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. 197Capillary Rise
8 MCQs6 revision cards9-step worked example
Source: NCERT Properties of Solids and LiquidsPYQ coverage: NEET 2020Official key: NTA-verifiedLast updated: 25 Sep 2026
Capillary Rise, explained for NEET
Surface tension applications — drops, bubbles, and capillary rise
The high-frequency trap in this topic is confusing the factor in the excess-pressure formula: drops have one free surface (ΔP = 2T/r), soap bubbles have two (ΔP = 4T/r), and an air bubble inside a liquid has one surface again (ΔP = 2T/r). NEET has tested this distinction repeatedly (2022, 2023, 2025).
Excess pressure inside curved surfaces. A spherical liquid drop in air encloses fluid behind a single curved surface. The inward pull of surface tension creates an excess internal pressure ΔP = 2T/r, where T is surface tension and r is the drop radius. A soap bubble floating in air, however, has an inner surface and an outer surface — both contribute, giving ΔP = 4T/r. An air bubble trapped inside a liquid has only the liquid-air interface (one surface), so it follows the drop formula: 2T/r. This three-way classification is the direct source of wrong options in NEET (NCERT Class 11 Physics, Chapter 9, page 193).
Capillary rise. When a narrow tube is dipped into a liquid, the liquid rises (or depresses) by:
h = 2T cos θ / (ρgr)
where θ is the contact angle, ρ is the liquid density, and r is the tube radius (NCERT Class 11 Physics, Chapter 9, page 194). For water-glass (θ ≈ 0°, cos θ = 1), the liquid rises. For mercury-glass (θ > 90°, cos θ < 0), the meniscus depresses. Smaller radius → greater rise — this inverse proportionality (h ∝ 1/r) is a common numerical test point.
Watch out: When a problem says "bubble," identify which kind — soap bubble in air (two surfaces, factor 4) or air bubble in liquid (one surface, factor 2). The word "bubble" alone is the trigger for this trap.
Can you answer these Capillary Rise MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Direct ApplicationPractice
Water (surface tension 0.072 N/m, angle of contact 0°, density 1000 kg/m³) rises in a clean glass capillary of radius 0.10 mm. Taking g = 10 m/s², the height of the water column is:
Show answer and why every option is right or wrong
Answer: C. C is correct. The surface tension acting round the rim of the meniscus supports the raised column: h = 2T cosθ/(rρg) = (2 × 0.072 × 1)/(1.0 × 10⁻⁴ × 1000 × 10) = 0.144 m = 14.4 cm.
Why A is wrong: A is wrong because 7.2 cm drops the factor of 2 in h = 2T cosθ/(rρg), which is the same result as using the diameter, 0.20 mm, in place of the radius.
Why B is wrong: B is wrong because 28.8 cm uses 4T, the factor from the excess pressure in a SOAP BUBBLE, which has two surfaces. A meniscus in a capillary has one.
Why D is wrong: D is wrong because 1.44 cm takes the radius as 1.0 mm instead of 0.10 mm, a slip in converting millimetres to metres.
MCQ 2Concept TrapPractice
Water rises to a height h in a capillary tube. If a tube of the same glass but half the radius is used, the water rises to:
Show answer and why every option is right or wrong
Answer: C. C is correct. h = 2T cosθ/(rρg), and nothing but r changes, so h ∝ 1/r. Halving the radius doubles the rise: the supporting force round the rim falls in proportion to r, but the weight of liquid to be held up falls in proportion to r².
Why A is wrong: A is wrong because h/2 has the height going WITH the radius. Narrower tubes lift liquid higher, which is why capillary action matters most in fine pores.
Why B is wrong: B is wrong because 4h makes h go as 1/r². The weight of the column goes as r², but the supporting surface-tension force goes as r, which leaves h ∝ 1/r.
Why D is wrong: D is wrong because h assumes the rise depends only on the liquid and the glass. The radius enters the formula directly.
MCQ 3Easy RecallPractice
Water rises in a glass capillary tube because the contact angle θ between water and glass satisfies:
Show answer and why every option is right or wrong
Answer: B. When θ < 90°, cos θ > 0, so h = 2T cos θ/(ρgr) is positive — the liquid rises (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A. At θ = 90°, cos θ = 0, giving h = 0 — no rise or depression occurs.
Why C is wrong: C. When θ > 90°, cos θ < 0, so h is negative — the liquid depresses (as mercury does in glass).
Why D is wrong: D. At θ = 180°, cos θ = −1, which gives maximum depression, not rise.
