Formula
Bulk modulus
K = -V·dP/dV = -(volumetric stress)/(volumetric strain). Negative sign: pressure increase compresses volume. K for water ≈ 2.2 × 10⁹ Pa.
-- NCERT Class 11 Physics, Ch. 8, p. 173Bulk Modulus
8 MCQs10 revision cards9-step worked example
Source: NCERT Properties of Solids and LiquidsOfficial key: NTA-verifiedLast updated: 25 Sep 2026
Bulk Modulus, explained for NEET
The trap that costs marks on bulk modulus questions is straightforward: you see a problem about compression and reach for Young's modulus. Young's modulus handles longitudinal stretching of a wire or rod — one direction, one cross-section. Bulk modulus handles uniform compression from all sides — a volume change under pressure. Mixing them up means using the wrong formula entirely, and no amount of correct arithmetic saves you.
Bulk modulus K measures a material's resistance to uniform compression. As defined in NCERT Class 11 Physics Chapter 8 (Mechanical Properties of Solids), page 173:
K = −V (dP/dV)
The negative sign ensures K is positive: when pressure increases (dP > 0), volume decreases (dV < 0). For finite changes, this becomes K = −P·V/ΔV, where ΔV is the change in volume under applied pressure P.
The reciprocal of bulk modulus is compressibility (1/K), which tells you how easily a material compresses. Gases have low K (high compressibility); solids have high K (low compressibility). Water at standard conditions has K ≈ 2.2 × 10⁹ Pa — large, but far smaller than steel's K ≈ 1.6 × 10¹¹ Pa.
The key distinction to lock in:
| Modulus | Deformation type | Formula |
|---|---|---|
| Young's (Y) | Longitudinal stretch/compression | Y = FL/(AΔL) |
| Bulk (K) | Uniform volumetric compression | K = −V(dP/dV) |
| Shear (G) | Tangential/angular distortion | G = shear stress / shear strain |
NEET questions on bulk modulus typically give you a pressure change and ask for volume change (or vice versa), or ask you to identify which modulus applies to a described scenario. The common confusion — applying Y when K is needed — shows up as a distractor in nearly every such question. Before you touch any formula, identify the deformation type: is it a stretch along one axis, or compression from all directions?
Can you answer these Bulk Modulus 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 bulk modulus of a material is defined as the ratio of:
Show answer and why every option is right or wrong
Answer: A. Bulk modulus K is defined as the ratio of volumetric (hydraulic) stress to volumetric strain, i.e., K = −V(dP/dV). This is stated in NCERT Class 11 Physics Chapter 8, page 172.
Why B is wrong: B describes shear modulus (G = shear stress / shear strain), which applies to tangential deformation, not volumetric compression.
Why C is wrong: C describes Young's modulus (Y = longitudinal stress / longitudinal strain), not bulk modulus. This is the most common confusion between Y and K (trap: mixing modulus types).
Why D is wrong: D is not a standard ratio for any elastic modulus. Tensile and compressive strains are both longitudinal — their ratio is not a material property.
MCQ 2Easy RecallPractice
The reciprocal of bulk modulus is called:
Show answer and why every option is right or wrong
Answer: A. Compressibility = 1/K. A material with high compressibility has low bulk modulus and deforms easily under pressure. NCERT Class 11 Physics Chapter 8, page 172.
Why B is wrong: B — Elasticity is a general property describing a body's ability to regain shape, not specifically the reciprocal of K.
Why C is wrong: C — Rigidity relates to shear modulus (modulus of rigidity, G), not bulk modulus.
Why D is wrong: D — Plasticity refers to permanent deformation beyond the elastic limit. It is not a reciprocal of any modulus.
MCQ 3Easy RecallPractice
Which elastic modulus is relevant when a solid rubber ball is submerged deep in the ocean and compressed uniformly by the water pressure?
Show answer and why every option is right or wrong
Answer: C. Uniform compression from all directions (hydrostatic pressure) is volumetric deformation, governed by bulk modulus K. NCERT Class 11 Physics Chapter 8, page 172.
Why A is wrong: A — Young's modulus applies to stretching or compression along one axis (e.g., pulling a wire). The ball is compressed from all sides, not along one direction (trap: using Y for volumetric compression).
