NEET Physics — Units, Dimensions and Measurement

Dimensions – Complete Notes, Revision, Important Questions & Downloads

Dimensions covers the foundational concept of Dimensional Equation and Formula — the systematic method of expressing any physical quantity as powers of fundamental quantities [M], [L], and [T]. NEET directly tests this topic by asking students to identify or match dimensional formulas: force has dimensions [MLT⁻²], pressure shares [ML⁻¹T⁻²] with stress and Young’s modulus, and work shares [ML²T⁻²] with torque and kinetic energy. In NEET 2023, students had to determine the dimensions of h/e (Planck’s constant divided by electron charge), requiring decomposition of compound quantities into base dimensions. Memorising the table of quantities sharing identical dimensional formulas is essential, because NEET frequently presents “which pair has the same dimensions” questions where confusing torque with angular momentum costs 4 marks.

⬇ Download Notes PDF View Important Questions →

1 SubtopicTheoryNCERT Class 11

Expected QuestionsQ

1–2

Dimensional formula identification and matching identical-dimension pairs are tested almost every year from this chapter.

Time Required⏱

1–2 hours

One focused session to learn the decomposition method and memorise the table of quantities sharing the same dimensional formula.

Difficulty⚡

Easy

Writing a dimensional formula follows a mechanical procedure: express the quantity in terms of fundamental quantities and note the exponents. The challenge lies in memorising the standard table and not confusing pairs like torque [ML²T⁻²] with angular momentum [ML²T⁻¹].

NRI USA Curriculum GapUS

Low–Medium

US AP Physics mentions dimensional analysis briefly for equation checking, but does not require students to write or recall dimensional formulas from memory. NEET demands rapid recall for 20+ standard quantities and their dimensional groupings.

1Subtopics

8+Practice Questions

4Free Downloads

1–2 hrsPrep Time

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NEET Weightage — Dimensions

Units, Dimensions and Measurement (Chapter 1)

NEET Year	Questions from this Topic	Bar	Marks
2024	1	1 Q	4
2023	1	1 Q	4
2022	0	0 Q	0
2021	1	1 Q	4
2020	1	1 Q	4
2019	1	1 Q	4
6-Year Total (2019–2024)	4–6		16–24

Dimensional formula questions typically ask “what are the dimensions of X” or “which pair shares the same dimensional formula” — both require instant recall of the standard [MLT] decomposition for 20+ quantities.
The table of quantities with identical dimensions is a high-yield memorisation target: work, kinetic energy, and torque all share [ML²T⁻²], while pressure, stress, and Young’s modulus share [ML⁻¹T⁻²].
NEET occasionally tests compound expressions: asking for dimensions of h/e (NEET 2023) or gravitational constant G requires multi-step decomposition starting from the defining equation.

📊

~0.7–1

Avg Questions / Year

🎯

16–24

Total Marks (6 yrs)

📈

Direct

Pattern

⚠️

Easy

Difficulty

Exam Strategy for Dimensions in NEET Physics

Memorise the standard dimensional formula table Commit the textbook pairings to memory: [ML²T⁻²] = work, energy, torque; [ML⁻¹T⁻²] = pressure, stress, Young’s modulus, energy density; [M⁰L⁰T⁻¹] = frequency, angular velocity, decay constant. The trap: confusing torque [ML²T⁻²] with force [MLT⁻²] because torque = force × distance adds an extra [L].

Practise decomposing compound quantities into base dimensions For any unfamiliar quantity, write its defining equation first (e.g., G = Fr²/(m₁m₂)), then replace each term with [MLT] powers: G = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. The trap: forgetting that r² contributes [L²], not [L], which changes the final L exponent.

Use dimensional consistency as an MCQ elimination tool When NEET asks “which equation is dimensionally correct”, compute [MLT] for each side of every option. Any LHS–RHS dimension mismatch immediately eliminates that option. Caution: a dimensionally correct equation may still be physically wrong because dimensionless constants like ½ or 2π are invisible to dimensional checks.