MCQ 4Direct ApplicationPractice
A capillary tube of radius 0.5 mm is dipped in water (surface tension T = 7.0 × 10⁻² N/m, density ρ = 1.0 × 10³ kg/m³, contact angle θ = 0°). Taking g = 10 m/s² (exact), the height of capillary rise is:
Show answer and why every option is right or wrong
Answer: D. h = 2T cos θ/(ρgr) = 2 × 7.0 × 10⁻² × 1 / (1.0 × 10³ × 10 × 5.0 × 10⁻⁴) = 0.14/5.0 = 2.8 × 10⁻² m = 2.8 cm.
Why A is wrong: A. 1.4 cm results from using T/r instead of 2T/r — forgetting the factor of 2 in the capillary rise formula.
Why B is wrong: B. 0.28 cm results from converting 0.5 mm as 5.0 × 10⁻³ m (treating it as 0.5 cm), making the radius ten times too large and the rise ten times too small.
Why C is wrong: C. 5.6 cm results from using 4T/r (the soap-bubble formula) instead of 2T cos θ/(ρgr). Capillary rise uses the single-surface derivation.
MCQ 5Concept TrapPractice
When a glass capillary is dipped into mercury, the mercury level inside the tube is LOWER than outside. The reason is that:
Show answer and why every option is right or wrong
Answer: A. A is correct. In h = 2T cosθ/(rρg), the sign of h is set by cosθ. Mercury does not wet glass (its angle of contact is about 140°), so cosθ is negative and h is negative: a depression instead of a rise.
Why B is wrong: B is wrong because a larger density only makes the MAGNITUDE of the rise or fall smaller. Density is always positive, so it cannot turn a rise into a fall.
Why C is wrong: C is wrong because mercury's surface tension, about 0.47 N/m, is actually much LARGER than water's. The depression comes from the contact angle, not from a weaker surface tension.
Why D is wrong: D is wrong because every liquid surface has surface tension. Not wetting the glass means a large angle of contact, and it is that angle that produces the depression.
MCQ 6Direct ApplicationPractice
Two capillary tubes of radii r and 2r are dipped in the same liquid. If h₁ and h₂ are the respective heights of rise, then h₁/h₂ is:
Show answer and why every option is right or wrong
Answer: A. From h = 2T cos θ/(ρgr), h is inversely proportional to r. So h₁/h₂ = (2r)/r = 2.
Why B is wrong: B. 1 implies h is independent of r, which contradicts the capillary rise formula.
Why C is wrong: C. 1/2 results from assuming h is directly proportional to r (h ∝ r), which is the inverse of the correct relationship.
Why D is wrong: D. 4 results from assuming h ∝ 1/r², which would be the case if the formula had r² in the denominator — it does not.
MCQ 7Concept TrapPractice
An air bubble of radius r is formed inside a liquid of surface tension T. The excess pressure inside this bubble compared to the surrounding liquid is:
Show answer and why every option is right or wrong
Answer: D. An air bubble inside a liquid has only one interface (liquid-air), so ΔP = 2T/r — the same as a liquid drop, not a soap bubble (NCERT Class 11 Physics, Chapter 9, page 193).
Why A is wrong: A. 4T/r is for a soap bubble in air (two surfaces). An air bubble in liquid has only one surface. This is the core bubble-vs-drop trap.
Why B is wrong: B. There is always excess pressure on the concave side of a curved interface due to surface tension — it is never zero for a finite bubble.
Why C is wrong: C. T/r is not the formula for any standard surface-tension configuration.
MCQ 8CalculationPractice
A soap bubble of radius 2.0 cm has surface tension T = 3.0 × 10⁻² N/m. The excess pressure inside the bubble and the total work done in forming it from flat film are, respectively:
Show answer and why every option is right or wrong
Answer: B. Soap bubble: ΔP = 4T/r = 4 × 3.0 × 10⁻² / 2.0 × 10⁻² = 6.0 Pa. Work = T × 2 × 4πR² = 3.0 × 10⁻² × 2 × 4π × (2.0 × 10⁻²)² = 3.0 × 10⁻² × 2 × 4π × 4.0 × 10⁻⁴ = 3.0 × 10⁻² × 1.005 × 10⁻² ≈ 3.0 × 10⁻⁴ J.
Why A is wrong: A. 3.0 Pa uses 2T/r (drop formula) instead of 4T/r (bubble formula). The work happens to match because of the numbers, but the pressure is wrong — a soap bubble has two surfaces.
