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Surface energy, surface tension, contact angle, drops, bubbles and capillarity: NEET MCQs with answers

75 questions on this topic of Properties of Solids and Liquids (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. A capillary tube with an internal bore of radius r is dipped vertically into a liquid of density ρ, surface tension T, and angle of contact θ. If the liquid rises to a vertical height h, what is the vertical height along the length of the tube if the tube is tilted at an angle α with the vertical?

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

The vertical height h = (2T cos θ) / (ρ g r) of the liquid column remains constant regardless of inclination. If the length of the column along the tube is l and it is inclined at an angle α to the vertical, then h = l cos α, which gives l = h / cos α.

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2. A capillary tube is immersed vertically in a liquid in an elevator. If the elevator accelerates vertically downwards with an acceleration a = g/3, the height to which the liquid rises in the tube compared to its height h₀ when stationary will be:

  1. h₀ / 2
  2. 2h₀ / 3
  3. 4h₀ / 3
  4. 3h₀ / 2
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Answer: (D) 3h₀ / 2

The height of capillary rise is h = (2T cos θ)/(r ρ g_eff). When accelerating downwards with a = g/3, the effective gravity is g_eff = g - a = 2g/3. Therefore, h = (2T cos θ)/(r ρ (2g/3)) = (3/2) h₀.

hard

3. Two spherical soap bubbles of radii R₁ and R₂ are placed in vacuum. Under isothermal conditions, if they combine without loss of air to form a single spherical bubble of radius R, then R is given by:

  1. R = R₁ + R₂
  2. R = (R₁⁴ + R₂⁴)^(1/4)
  3. R = (R₁³ + R₂³)^(1/3)
  4. R = √(R₁² + R₂²)
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Answer: (D) R = √(R₁² + R₂²)

Inside a bubble in vacuum, the absolute pressure is P = 4T/r. By Boyle's law at constant temperature, P₁V₁ + P₂V₂ = PV. Since V = (4/3)πr³, we have (4T/R₁)(4/3 π R₁³) + (4T/R₂)(4/3 π R₂³) = (4T/R)(4/3 π R³), which simplifies directly to R₁² + R₂² = R², or R = √(R₁² + R₂²).

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4. The excess pressure inside a soap bubble of radius 5 cm, made of a liquid with surface tension 0.02 N/m, is:

  1. 3.2 Pa
  2. 1.6 Pa
  3. 0.8 Pa
  4. 0.4 Pa
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Answer: (B) 1.6 Pa

A soap bubble has two surfaces: ΔP = 4T/r = 4 × 0.02/0.05 = 1.6 Pa.

easy

5. A liquid wets a solid completely. The angle of contact between this liquid and the solid surface is:

  1. 90°
  2. 45°
  3. 0°
  4. 135°
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Answer: (C) 0°

When a liquid completely wets a solid surface, the adhesive forces between liquid and solid molecules dominate completely over cohesive forces, making the contact angle equal to 0° (or nearly 0°, as in the pure water-clean glass system).

hard

6. A uniform thin glass rod of radius r and length L is dipped vertically to a depth d in a liquid of density ρ, surface tension T, and angle of contact θ. What is the net downward force exerted by the liquid on the rod?

  1. 2π r T sin θ - π r² d ρ g
  2. 2π r T cos θ + π r² d ρ g
  3. 2π r T cos θ - π r² d ρ g
  4. 2π r T cos θ
Show answer and explanation

Answer: (C) 2π r T cos θ - π r² d ρ g

The liquid exerts an upward buoyant force F_B = (π r² d) ρ g due to displaced volume, and a vertical surface tension force. Along the perimeter of contact, surface tension acts along the meniscus at angle θ to the vertical wall, pulling the rod downwards with force F_ST = (2π r) T cos θ. Hence, the net downward force is F_net = F_ST - F_B = 2π r T cos θ - π r² d ρ g.

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7. The excess pressure inside a soap bubble of radius 5 cm, made of a liquid with surface tension 0.05 N/m, is:

  1. 2 Pa
  2. 1 Pa
  3. 8 Pa
  4. 4 Pa
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Answer: (D) 4 Pa

A soap bubble has two surfaces: ΔP = 4T/r = 4 × 0.05/0.05 = 4 Pa.

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8. The excess pressure inside a soap bubble of radius 4 cm, made of a liquid with surface tension 0.02 N/m, is:

  1. 1 Pa
  2. 4 Pa
  3. 2 Pa
  4. 0.5 Pa
Show answer and explanation

Answer: (C) 2 Pa

A soap bubble has two surfaces: ΔP = 4T/r = 4 × 0.02/0.04 = 2 Pa.

hard

9. When a clean capillary tube is placed vertically in water, the water column rises to a height h. If the potential energy of the raised water column is U, then the total mechanical work done by the force of surface tension during this rise is:

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

The total upward force due to surface tension is F = 2πrT. The distance through which this force acts is h, so the work done by surface tension is W = F · h = (2πrT)h. Since h = 2T/(rρg), we have 2πrT = πr²hρg = mg. Hence, W = mgh. Meanwhile, the center of mass of the liquid column rises by h/2, giving a potential energy U = mg(h/2). Therefore, W = 2U.

easy

10. A glass capillary tube of length 12 cm is dipped vertically into water. Water normally rises to a height of 15 cm in this capillary. What happens to the water column in the tube?

  1. Water overflows continuously from the top end.
  2. Water fountains out up to a height of 3 cm above the top.
  3. Water rises up to 6 cm and stays there.
  4. Water rises up to the top (12 cm) and forms a meniscus of larger radius of curvature without overflowing.
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Answer: (D) Water rises up to the top (12 cm) and forms a meniscus of larger radius of curvature without overflowing.

When the length of the capillary tube is insufficient (l < h), water rises to the very top of the tube and adjusts the curvature of its meniscus such that h₁ R₁ = h₂ R₂. Since the radius of curvature increases, the meniscus becomes flatter and water does not overflow.

easy

11. The angle of contact between a liquid and a solid depends primarily on:

  1. The angle of inclination of the solid surface to the liquid surface
  2. The nature of the liquid and the solid in contact
  3. The radius of the capillary tube
  4. The volume of the liquid taken
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Answer: (B) The nature of the liquid and the solid in contact

The angle of contact is a characteristic property of a given solid-liquid-medium interface. It depends on the adhesive forces between liquid and solid molecules relative to the cohesive forces between liquid molecules, as well as impurities and temperature, but is independent of the inclination of the wall or the dimensions of the vessel.

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12. The excess pressure inside a soap bubble of radius 2 cm, made of a liquid with surface tension 0.05 N/m, is:

  1. 10 Pa
  2. 20 Pa
  3. 5 Pa
  4. 2.5 Pa
Show answer and explanation

Answer: (A) 10 Pa

A soap bubble has two surfaces: ΔP = 4T/r = 4 × 0.05/0.02 = 10 Pa.

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