Liquid drop: ΔP = 2T/r (one surface). Soap bubble: ΔP = 4T/r (two surfaces). Smaller drops have higher internal pressure.
-- NCERT Class 11 Physics, Ch. 9, p. 196Excess Pressure Curved Surface
8 MCQs6 revision cards9-step worked example
Source: NCERT Properties of Solids and LiquidsPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 26 Sep 2026
Excess Pressure Curved Surface, explained for NEET
The single highest-frequency trap in this topic is confusing the factor of 2 with the factor of 4 in the excess pressure formula. If you use 2T/r for a soap bubble, you lose the mark and gain a negative — every time.
The core idea. A curved liquid surface under surface tension generates an excess pressure on the concave side. For a spherical liquid drop in air, the surface has one free boundary, giving excess pressure ΔP = 2T/r (NCERT Class 11 Physics, Chapter 9, page 196). For a soap bubble in air, there are two surfaces — an inner surface and an outer surface — so the excess pressure doubles to ΔP = 4T/r.
Why two surfaces for a bubble? A liquid drop is a solid sphere of liquid bounded by one air-liquid interface. A soap bubble is a thin film enclosing air; the film has an inner air-liquid interface and an outer air-liquid interface. Each interface contributes 2T/r, totalling 4T/r.
Air bubble inside a liquid is the third case NEET likes to test. An air bubble submerged in water has only one interface (air inside, liquid outside) — so it behaves like a drop: ΔP = 2T/r.
Summary of the three cases:
| Geometry | Number of surfaces | Excess pressure |
|---|---|---|
| Liquid drop in air | 1 | 2T/r |
| Air bubble in liquid | 1 | 2T/r |
| Soap bubble in air | 2 | 4T/r |
Watch-out: When a problem says "bubble," check whether it is a soap bubble (in air, thin film) or an air bubble (submerged in liquid). The word "bubble" alone is not enough — the context decides the factor.
Can you answer these Excess Pressure Curved Surface 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 excess pressure inside a soap bubble of radius r and surface tension T is:
Show answer and why every option is right or wrong
Answer: B. A soap bubble has two surfaces (inner and outer), each contributing 2T/r. Total excess pressure = 4T/r (NCERT Class 11 Physics, Chapter 9, page 196).
Why A is wrong: A. T/r has no physical basis in the excess pressure derivation — neither a single surface nor two surfaces yield this result.
Why C is wrong: C. 2T/r is the formula for a liquid drop or an air bubble in liquid (one surface). A soap bubble has two surfaces, so the factor is 4, not 2. (Trap: confusing drop and bubble formulas.)
Why D is wrong: D. 8T/r would require four surfaces, which no standard geometry has. This has no physical basis.
MCQ 2Easy RecallPractice
The excess pressure inside a spherical liquid drop of radius r in air is:
Show answer and why every option is right or wrong
Answer: B. A liquid drop in air has one air-liquid interface. The excess pressure due to surface tension across one spherical surface is 2T/r (NCERT Class 11 Physics, Chapter 9, page 196).
Why A is wrong: A. 4T/r applies to a soap bubble (two surfaces), not a liquid drop (one surface). (Trap: applying the bubble formula to a drop.)
Why C is wrong: C. T/r is half the correct value. The Laplace pressure for a sphere involves 2T/r, not T/r.
Why D is wrong: D. T/2r further halves the incorrect T/r result — no standard geometry gives this.
MCQ 3Easy RecallPractice
An air bubble is trapped inside water. The number of free surfaces contributing to excess pressure inside this bubble is:
Show answer and why every option is right or wrong
Answer: C. An air bubble submerged in liquid has one interface — the boundary between the air inside and the surrounding liquid. Hence one surface contributes, and ΔP = 2T/r (NCERT Class 11 Physics, Chapter 9, page 197).
Why A is wrong: A. Zero surfaces would mean no excess pressure at all, which contradicts the existence of surface tension at any curved interface.
Why B is wrong: B. Two surfaces apply to a soap bubble (thin film with inner and outer surfaces). An air bubble in liquid is not a thin film — it is a single air-liquid boundary. (Trap: confusing air bubble in liquid with soap bubble in air.)
Why D is wrong: D. Three surfaces has no physical basis for any standard geometry studied in this chapter.
MCQ 4Direct ApplicationPractice
A soap bubble has radius 1.0 × 10⁻² m and the surface tension of the soap solution is 2.5 × 10⁻² N/m. The excess pressure inside the bubble is:
Show answer and why every option is right or wrong
Answer: A. Soap bubble: ΔP = 4T/r = 4 × 2.5 × 10⁻² / 1.0 × 10⁻² = 10 Pa (NCERT Class 11 Physics, Chapter 9, page 196).