Flag all dimensionless quantities in a single list Strain, refractive index, relative density, angle (radian), solid angle (steradian), Poisson’s ratio, and relative permittivity are all [M⁰L⁰T⁰]. NEET tests this by mixing one dimensionless quantity among three dimensioned options. Memorise the complete list to answer these recall questions in under 15 seconds.

Download Study Notes — Dimensions

PDF · Cheat Sheet · MCQ Set · PYQ

📘

Dimensions — Full Notes

Complete notes covering the concept of dimensions, dimensional equations, dimensional formulas, and the full table of quantities sharing the same dimensions with worked derivations for force, energy, pressure, and gravitational constant.

1 subtopicWorked derivationsComplete dimension table

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📗

Dimensions — Formula Sheet

One-page reference: dimensional formulas for 25+ standard physical quantities grouped by shared dimensions, plus the step-by-step decomposition method with key formulas, conditions, and one worked example per group.

1 pageAll key formulas

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Dimensions — MCQ Practice

15 NEET-style MCQs testing dimensional formula identification, matching quantities with identical dimensions, and decomposing compound expressions like h/e and the universal gravitational constant G.

15 MCQsDetailed solutions

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Dimensions — PYQ Practice

Collection of previous year NEET questions on dimensional formulas including NEET 2019 (surface tension dimensions) and NEET 2023 (h/e dimensions), with full worked solutions and option-by-option analysis.

Year-tagged PYQsAnswer key included

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Subtopics in Dimensions

2-Column Table

Column A	Column B
Dimensional Equation and Formula↗

Rapid Revision — Dimensions

Concept → Trap → Example

1) Dimensional Equation and Formula

Core Definitions + Dimension Table

Dimensions are the powers to which fundamental quantities [M], [L], [T] are raised to represent a physical quantity. Dimensional equation: [Force] = [MLT⁻²]. Dimensional formula: the RHS expression [MLT⁻²]. Key groupings from the textbook table: Work = Torque = KE = [ML²T⁻²]; Pressure = Stress = Young’s modulus = [ML⁻¹T⁻²]; Momentum = Impulse = [MLT⁻¹]; Angular momentum = Planck’s constant = [ML²T⁻¹].

To write a dimensional formula: start from the defining equation (e.g., Pressure = Force/Area), substitute dimensions for each quantity ([MLT⁻²]/[L²] = [ML⁻¹T⁻²]), and simplify the exponents.
The square bracket notation [] indicates the expression represents dimensions, not magnitudes: [Force] = [MLT⁻²] denotes the dimensional formula of force, not a numerical value.
Common NEET trap: angular momentum [ML²T⁻¹] and Planck’s constant [ML²T⁻¹] share the same dimensions, but torque [ML²T⁻²] does not — the T exponent differs by one (⁻1 vs ⁻2), which students often overlook.

Example (NEET-style)Derive dimensions for the universal gravitational constant G: from F = Gm₁m₂/r², rearrange G = Fr²/(m₁m₂). Substituting: [G] = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. NEET frequently tests this exact decomposition for 4 marks.

US Curriculum Gaps — Dimensions for NEET Physics

NRI students from US high schools may find these specific gaps when preparing for NEET Physics on Dimensions.

Dimensional Formula Recall (not required in AP Physics 1 or AP Physics C)

US AP Physics courses treat dimensional analysis as an equation-checking tool but never require students to write or recall dimensional formulas from memory. NEET expects instant recall of [MLT] decompositions for 20+ physical quantities and frequently tests which pairs share identical dimensions.

AP Physics 1 and C use named units (N, J, Pa) rather than dimensional formulas ([MLT⁻²], [ML²T⁻²], [ML⁻¹T⁻²]) — NEET requires fluency in both representations.
NEET asks “which pair has the same dimensions” requiring memorised groupings like work/torque/kinetic energy sharing [ML²T⁻²].
Practice writing dimensional formulas for at least 25 quantities from the textbook table before attempting NEET mock tests.

Dimensionless Quantities Identification (limited coverage in US Physics courses)

US high school physics does not systematically classify quantities as dimensionless. NEET asks students to identify which quantities have [M⁰L⁰T⁰] dimensions, including strain, refractive index, relative density, angle in radians, and Poisson’s ratio.

