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Fundamental and Derived Units

NEET > Physics > Physical World and Measurement > Units, Dimensions and Measurement > Fundamental and Derived Units

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NEET Physics · Chapter 1 · Topic 4 of 22

Fundamental and Derived Units – Complete Notes, Revision, Important Questions & Downloads

This topic covers two foundational categories of measurement: Fundamental Units — the independently defined base standards for mass, length, time, electric current, temperature, amount of substance, and luminous intensity — and Derived Units, which are algebraic combinations of these base units (e.g., velocity in m/s, force in kg·m/s²). NEET Physics tests this topic through questions on identifying whether a given unit is fundamental or derived, expressing derived units in terms of SI base units, and converting between CGS, MKS, FPS, and SI systems. For instance, knowing that 1 newton = 1 kg·m·s⁻² immediately tells you force is a derived quantity with three fundamental-unit factors.

⬇ Download Notes PDFView Important Questions →
Class 11Theory-BasedNCERT Ch 1
Expected QuestionsQ
0–1
Fundamental and Derived Units rarely appears as a standalone NEET question, but the concepts underpin every dimensional analysis and unit conversion problem in the exam.
Time Required⏱
30–45 min
Quick conceptual study — memorise the 7 SI base units with symbols and at least 5 common derived units with their base-unit decompositions.
Difficulty⚡
Easy
Definitions are straightforward; the challenge lies in recalling correct SI base unit symbols and not confusing practical units (e.g., light year) with derived units.
NRI USA Curriculum GapUS
Moderate
US AP Physics 1 introduces SI units but does not require memorising FPS/CGS systems or the full SI prefix table (atto to exa). NRI students need to learn these additional systems explicitly.
7Subtopics
4Practice Questions
4Free Downloads
30 minPrep Time
⬇ Get Free Downloads

NEET Weightage Analysis

Chapter 1: Units, Dimensions and Measurement
NEET YearQuestions from this TopicBarMarks
20241
 
1 Q
4
20231
 
1 Q
4
20222
 
2 Q
8
20211
 
1 Q
4
20201
 
1 Q
4
20191
 
1 Q
4
Total Questions (2019–2024)7 28
NEET questions from this chapter often ask students to identify whether a given physical quantity’s unit is fundamental or derived, or to express a derived unit in terms of SI base units.
Conversion between CGS and SI units (e.g., 1 dyne = 10⁻⁵ N, 1 erg = 10⁻⁷ J) frequently appears as a sub-step in mechanics and electrostatics numericals.

The 2019 NCERT edition redefined four SI base units (kilogram, ampere, kelvin, mole) using fixed numerical values of fundamental constants — NEET 2020 onwards may reference these updated definitions.
📊
~1.2
Avg Questions / Year
🎯
28
Total Marks (6 yrs)
📈
Indirect
Pattern
⚠️
Easy
Difficulty

How to Prepare Fundamental and Derived Units for NEET

1

Memorise the 7 SI base units and 2 supplementary units Write out the table: Length–metre–m, Mass–kilogram–kg, Time–second–s, Current–ampere–A, Temperature–kelvin–K, Amount–mole–mol, Luminous intensity–candela–cd, plus radian (rad) and steradian (sr). Self-test by covering the symbol column. The most common NEET trap is writing lowercase k for kelvin (which is the kilo prefix) instead of uppercase K.

2

Build a derived-unit decomposition table For each major derived unit (newton, joule, watt, pascal, hertz, coulomb), write the expression in base units. Example: 1 N = 1 kg·m·s⁻². This skill is tested when NEET gives a formula and asks for the SI unit of an unknown quantity — you decompose each factor into base units and combine the exponents.

3

Practise CGS–SI conversion using dimensional decomposition Convert at least 5 derived quantities between CGS and SI (1 erg = 10⁻⁷ J, 1 dyne = 10⁻⁵ N, 1 poise = 0.1 Pa·s). NEET uses these as embedded sub-steps in numericals — the trap is forgetting to convert ALL base-unit factors, not just one.