Why B is wrong: B. 5.0 Pa results from using 2T/r — the drop formula instead of the bubble formula. A soap bubble has two surfaces, requiring 4T/r. (Trap: using the drop formula for a bubble.)
Why C is wrong: C. 2.5 Pa results from using T/r, which is not the correct formula for any standard geometry.
Why D is wrong: D. 20 Pa results from using 8T/r, which would require four surfaces — no standard geometry gives this.
MCQ 5Direct ApplicationPractice
A spherical liquid drop of radius 5.0 × 10⁻³ m is formed from a liquid with surface tension 7.0 × 10⁻² N/m. The excess pressure inside the drop is:
Show answer and why every option is right or wrong
Answer: D. Liquid drop: ΔP = 2T/r = 2 × 7.0 × 10⁻² / 5.0 × 10⁻³ = 28 Pa (NCERT Class 11 Physics, Chapter 9, page 196).
Why A is wrong: A. 14 Pa results from using T/r instead of 2T/r, missing the factor of 2 from the Laplace equation for a single spherical surface.
Why B is wrong: B. 7.0 Pa results from using T/2r, which has no physical basis.
Why C is wrong: C. 56 Pa results from using 4T/r — the soap-bubble formula. A liquid drop has only one surface, so the correct factor is 2, not 4. (Trap: applying the bubble formula to a drop.)
MCQ 6Direct ApplicationPractice
Two soap bubbles of radii r and 2r are made from the same soap solution. The ratio of excess pressure inside the smaller bubble to that inside the larger bubble is:
Show answer and why every option is right or wrong
Answer: A. For both bubbles, ΔP = 4T/r_i. Ratio = (4T/r) / (4T/2r) = 2r/r = 2 : 1. Smaller bubble has higher excess pressure (NCERT Class 11 Physics, Chapter 9, page 196).
Why B is wrong: B. 1 : 2 inverts the ratio — the smaller bubble has the higher excess pressure because ΔP ∝ 1/r, not ΔP ∝ r.
Why C is wrong: C. 1 : 4 would arise if ΔP ∝ r², which is incorrect. Excess pressure is inversely proportional to radius.
Why D is wrong: D. 4 : 1 would arise if ΔP ∝ 1/r², but the relationship is ΔP ∝ 1/r. The ratio of radii is 1 : 2, so the pressure ratio is 2 : 1, not 4 : 1.
MCQ 7CalculationPractice
A soap bubble of radius 1.0 × 10⁻² m is blown further until its radius becomes 2.0 × 10⁻² m. If the surface tension is 3.0 × 10⁻² N/m, the change in excess pressure is:
Show answer and why every option is right or wrong
Answer: D. Initial ΔP₁ = 4T/r₁ = 4 × 3.0 × 10⁻² / 1.0 × 10⁻² = 12 Pa. Final ΔP₂ = 4T/r₂ = 4 × 3.0 × 10⁻² / 2.0 × 10⁻² = 6.0 Pa. Change = 12 − 6.0 = 6.0 Pa decrease (larger radius → lower excess pressure) (NCERT Class 11 Physics, Chapter 9, page 196).
Why A is wrong: A. Both the magnitude and direction are wrong — the pressure decreases (not increases) and the change is 6.0 Pa, not 12 Pa.
Why B is wrong: B. The excess pressure decreases when radius increases (ΔP ∝ 1/r). It does not increase.
Why C is wrong: C. 12 Pa would be the change only if the final excess pressure were zero, which is not the case for a finite-radius bubble.
MCQ 8CalculationPractice
A soap bubble of radius R is formed. The total work done against surface tension is W. If a second bubble of radius 2R is formed from the same solution, the work done is:
Show answer and why every option is right or wrong
Answer: C. Work done to form a soap bubble = surface tension × total surface area = T × 2 × 4πR² = 8πR²T (two surfaces). For radius 2R: W₂ = T × 2 × 4π(2R)² = 32πR²T. Ratio W₂/W₁ = 32πR²T / 8πR²T = 4. So W₂ = 4W (NCERT Class 11 Physics, Chapter 9, page 194).
Why A is wrong: A. 2W would be correct if work scaled linearly with radius (W ∝ R), but work is proportional to surface area, which scales as R². Doubling R quadruples the area.
Why B is wrong: B. W/2 inverts the relationship — a larger bubble requires more work, not less.
Why D is wrong: D. W/4 inverts the scaling — the larger bubble has 4 times the surface area and thus requires 4 times the work, not one-quarter.
