Formula
Capillary rise
h = 2 T cos θ / (ρ g r), where θ is contact angle, r is capillary tube radius. Rises if θ < 90° (wetting), depresses if θ > 90° (e.g. mercury in glass).
-- NCERT Class 11 Physics, Ch. 9, p. 197Angle of Contact
8 MCQs3 revision cards9-step worked example
Source: NCERT Properties of Solids and LiquidsOfficial key: NTA-verifiedLast updated: 21 Sep 2026
Angle of Contact, explained for NEET
The angle of contact (θ) is the angle between the tangent to the liquid surface at the point of contact and the solid surface, measured inside the liquid. This single parameter decides whether a liquid wets a surface or not — and whether it rises or falls in a capillary tube.
Why it matters for capillary rise. The capillary-rise formula h = 2T cos θ / (ρgr) contains cos θ as a multiplier (NCERT Class 11 Physics, Chapter 9, page 194). When θ < 90°, cos θ is positive and the liquid rises (wetting). When θ > 90°, cos θ is negative and the liquid depresses (non-wetting). When θ = 90°, the meniscus is flat and there is no capillary rise at all.
The key facts NEET expects you to recall:
- Water–glass: θ ≈ 0° (strongly wetting, concave meniscus).
- Mercury–glass: θ ≈ 140° (non-wetting, convex meniscus).
- Pure water on clean silver: θ = 0° (complete wetting).
- The contact angle depends on the liquid-solid-gas triplet — change any one and θ changes.
Common confusion: Students treat the angle of contact as a property of the liquid alone. It is a property of the solid-liquid-gas interface together. Mercury on glass has θ ≈ 140°, but mercury on other surfaces can behave differently. Similarly, adding detergent to water changes θ because it alters the surface tension at the liquid-air interface.
Watch-out for meniscus shape questions. If θ < 90°, the meniscus is concave (edges curve up). If θ > 90°, the meniscus is convex (edges curve down). NEET sometimes gives you the meniscus shape and asks you to infer whether the liquid wets the surface.
Can you answer these Angle of Contact MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The angle of contact for water on a clean glass surface is approximately:
Show answer and why every option is right or wrong
Answer: B. Water on clean glass has nearly complete wetting. The contact angle is approximately 0° (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because θ = 90° would mean no wetting and no capillary rise, which contradicts the well-known rise of water in glass capillaries.
Why C is wrong: C is wrong because θ ≈ 140° is the contact angle for mercury on glass (non-wetting), not water on glass.
Why D is wrong: D is wrong because 60° is not the standard NCERT value for the water-glass contact angle. The correct value is approximately 0°.
MCQ 2Easy RecallPractice
The angle of contact is measured between the tangent to the liquid surface at the point of contact and the solid surface. This angle is measured:
Show answer and why every option is right or wrong
Answer: D. By definition, the angle of contact is always measured through the liquid — i.e., inside the liquid (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because measuring outside the liquid would give the supplementary angle, not the contact angle as defined in NCERT.
Why B is wrong: B is wrong because the convention for measuring the angle of contact does not change with wetting behaviour. It is always measured inside the liquid.
Why C is wrong: C is wrong because the angle of contact is between the tangent to the liquid surface and the solid surface, not measured along the solid surface alone.
MCQ 3Easy RecallPractice
The contact angle for mercury on glass is approximately:
Show answer and why every option is right or wrong
Answer: A. Mercury does not wet glass. Its contact angle is approximately 140° (NCERT Class 11 Physics, Chapter 9, page 194).
Why B is wrong: B is wrong because θ = 90° would give a flat meniscus and zero capillary effect. Mercury on glass shows clear capillary depression, indicating θ > 90°.
Why C is wrong: C is wrong because θ ≈ 0° describes complete wetting (e.g., water on clean glass), not mercury on glass.
Why D is wrong: D is wrong because θ = 180° would mean perfectly non-wetting with no adhesion at all. Mercury on glass has θ ≈ 140°, not 180°.
MCQ 4Direct ApplicationPractice
A liquid in a capillary tube shows a convex meniscus. Which of the following is true about its angle of contact?
Show answer and why every option is right or wrong
Answer: D. A convex meniscus (edges curving downward) indicates that cohesive forces dominate over adhesive forces, so the liquid does not wet the surface and θ > 90° (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because θ = 0° corresponds to complete wetting and a strongly concave meniscus, not a convex one.
Why B is wrong: B is wrong because θ < 90° produces a concave meniscus (liquid wets the surface and rises). A convex meniscus requires θ > 90°.
Why C is wrong: C is wrong because θ = 90° gives a flat meniscus (neither concave nor convex), not a convex shape.
MCQ 5Direct ApplicationPractice
In the capillary-rise formula h = 2T cos θ / (ρgr), if the angle of contact is exactly 90°, the capillary rise h equals:
Show answer and why every option is right or wrong
Answer: A. When θ = 90°, cos 90° = 0, so h = 2T × 0 / (ρgr) = 0. There is no capillary rise or depression (NCERT Class 11 Physics, Chapter 9, page 194).
Why B is wrong: B is wrong because depression requires θ > 90° so that cos θ < 0. At exactly 90°, cos θ = 0 and h = 0.
Why C is wrong: C is wrong because maximum rise occurs when θ = 0° (cos 0° = 1), not when θ = 90°.