US courses define strain as a ratio but rarely frame it formally as a dimensionless quantity with [M⁰L⁰T⁰] notation.
NEET trap: surface tension has dimensions [MT⁻²] and is NOT dimensionless, but students confuse it with the dimensionless “surface energy per unit area” label.
Memorise all [M⁰L⁰T⁰] entries: strain, refractive index, relative density, angle, solid angle, Poisson’s ratio, relative permittivity, dielectric constant.

Previous Year Questions — Dimensions

3 previous year NEET questions

1The dimensions of surface tension are: (NEET 2019)NEET 2019

[ML⁻¹T⁻²]

[MLT⁻²]

[MT⁻²]

[ML²T⁻²]

Surface tension γ = Force / Length = [MLT⁻²] / [L] = [ML⁰T⁻²] = [MT⁻²]. Option (c) is correct. Option (a) [ML⁻¹T⁻²] is the dimensional formula for pressure (Force/Area), where division is by [L²] instead of [L] — this is the most common error because students confuse force per unit length with force per unit area. Option (b) [MLT⁻²] represents force itself without any division by length. Option (d) [ML²T⁻²] is the dimension of energy or work (force times distance). The key: surface tension is force per unit length, not force alone or force per unit area.

2Out of the following pairs, which one has identical dimensions? (NEET 2019)NEET 2019

Impulse and surface tension

Angular momentum and work

Work and torque

Young’s modulus and energy

Work = Force × displacement = [MLT⁻²][L] = [ML²T⁻²]. Torque = Force × lever arm = [MLT⁻²][L] = [ML²T⁻²]. Both have identical dimensions [ML²T⁻²], making option (c) correct. Option (a): Impulse = [MLT⁻¹] while surface tension = [MT⁻²] — these differ in both L and T exponents. Option (b): Angular momentum = [ML²T⁻¹] while work = [ML²T⁻²] — the T exponent differs (⁻1 vs ⁻2). Option (d): Young’s modulus = [ML⁻¹T⁻²] while energy = [ML²T⁻²] — the L exponent differs (⁻1 vs 2). This question tests memorisation of the standard dimension table.

3The dimensional formula of Planck’s constant divided by electronic charge (h/e) is: (NEET 2023)NEET 2023

[ML²T⁻²A⁻¹]

[ML²T⁻³A⁻¹]

[ML²T⁻¹A⁻¹]

[MLT⁻²A⁻¹]

Planck’s constant h: from E = hν, h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Electronic charge e = current × time = [AT]. Therefore h/e = [ML²T⁻¹]/[AT] = [ML² · T⁻¹ · A⁻¹ · T⁻¹] = [ML²T⁻²A⁻¹]. Option (a) is correct. Option (b) [ML²T⁻³A⁻¹] represents voltage (V = W/q), not h/e. Option (c) [ML²T⁻¹A⁻¹] forgets to subtract the extra T⁻¹ from dividing by the time component of charge. Option (d) is missing one power of L. The critical step: charge e = [AT] contributes both A⁻¹ and T⁻¹ when placed in the denominator.

Practice Problems — Dimensions

Click "Reveal Answer" after attempting

1The dimensional formula of the universal gravitational constant G is:

[M⁻¹L³T⁻²]

[M⁻²L³T⁻²]

[ML³T⁻²]

[ML⁻³T²]

👁 Reveal Answer

Option (a): [M⁻¹L³T⁻²]. From Newton’s gravitation law F = Gm₁m₂/r², rearranging gives G = Fr²/(m₁m₂). Substituting dimensions: G = [MLT⁻²][L²]/[M][M] = [ML³T⁻²]/[M²] = [M⁻¹L³T⁻²]. Option (b) has M⁻², which would require dividing by M³. Option (c) keeps M positive, forgetting the two mass terms in the denominator.

2Which of the following quantities is dimensionless?

Surface tension

Strain

Angular momentum

Pressure

👁 Reveal Answer

Option (b): Strain. Strain = change in length / original length = [L]/[L] = [M⁰L⁰T⁰], which is dimensionless. Surface tension = [MT⁻²], angular momentum = [ML²T⁻¹], and pressure = [ML⁻¹T⁻²] — all have non-zero exponents. Strain belongs to the dimensionless family alongside refractive index, relative density, and Poisson’s ratio.