4

Identify practical-unit naming traps A light year is a unit of length (fundamental quantity), not time — NEET exploits the word year in the name. Similarly, a parsec is a length unit. When NEET asks which is a fundamental unit, eliminate options that look like base quantities but are actually derived (e.g., kg/m³ is density, a derived quantity).

Download Study Materials

PDF · Cheat Sheet · MCQ Set · PYQ
📘
Fundamental and Derived Units — Full Notes
Complete coverage of fundamental units (7 SI base quantities), derived units, all four systems of units (CGS, MKS, FPS, SI), SI supplementary units, and worked examples of unit decomposition and system-to-system conversion.
PDF12 pages
Download Notes
📗
Fundamental and Derived Units — Formula Sheet
Key formulas, SI base unit table, derived unit decompositions (N, J, W, Pa, Hz), CGS–SI conversion factors, and SI prefix table from atto (10⁻¹⁸) to exa (10¹⁸).
PDF3 pages
Download Formula Sheet
📕
Fundamental and Derived Units — MCQ Practice
25 NEET-style MCQs covering unit classification, base-to-derived decomposition, system conversions, and SI prefix application with detailed step-by-step solutions.
PDF8 pages
Download MCQs
📙
Fundamental and Derived Units — PYQ Compilation
Previous year NEET and AIPMT questions (2010–2024) on unit classification, SI system identification, and inter-system unit conversions with detailed answer keys.
PDF6 pages
Download PYQs

Subtopics in Fundamental and Derived Units

2-Column Table
Column AColumn B
Fundamental Units↗
Derived Units↗
System of units↗
CGS system↗
MKS system↗
FPS system↗
S.I. system↗

Rapid Revision Cards

Concept → Trap → Example

1) Fundamental Units

Definition & SI Table

A fundamental (base) unit is an independently defined unit of a fundamental quantity. The SI system defines 7 base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd), plus 2 supplementary units: radian (rad) for plane angle and steradian (sr) for solid angle.

  • In mechanics, only 3 fundamental quantities are needed (mass, length, time), but this choice is not unique — any 3 independent mechanical quantities could serve as fundamental. If speed and time are chosen, length becomes derived.
  • The SI system extends MKS by adding ampere, kelvin, mole, and candela to cover electromagnetism, thermodynamics, chemistry, and photometry respectively.
  • Trap: the unit symbol for kelvin is uppercase K, not lowercase k. Lowercase k is the SI prefix for kilo (10³). Confusing these on a NEET answer sheet changes the physical quantity entirely.
Example (NEET-style)If speed (v) and time (t) are chosen as fundamental quantities instead of length and time, then length becomes a derived quantity: L = v × t. For v = 3 m/s and t = 2 s, L = 6 m — here the metre is a derived unit expressed as (m/s)·s, not an independent standard.

2) Derived Units

Decomposition & Conversion

A derived unit is expressed as a product of fundamental units raised to appropriate powers. Key decompositions: velocity = m·s⁻¹, acceleration = m·s⁻², force (N) = kg·m·s⁻², energy (J) = kg·m²·s⁻², power (W) = kg·m²·s⁻³, pressure (Pa) = kg·m⁻¹·s⁻².

  • To convert a derived unit between systems, decompose into base units and convert each factor independently: 1 J = 1 kg·m²·s⁻² = (10³ g)·(10² cm)²·s⁻² = 10⁷ erg.
  • Every derived unit can be expressed using exactly 7 SI base units with integer or fractional exponents — this expression is the dimensional formula of the unit.
  • Trap: a light year contains the word year but measures length (distance light travels in one year ≈ 9.46 × 10¹⁵ m). NEET uses this naming confusion as a distractor — always check what physical quantity a unit measures.
Example (NEET-style)To verify that 1 pascal = kg·m⁻¹·s⁻²: Pressure = Force/Area = (kg·m·s⁻²)/(m²) = kg·m⁻¹·s⁻². In CGS, the corresponding unit is 1 barye = 1 g·cm⁻¹·s⁻² = 0.1 Pa, so 1 Pa = 10 barye.