Why D is wrong: D is wrong because infinity would require r → 0 in the denominator, not θ = 90°. cos 90° = 0 makes h = 0.
MCQ 6Direct ApplicationPractice
A student observes that a liquid rises in a capillary tube. Adding a small amount of detergent to the liquid is found to decrease the surface tension. If the contact angle remains approximately the same, the new capillary rise will:
Show answer and why every option is right or wrong
Answer: B. From h = 2T cos θ / (ρgr), if θ, ρ, g, and r are unchanged and T decreases, h decreases proportionally (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because h is directly proportional to T. Decreasing T decreases h, not increases it.
Why C is wrong: C is wrong because h depends on T. A reduction in surface tension directly reduces the capillary rise.
Why D is wrong: D is wrong because h becomes zero only if T = 0 or cos θ = 0. Detergent reduces T but does not eliminate it entirely.
MCQ 7Concept TrapPractice
The angle of contact of a liquid on a solid surface depends on:
Show answer and why every option is right or wrong
Answer: C. The contact angle is determined by the balance of cohesive (liquid-liquid), adhesive (liquid-solid), and liquid-gas surface forces. All three phases matter — changing the solid, the liquid, or the surrounding gas/vapour changes θ (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because the same liquid (e.g., water) has different contact angles on glass versus wax, so the solid matters too.
Why B is wrong: B is wrong because the same solid (e.g., glass) has different contact angles with water versus mercury, so the liquid matters too.
Why D is wrong: D is wrong because although temperature can affect θ (by changing surface tension), it is not the sole determining factor. The solid-liquid-gas combination is the primary determinant.
MCQ 8Concept TrapPractice
A liquid has a contact angle of 120° with a particular solid. In a capillary tube made of this solid, the liquid will:
Show answer and why every option is right or wrong
Answer: C. θ = 120° > 90°, so cos 120° = −0.5, which makes h negative in h = 2T cos θ / (ρgr). A negative h means capillary depression. The meniscus is convex because θ > 90° (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A is wrong because a concave meniscus and capillary rise occur only when θ < 90° (wetting liquid). θ = 120° is non-wetting.
Why B is wrong: B is wrong because the liquid neither rises nor falls only when θ = 90° (cos θ = 0). At θ = 120°, cos θ = −0.5 ≠ 0.
Why D is wrong: D is wrong because a convex meniscus correctly indicates θ > 90°, but such a liquid depresses (falls), not rises. Rise requires cos θ > 0.
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Angle of Contact: quick recall before you leave
How do you solve a Angle of Contact question? A worked example
- 1
Given
A capillary tube of radius r = 0.50 mm = 5.0 × 10⁻⁴ m is dipped in a liquid of surface tension T = 7.0 × 10⁻² N/m and density ρ = 1.0 × 10³ kg/m³. The angle of contact is θ = 0°. Take g = 9.8 m/s² (exact for this problem).
- 2
Required
Find the capillary rise h.
- 3
Concept
Capillary rise is governed by the balance between upward surface-tension force along the contact perimeter and the downward weight of the liquid column. The formula h = 2T cos θ / (ρgr) captures this balance.
- 4
Formula
h = 2T cos θ / (ρgr)
- 5
Substitution
h = 2 × (7.0 × 10⁻²) × cos 0° / (1.0 × 10³ × 9.8 × 5.0 × 10⁻⁴)
- 6
Calculation
Numerator: 2 × 7.0 × 10⁻² × 1 = 1.4 × 10⁻¹ = 0.14
Denominator: 1.0 × 10³ × 9.8 × 5.0 × 10⁻⁴ = 4.9
h = 0.14 / 4.9 = 2.857 × 10⁻² m
Note: g = 9.8 m/s² is treated as exact (problem-defined), and cos 0° = 1 is exact. The limiting significant figures come from T (2 sig figs), ρ (2 sig figs), and r (2 sig figs), so the answer is reported to 2 significant figures. - 7
Final answer
h ≈ 2.9 × 10⁻² m ≈ 2.9 cm
- 8
Common trap
If the problem changed to θ = 140° (mercury on glass), students must remember that cos 140° ≈ −0.766, making h negative — the liquid depresses rather than rises. Forgetting to check the sign of cos θ is a frequent error.
- 9
Similar NEET-style question
A capillary tube of radius 0.40 mm is dipped in mercury (T = 0.49 N/m, ρ = 1.36 × 10⁴ kg/m³, θ = 140°). Find the capillary depression. [Answer: apply the same formula; cos 140° ≈ −0.766 gives a negative h, indicating depression.]
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What to remember before solving Angle of Contact questions
Which Angle of Contact formulas do you need for NEET?
1 formula — click to collapse
Capillary rise/depression
Height a liquid rises (or falls) in a capillary tube. cos(theta) > 0: rises (wetting); < 0: depresses.
| Symbol | Quantity | SI Unit |
|---|---|---|
| h | capillary height | m |
| T | surface tension | N/m |
| theta | contact angle | rad |
| rho | density | kg/m^3 |
| r | tube radius | m |
Valid when
- Narrow tube (capillary regime)
- Constant theta
More in Properties of Bulk Matter: 5 exam traps and mistakes · 11 formulas · 5 question patterns from its other lessons.
Angle of Contact questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
All 17 past-paper questions from Properties of Bulk Matter →
Sources
NCERT refs: Class 11 Physics Chapter 9, p.194
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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