/T = Δr/r + Δh/h. Percentage error = (0.002 / 0.100) × 100% + (0.05 / 5.00) × 100% = 2.0% + 1.0% = 3.0%.

easy

5. In a capillary tube experiment, how is the internal diameter of the capillary bore measured most accurately in the laboratory?

  1. By weighing the whole capillary tube before and after filling it with water on a spring balance
  2. By inserting a standard vernier caliper jaw directly inside the capillary bore
  3. By cutting the tube transversely and using a traveling microscope with horizontal and vertical crosswire displacement across two perpendicular diameters
  4. By measuring the outer diameter using a screw gauge and dividing the result by 2
Show answer and explanation

Answer: (C) By cutting the tube transversely and using a traveling microscope with horizontal and vertical crosswire displacement across two perpendicular diameters

The standard laboratory method involves breaking/cutting the capillary tube cleanly at the meniscus position, mounting it horizontally, and measuring two mutually perpendicular diameters of the circular bore using the crosswire of a traveling microscope to calculate the mean radius.

hard

6. A glass capillary tube is dipped in water, producing a rise h. If the entire apparatus is placed inside an elevator accelerating downwards with an acceleration a = g/4, and simultaneously a small amount of detergent is added that halves the surface tension without changing the contact angle (θ = 0°) or density, the new height of capillary rise will be:

  1. (4/3) h
  2. (3/4) h
  3. (2/3) h
  4. (1/2) h
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Answer: (C) (2/3) h

The capillary rise is governed by effective gravity: h' = (2 T' cos θ) / (r ρ g_eff). Here, g_eff = g - a = g - g/4 = 3g/4, and T' = T/2. Thus, h' = [2 (T/2) cos θ] / [r ρ (3g/4)] = (1/2) / (3/4) × [2 T cos θ / (r ρ g)] = (4/6) h = (2/3) h.

medium

7. Consider the following two statements regarding the capillary rise method: Statement I: The radius of the bore of the capillary tube must be determined at the exact position where the meniscus is formed. Statement II: If the bore of the capillary tube is non-uniform, the height of liquid rise depends exclusively on the radius at the bottom opening immersed in the liquid. Choose the correct option:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect

Capillary rise is governed by the pressure difference across the curved meniscus formed at the top of the liquid column. Therefore, the radius that determines the upward force is the radius at the position of the meniscus, not at the bottom opening. Statement I is correct and Statement II is incorrect.

medium

8. In a laboratory experiment to determine the surface tension of water using a traveling microscope, the vernier scale has 50 divisions matching 49 main scale divisions (1 MSD = 0.5 mm). The microscope is focused on the flat surface of water in the beaker and then on the lower meniscus in the capillary. If the main scale reading for the meniscus is 6.50 cm with a vernier coincidence of 24, and for the flat surface is 1.80 cm with a vernier coincidence of 14, what is the observed capillary rise h?

  1. 4.690 cm
  2. 4.800 cm
  3. 4.720 cm
  4. 4.710 cm
Show answer and explanation

Answer: (D) 4.710 cm

Least count = 1 MSD - 1 VSD = 0.5 mm - (49/50) × 0.5 mm = 0.5/50 mm = 0.01 mm = 0.001 cm. Reading for meniscus = 6.50 + 24 × 0.001 = 6.524 cm. Reading for flat surface = 1.80 + 14 × 0.001 = 1.814 cm. Capillary rise h = 6.524 - 1.814 = 4.710 cm.

medium

9. In an experiment to measure surface tension by capillary rise, the radius of the capillary tube is found to be 0.40 mm using a microscope. The height of water column is recorded as 3.60 cm. If the contact angle is 0° and density is 1000 kg/m³, the value of surface tension is: (Take g = 9.8 m/s²)

  1. 0.035 N/m
  2. 0.054 N/m
  3. 0.141 N/m
  4. 0.071 N/m
Show answer and explanation

Answer: (D) 0.071 N/m

Using the formula T = (r h ρ g)/(2 cos θ) with θ = 0°: T = (0.40 × 10⁻³ m × 0.036 m × 1000 kg/m³ × 9.8 m/s²) / 2 = (1.44 × 10⁻⁵ × 9800) / 2 = 0.14112 / 2 ≈ 0.0706 N/m ≈ 0.071 N/m.

medium

10. In a capillary rise setup, a capillary tube of internal radius r = 0.4 mm is held vertically in a beaker containing a detergent solution of density 1000 kg/m³. The liquid rises to a height of 2.0 cm, and the meniscus makes a contact angle of 60° with the tube wall. Taking g = 10 m/s², the surface tension of the detergent solution is:

  1. 0.010 N/m
  2. 0.040 N/m
  3. 0.020 N/m
  4. 0.080 N/m
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Answer: (D) 0.080 N/m

Using the relation T = (r · h · ρ · g) / (2 cos θ): r = 0.4 × 10⁻³ m, h = 2.0 × 10⁻² m, ρ = 1000 kg/m³, g = 10 m/s², and cos 60° = 0.5. T = (0.4 × 10⁻³ × 2.0 × 10⁻² × 1000 × 10) / (2 × 0.5) = (0.08) / 1.0 = 0.080 N/m.

medium

11. The capillary tube must be thoroughly clean before the experiment because grease or dirt would:

  1. Increase gravity
  2. Make the tube wider
  3. Have no effect
  4. Change the contact angle and surface tension, giving wrong results
Show answer and explanation

Answer: (D) Change the contact angle and surface tension, giving wrong results

Contamination alters the contact angle and the effective surface tension, changing the capillary rise and introducing error.

NCERT Class 11

hard

12. In a capillary rise setup, a capillary tube of uniform radius r is dipped into water. The potential energy stored in the elevated liquid column is U, and the total work done by the surface tension forces during the rise is W. Neglecting meniscus correction, the ratio U / W is:

  1. 1
  2. 1/4
  3. 1/2
  4. 2
Show answer and explanation

Answer: (C) 1/2

The work done by surface tension during the rise is W = Force × displacement = (2πr T) × h. Since h = 2T/(ρ g r), 2πr T = π r² ρ g h, so W = π r² ρ g h². The gravitational potential energy of the elevated column (mass m = π r² h ρ, center of mass at h/2) is U = m g (h/2) = (1/2) π r² ρ g h². Hence, U / W = 1/2. The remaining 50% is dissipated as heat due to viscous resistance.

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