Why C is wrong: C. 6.0 Pa is correct for pressure, but 6.0 × 10⁻⁴ J doubles the work — this error arises from counting four surfaces instead of two.
Why D is wrong: D. Both values are wrong: 3.0 Pa uses the drop formula for pressure, and 6.0 × 10⁻⁴ J overcounts surfaces for work.
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Capillary Rise: quick recall before you leave
How do you solve a Capillary Rise question? A worked example
- 1
Given
• Tube radius: r = 1.0 × 10⁻³ m (the same tube in both parts)• Mercury: T = 0.465 N/m, θ = 140°, ρ = 13.6 × 10³ kg/m³• Water: T = 7.3 × 10⁻² N/m, θ = 0°, ρ = 1.0 × 10³ kg/m³• g = 9.8 m/s²
- 2
Required
(a) The height h of mercury in the tube, with its sign.
(b) The height h of water in the same tube, and the reason the two differ. - 3
Concept
Surface tension pulls on the liquid along the line where it meets the glass, and the vertical part of that pull supports (or hangs) a column of liquid. Balancing it against the column's weight gives h ρ g = 2T cos θ / r (NCERT Class 11 Physics, Chapter 9, page 197).
Everything in that expression is positive except cos θ. A liquid that wets the glass has θ < 90°, so cos θ > 0 and h comes out positive — the liquid RISES. A liquid that does not wet it has θ > 90°, so cos θ < 0 and h comes out negative — the liquid is DEPRESSED. The sign is not a separate rule to memorise; it is already in the formula. - 4
Formula
h = 2T cos θ / (ρ g r)
- 5
Substitution
(a) Mercury: h = 2 × 0.465 × cos 140° / (13.6 × 10³ × 9.8 × 1.0 × 10⁻³)
(b) Water: h = 2 × 7.3 × 10⁻² × cos 0° / (1.0 × 10³ × 9.8 × 1.0 × 10⁻³) - 6
Calculation
(a) cos 140° = −0.766, so the numerator is 2 × 0.465 × (−0.766) = −0.712 N/m.
The denominator is 13.6 × 10³ × 9.8 × 1.0 × 10⁻³ = 133.3 N/m³ × m.
h = −0.712 / 133.3 = −5.34 × 10⁻³ m = −5.3 mm
(b) cos 0° = 1, so the numerator is 2 × 7.3 × 10⁻² × 1 = 0.146 N/m.
The denominator is 1.0 × 10³ × 9.8 × 1.0 × 10⁻³ = 9.80 N/m³ × m.
h = 0.146 / 9.80 = 1.49 × 10⁻² m = 14.9 mm
Note on exact values: cos 0° = 1 and the factor 2 in the formula are exact, and g is problem-defined. The two-significant-figure radius sets the precision. - 7
Final answer
(a) h = −5.3 mm — the mercury stands 5.3 mm BELOW the outside level.
(b) h = +14.9 mm — the water stands 14.9 mm above it.
Same tube, opposite results, and the whole difference is the sign of cos θ: mercury does not wet glass (θ = 140°, cos θ negative), water does (θ = 0°, cos θ positive). The larger surface tension of mercury does not win — it makes the depression deeper, not a rise. - 8
Common trap
The usual mistake is to drop the cos θ and compute 2T/(ρgr), which for mercury gives +7.0 mm — the right size, the wrong sign, and the wrong physics. It reports mercury climbing a glass tube, which is the opposite of what anyone has ever seen it do. If an answer for mercury in glass comes out positive, the cos θ has gone missing.
- 9
Similar NEET-style question
Water rises 6.0 cm in a capillary tube. The tube is broken so that only 4.0 cm of it stands above the water surface. Does the water overflow? Approach: it cannot rise past the end, and it does not spill. The column stops at 4.0 cm and the meniscus flattens instead — the radius of curvature increases until 2T cos θ / R balances the shorter column. Surface tension supplies whatever curvature the situation needs, up to its maximum.
What to remember before solving Capillary Rise questions
Which Capillary Rise 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.
Capillary Rise questions from past NEET papers
1 question from NEET 2020. Answers verified against NTA official keys. — click to collapse
NEET 2020
120.0 g
22.5 g
35.0 g
410.0 g
NTA Answer: Option 4(final)
All 17 past-paper questions from Properties of Bulk Matter →
Sources
NCERT refs: Class 11 Physics Chapter 9, p.193 | 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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