Why B is wrong: B — Shear modulus applies to tangential deformation that changes shape without changing volume. Hydrostatic pressure changes volume, not shape.
Why D is wrong: D — Poisson's ratio is a dimensionless ratio of lateral strain to longitudinal strain under uniaxial stress. It is not an elastic modulus and does not describe volumetric compression.
MCQ 4Direct ApplicationPractice
A metal cube of volume 1.00 × 10⁻³ m³ is subjected to a uniform pressure of 2.00 × 10⁸ Pa. If the bulk modulus of the metal is 1.00 × 10¹¹ Pa, the change in volume is:
Show answer and why every option is right or wrong
Answer: C. From K = −PV/ΔV, we get ΔV = −PV/K = −(2.00 × 10⁸ × 1.00 × 10⁻³)/(1.00 × 10¹¹) = −2.00 × 10⁻⁶ m³. NCERT Class 11 Physics Chapter 8, page 172.
Why A is wrong: A — This value (5.00 × 10⁻⁶) does not follow from any correct rearrangement of the bulk modulus formula; likely an arithmetic distractor.
Why B is wrong: B results from omitting the volume V in the numerator — i.e., computing ΔV = −P/K instead of −PV/K. This is a formula misapplication.
Why D is wrong: D results from a two-power-of-ten slip — dividing by 10⁹ instead of 10¹¹ — yielding a result a hundred times too large.
MCQ 5Direct ApplicationPractice
A wire is stretched by a force along its length, and its elongation is measured. The modulus that describes this deformation is:
Show answer and why every option is right or wrong
Answer: D. Longitudinal stretching of a wire is described by Young's modulus Y = FL/(AΔL). NCERT Class 11 Physics Chapter 8, page 170.
Why A is wrong: A — Bulk modulus applies to uniform volumetric compression, not longitudinal stretching of a wire (trap: confusing Y and K).
Why B is wrong: B — Shear modulus applies when tangential forces cause angular deformation, not when a wire is pulled along its length.
Why C is wrong: C — Compressibility (1/K) is the reciprocal of bulk modulus and describes volume change under pressure, not elongation of a wire.
MCQ 6Direct ApplicationPractice
The bulk modulus of water is 2.2 × 10⁹ Pa. The pressure required to reduce the volume of 1.00 × 10⁻² m³ of water by 0.10% is:
Show answer and why every option is right or wrong
Answer: B. 0.10% volume reduction means ΔV/V = 1.0 × 10⁻³. From K = P/(ΔV/V), we get P = K × (ΔV/V) = 2.2 × 10⁹ × 1.0 × 10⁻³ = 2.2 × 10⁶ Pa. NCERT Class 11 Physics Chapter 8, page 172.
Why A is wrong: A — This corresponds to using 0.10% as 1.0 × 10⁻⁴ instead of 1.0 × 10⁻³ (misinterpreting the percentage).
Why C is wrong: C — This corresponds to treating 0.10% as 1.0 × 10⁻² (i.e., confusing 0.10% with 1.0%), giving a result ten times too large.
Why D is wrong: D — This corresponds to using ΔV/V = 0.10 (treating the percentage as a plain fraction without dividing by 100), giving a result 100 times too large.
MCQ 7Concept TrapPractice
A solid sphere is placed at the bottom of a deep lake. Compared to its volume at the surface, its volume at depth will be:
Show answer and why every option is right or wrong
Answer: D. Hydrostatic pressure compresses the sphere uniformly. The fractional volume decrease ΔV/V = −P/K depends on the bulk modulus. Solids have large K, so the decrease is small but nonzero. NCERT Class 11 Physics Chapter 8, page 172.
Why A is wrong: A — Increased external pressure compresses the sphere; it does not expand it. Pressure acts inward.
Why B is wrong: B — While solids have very high bulk modulus, they are not perfectly incompressible. Volume does decrease slightly under high pressure.
Why C is wrong: C — The volume change is proportional to ΔP/K, which for typical solids at lake-scale depths is far less than 50%. There is no reason volume would halve.