3The dimensional formula [ML⁻¹T⁻²] corresponds to which set of quantities?

Pressure, stress, and Young’s modulus

Work, energy, and torque

Force, thrust, and weight

Momentum, impulse, and force

👁 Reveal Answer

Option (a): Pressure, stress, and Young’s modulus. Pressure = Force/Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]. Stress = Force/Area, same result. Young’s modulus = Stress/Strain = [ML⁻¹T⁻²]/[1] = [ML⁻¹T⁻²]. Option (b) gives [ML²T⁻²]. Option (c) gives [MLT⁻²]. Option (d) mixes [MLT⁻¹] and [MLT⁻²].

4If energy E, velocity v, and time T are chosen as fundamental quantities, the dimensional formula of force in terms of E, v, and T is:

[Ev⁻¹T⁻¹]

[EvT⁻¹]

[Ev⁻¹T⁰]

[E²v⁻¹T⁻¹]

👁 Reveal Answer

Option (a): [Ev⁻¹T⁻¹]. In SI: E = [ML²T⁻²], v = [LT⁻¹], T = [T]. From v and T: L = vT. From E = Mv²T⁻² × T² ... simplifying: M = E/v². Force = MLT⁻² = (E/v²)(vT)(T⁻²) = Ev⁻¹T⁻¹. Option (b) has v in the numerator. Option (c) eliminates T incorrectly. Option (d) squares E without justification.

5The time period T of a simple pendulum depends on length l and acceleration due to gravity g. Using dimensional analysis, T is proportional to:

√(l/g)

√(g/l)

l/g

g/l

👁 Reveal Answer

Option (a): √(l/g). Let T = k × lᵃ × gᵇ. Dimensions: [T] = [Lᵃ][LT⁻²]ᵇ = [Lᵃ⁺ᵇ T⁻²ᵇ]. Equating exponents: for T: 1 = ⁻2b, so b = ⁻1/2. For L: 0 = a + b = a ⁻ 1/2, so a = 1/2. Therefore T = k√(l/g). Option (b) inverts the ratio. Options (c) and (d) give dimensions [T²] or [T⁻²], not [T].

Physics — Dimensions Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Dimensional Equation and Formula: Write the dimensional formula of force from its defining equationStarting from Force = mass × acceleration = mass × (length/time²), derive [Force] = [MLT⁻²] and verify each exponent independently.

Dimensional Equation and Formula: Decompose the gravitational constant G into base dimensionsFrom F = Gm₁m₂/r², isolate G, substitute [MLT] for each quantity, and confirm G = [M⁻¹L³T⁻²].

Dimensional Equation and Formula: Recite 5 groups of quantities with identical dimensions from memoryWrite the [ML²T⁻²] group (work, energy, torque), [ML⁻¹T⁻²] group (pressure, stress, Young’s modulus), [MLT⁻¹] group (momentum, impulse), [M⁰L⁰T⁰] group (strain, refractive index, angle), and [M⁰L⁰T⁻¹] group (frequency, angular velocity, decay constant) with all member quantities.

Dimensional Equation and Formula: Identify all dimensionless quantities from a mixed listGiven 10 physical quantities, correctly classify each as dimensionless [M⁰L⁰T⁰] or dimensioned, flagging strain, refractive index, relative density, angle, and Poisson’s ratio.

Dimensional Equation and Formula: Solve a compound-quantity dimensional formula problem end-to-endCompute the dimensions of h/e (Planck’s constant / electronic charge): start from h = [ML²T⁻¹], e = [AT], and derive h/e = [ML²T⁻²A⁻¹] with full working.

Frequently Asked Questions — Dimensions

Notes · Downloads · Revision · Important Questions

What is the difference between a dimensional equation and a dimensional formula?