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Excess Pressure Curved Surface: quick recall before you leave
How do you solve a Excess Pressure Curved Surface question? A worked example
Pattern: Excess pressure / surface energy of a soap bubble (aligned with PYQ pattern NEET pattern: surface tension bubble — observed in NEET 2022, 2023, 2025).
- 1
Given
A soap bubble of radius r = 5.0 × 10⁻³ m is formed from a soap solution with surface tension T = 4.0 × 10⁻² N/m.
- 2
Required
(a) Excess pressure inside the bubble.
(b) Work done in forming the bubble from a flat film. - 3
Concept
A soap bubble has two surfaces (inner and outer). Each surface contributes 2T/r to the excess pressure, giving a total of 4T/r. The work done equals the surface tension multiplied by the total new surface area created (NCERT Class 11 Physics, Chapter 9, page 194).
- 4
Formula
(a) ΔP = 4T/r
(b) W = T × total area = T × 2 × 4πr² - 5
Substitution
(a) ΔP = 4 × 4.0 × 10⁻² / 5.0 × 10⁻³
(b) W = 4.0 × 10⁻² × 2 × 4π × (5.0 × 10⁻³)² - 6
Calculation
(a) ΔP = 16.0 × 10⁻² / 5.0 × 10⁻³ = 32 Pa
(b) W = 4.0 × 10⁻² × 2 × 4π × 25.0 × 10⁻⁶
W = 4.0 × 10⁻² × 200π × 10⁻⁶
W = 4.0 × 10⁻² × 6.283 × 10⁻⁴
W = 2.513 × 10⁻⁵ J ≈ 2.5 × 10⁻⁵ J
Note on exact constants: the factors 4 (number of surfaces × Laplace factor), 2 (two surfaces), and π are exact mathematical constants and do not limit significant figures. The answer is reported to 2 significant figures, matching the precision of the given data. - 7
Final answer
(a) Excess pressure = 32 Pa
(b) Work done = 2.5 × 10⁻⁵ J - 8
Common trap
Using 2T/r instead of 4T/r gives ΔP = 16 Pa — exactly half the correct answer. This is the classic drop-vs-bubble confusion. If a NEET option shows exactly half your answer for a soap bubble problem, recheck whether you used the factor of 4.
- 9
Similar NEET-style question
Two soap bubbles of radii r₁ = 2.0 × 10⁻² m and r₂ = 4.0 × 10⁻² m are formed from the same solution (T = 2.5 × 10⁻² N/m). Find the difference in excess pressure between the two bubbles. (Answer: ΔP₁ − ΔP₂ = 4T/r₁ − 4T/r₂ = 5.0 − 2.5 = 2.5 Pa.)
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What to remember before solving Excess Pressure Curved Surface questions
Which Excess Pressure Curved Surface formulas do you need for NEET?
1 formula — click to collapse
Excess pressure inside drop/bubble
Excess internal pressure due to surface tension. Bubble has 2 surfaces, hence factor 4.
| Symbol | Quantity | SI Unit |
|---|---|---|
| Delta_P | excess pressure | Pa |
| T | surface tension | N/m |
| r | radius | m |
Valid when
- Spherical drop or bubble
- Constant T (one fluid pair)
Where do students lose marks on Excess Pressure Curved Surface?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
2 items — click to collapse
Category: Similar Terms
Student uses 2T/r for soap bubble (drop formula). Bubble has 2 surfaces → 4T/r.
When it triggers
Question mentions soap bubble OR liquid drop OR air bubble in liquid.
How to avoid
Drop in air: 1 surface → 2T/r. Soap bubble in air: 2 surfaces → 4T/r. Air bubble in liquid: 1 surface → 2T/r.
Root cause: concept gap
Correction
Drop in air: 1 surface → ΔP = 2T/r. Soap bubble: 2 surfaces (inner + outer) → ΔP = 4T/r. Air bubble inside liquid: 1 surface → 2T/r.
More in Properties of Bulk Matter: 3 exam traps and mistakes · 11 formulas · 4 question patterns from its other lessons.
Excess Pressure Curved Surface questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
If a soap bubble expands, the pressure inside the bubble
1Is equal to the atmospheric pressure
2Decreases
3Increases
4Remains the same
NTA Answer: Option 2(final)
All 17 past-paper questions from Properties of Bulk Matter →
How does NEET ask about Excess Pressure Curved Surface?
1 recurring pattern from past papers — click to collapse
Energy to form a bubble of given radius from soap solution; or pressure inside vs outside. Bubble has 2 surfaces (factor 4T/r).
Direct ApplicationEasy
Common distractors
uses 2T r instead of 4T r for bubble
Treats soap bubble like a drop
Sources
NCERT refs: Class 11 Physics Chapter 9, p.196
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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