MCQ 8CalculationPractice
A hydraulic press subjects a copper block (K = 1.40 × 10¹¹ Pa) and an aluminium block (K = 7.00 × 10¹⁰ Pa) of identical initial volume to the same pressure. The ratio of volume strain of copper to aluminium is:
Show answer and why every option is right or wrong
Answer: B. Volume strain = ΔV/V = P/K. For the same pressure, the ratio is K_Al / K_Cu = (7.00 × 10¹⁰) / (1.40 × 10¹¹) = 1/2. So (ΔV/V)_Cu : (ΔV/V)_Al = 1 : 2. The stiffer material (higher K) has less volume strain.
Why A is wrong: A — This reverses the ratio. Higher K means less strain, not more. Copper has the higher K, so its volume strain is smaller, not larger.
Why C is wrong: C — Equal volume strain would require equal bulk moduli. Copper and aluminium have different K values (1.40 × 10¹¹ vs 7.00 × 10¹⁰ Pa).
Why D is wrong: D — 4:1 would require the K values to differ by a factor of 4. They differ by a factor of 2.
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Bulk Modulus: quick recall before you leave
How do you solve a Bulk Modulus question? A worked example
- 1
Given
A steel block has volume V = 2.00 × 10⁻⁴ m³ and bulk modulus K = 1.60 × 10¹¹ Pa. It is subjected to a uniform hydraulic pressure of P = 3.20 × 10⁸ Pa.
- 2
Required
Find the change in volume ΔV.
- 3
Concept
Bulk modulus relates volumetric stress (applied pressure) to volumetric strain (fractional volume change). The material is compressed uniformly from all sides — this is the defining scenario for K, not Y.
NCERT Class 11 Physics Chapter 8, page 172. - 4
Formula
K = −PV/ΔV
Rearranging: ΔV = −PV/K - 5
Substitution
ΔV = −(3.20 × 10⁸ Pa)(2.00 × 10⁻⁴ m³) / (1.60 × 10¹¹ Pa)
- 6
Calculation
Numerator: 3.20 × 10⁸ × 2.00 × 10⁻⁴ = 6.40 × 10⁴
ΔV = −6.40 × 10⁴ / 1.60 × 10¹¹ = −4.00 × 10⁻⁷ m³
Note on exact values: the factor 2 in "2.00" and the ratio 6.40/1.60 = 4.00 are exact arithmetic within the given precision. All given values carry 3 significant figures; the result is reported to 3 significant figures. - 7
Final answer
ΔV = −4.00 × 10⁻⁷ m³
The negative sign confirms volume decreases under compression, as expected. - 8
Common trap
A common confusion is reaching for Young's modulus (Y = FL/AΔL) when the problem describes uniform compression. Y applies to longitudinal stretching along one axis. If the problem says "hydraulic pressure," "submerged," or "compressed from all sides," the correct modulus is K, not Y.
- 9
Similar NEET-style question
An iron cube of side 10.0 cm is subjected to a uniform hydraulic pressure of 5.00 × 10⁷ Pa. If the bulk modulus of iron is 1.00 × 10¹¹ Pa, find the decrease in volume of the cube.
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What to remember before solving Bulk Modulus questions
Which Bulk Modulus formulas do you need for NEET?
1 formula — click to collapse
Bulk modulus
Resistance of a material to uniform compression. Inverse: compressibility.
| Symbol | Quantity | SI Unit |
|---|---|---|
| K | bulk modulus | Pa |
| V | volume | m^3 |
| P | pressure | Pa |
Valid when
- Isotropic compression
- Within elastic regime
Where do students lose marks on Bulk Modulus?
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 Y formula when problem is about volumetric compression (use K) or vice versa.
When it triggers
Problem describes longitudinal stretching (use Y), volumetric pressure (use K), or shear (use G).
How to avoid
Y: longitudinal stress/strain. K: volumetric. G: shear. Match modulus to deformation type.
Root cause: formula misuse
Correction
Y for longitudinal stretch (FL/A·ΔL); K for volumetric compression (-V·dP/dV); G for shear. Match modulus type to deformation type before computing.
More in Properties of Bulk Matter: 3 exam traps and mistakes · 11 formulas · 5 question patterns from its other lessons.
Bulk Modulus 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
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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