A dimensional equation is the complete expression equating a physical quantity to its base-quantity representation: [Force] = [MLT⁻²]. The dimensional formula is only the right-hand side: [MLT⁻²]. In practice, NEET uses both terms interchangeably, but strictly the equation includes the quantity name on the left while the formula is just the [MLT] expression.

Why do work and torque have the same dimensional formula [ML²T⁻²] if they are physically different?

Work = force × displacement = [MLT⁻²][L] = [ML²T⁻²]. Torque = force × lever arm = [MLT⁻²][L] = [ML²T⁻²]. Both involve force multiplied by a length, giving identical dimensions. They differ in physical meaning: work is a scalar (dot product F·d), while torque is a pseudovector (cross product r×F). Dimensional analysis cannot distinguish between quantities sharing the same dimensional formula — this is a known limitation that NEET explicitly tests.

How do I quickly determine the dimensional formula of an unfamiliar quantity?

Step 1: Recall or construct the defining equation (e.g., pressure = force/area). Step 2: Replace each quantity with its known [MLT] dimensions. Step 3: Apply exponent arithmetic (multiply = add exponents, divide = subtract exponents). For compound quantities like h/e, decompose each part separately first, then combine. This systematic approach takes under 30 seconds with practice.

Which quantities are dimensionless, and how does NEET test them?

Dimensionless quantities have [M⁰L⁰T⁰]: strain, refractive index, relative density, angle (radian), solid angle (steradian), Poisson’s ratio, relative permittivity (dielectric constant), and distance gradient. NEET presents a list of 4 quantities and asks “which is dimensionless” — the trap is including a quantity like surface tension [MT⁻²] that sounds like a ratio but has dimensions.

Can two different physical quantities have the same dimensional formula?

Yes. The textbook provides a comprehensive table: frequency, angular frequency, angular velocity, velocity gradient, and decay constant all share [M⁰L⁰T⁻¹]. Work, kinetic energy, potential energy, internal energy, and torque share [ML²T⁻²]. Momentum and impulse share [MLT⁻¹]. NEET exploits this by asking “which pair has the same dimensions” — you need these groupings memorised.

What are the dimensions of Planck’s constant and how is it derived?

From E = hν (energy = Planck’s constant × frequency): h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. The SI unit is joule-second (J·s). Angular momentum also has dimensions [ML²T⁻¹], which is why Planck’s constant is sometimes called the quantum of angular momentum — NEET tests this in matching-dimension questions.

Does the dimensional formula depend on the system of units (CGS vs SI)?

No. Dimensional formulas are independent of the unit system because they express the fundamental nature of the quantity, not its numerical value. Force is [MLT⁻²] whether measured in newtons (SI) or dynes (CGS). Only the numerical values and unit names change: 1 N = 10⁵ dyne, but both represent the same dimensional formula [MLT⁻²].

Why can dimensional analysis not detect numerical constants like 1/2 or 2π?

Dimensional analysis compares only the powers of fundamental quantities on both sides of an equation. Pure numbers (1/2, 2π, 4/3) have no dimensions [M⁰L⁰T⁰], so they are invisible to dimensional checks. For instance, KE = mv² and KE = (1/2)mv² both have dimensions [ML²T⁻²], but only the second is physically correct. NEET tests this limitation by offering “can determine dimensionless constants” as a wrong option.

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Dimensions

Dimensions – Complete Notes, Revision, Important Questions & Downloads

1) Dimensional Equation and Formula

Dimensional Formula Recall (not required in AP Physics 1 or AP Physics C)

Dimensionless Quantities Identification (limited coverage in US Physics courses)

Physics — Dimensions Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Dimensional Equation and Formula

Subtopics

Dimensional Equation and Formula

NEET > Physics > Physical World and Measurement Chapters

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Dimensions

Overview content

Dimensions – Complete Notes, Revision, Important Questions & Downloads

1) Dimensional Equation and Formula

Dimensional Formula Recall (not required in AP Physics 1 or AP Physics C)

Dimensionless Quantities Identification (limited coverage in US Physics courses)

Physics — Dimensions Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Dimensional Equation and Formula

Subtopics

Dimensional Equation and Formula

NEET > Physics > Physical World and Measurement Chapters

Comments

Leave a comment

Comments (0)