US Curriculum Gaps

If you studied physics in the US school system, watch out for these differences when preparing for NEET.

Multiple Unit Systems Not Covered in AP Physics 1

AP Physics 1 uses only SI units throughout the course. NEET expects familiarity with CGS (centimetre-gram-second), MKS (metre-kilogram-second), and FPS (foot-pound-second) systems, including the ability to convert derived units across all four systems.

  • Learn the CGS equivalents: 1 N = 10⁵ dyne, 1 J = 10⁷ erg, 1 W = 10⁷ erg/s
  • Practise converting compound derived units by decomposing each base-unit factor with its correct power exponent
  • FPS is rarely tested numerically but you must know the base units: foot (length), pound (mass), second (time)

SI Prefixes and Supplementary Units Not Emphasised in US College Physics

US algebra-based College Physics covers SI base units but rarely requires the full prefix table from atto (10⁻¹⁸) to exa (10¹⁸). NEET questions may ask you to express a measurement using the correct SI prefix or to identify supplementary units like radian and steradian.

  • Memorise key prefixes: nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), kilo (10³), mega (10⁶), giga (10⁹)
  • Know that radian (plane angle) and steradian (solid angle) are SI supplementary units — dimensionless but formally defined
  • Watch for prefix symbol traps: M = mega (10⁶) vs m = milli (10⁻³) — case matters and represents a 10⁹ factor difference

NEET-Style Practice Questions

2 Questions
1In a new system of units, the unit of mass is 10 kg, the unit of length is 1 km, and the unit of time is 1 minute. The numerical value of 1 newton of force expressed in this new system is:Derived Units
0.036
0.36
3.6
36
Force has the dimensional formula [M L T⁻²]. To convert 1 N from SI to the new system: n₂ = n₁ × (M₁/M₂) × (L₁/L₂) × (T₁/T₂)⁻². Substituting SI values: n₂ = 1 × (1 kg / 10 kg) × (1 m / 1000 m) × (1 s / 60 s)⁻² = 0.1 × 0.001 × 3600 = 0.36. Option (A) 0.036 results from using (T₁/T₂)⁻¹ instead of the correct (T₁/T₂)⁻² exponent. Option (C) 3.6 omits the length conversion factor entirely. Option (D) 36 omits the mass conversion factor. The key skill is correctly applying each base-unit ratio with its dimensional exponent from the dimensional formula.
2The dimensional formula of the coefficient of viscosity is [M L⁻¹ T⁻¹]. The number of poise (CGS unit) equivalent to 1 poiseuille (1 Pa·s, the SI unit of viscosity) is:Fundamental Units
0.1
1
10
100
Viscosity has dimension [M¹ L⁻¹ T⁻¹]. Converting 1 Pa·s from SI to CGS: n₂ = n₁ × (M₁/M₂) × (L₁/L₂)⁻¹ × (T₁/T₂)⁻¹ where M₁ = 1 kg, M₂ = 1 g, L₁ = 1 m, L₂ = 1 cm, T₁ = T₂ = 1 s. So n₂ = 1 × (1000/1) × (100/1)⁻¹ × (1/1)⁻¹ = 1000 × 0.01 × 1 = 10 poise. The critical step is applying the negative exponent on the length ratio: (L₁/L₂)⁻¹ = (100)⁻¹ = 0.01. Students who forget the negative exponent and use (L₁/L₂)¹ = 100 get 100000, which is wrong. Option (A) 0.1 results from inverting the entire conversion. Option (D) 100 drops the length factor.

Scenario-Based Practice

Click "Reveal Answer" after attempting
1A rocket engine produces a thrust of 2 × 10⁶ dyne. When this thrust is expressed in SI units (newtons), the value is:
0.2 N
2 N
20 N
200 N
👁 Reveal Answer
Correct answer: 20 N. Since 1 dyne = 1 g·cm·s⁻² = 10⁻³ kg × 10⁻² m × s⁻² = 10⁻⁵ N, we get 2 × 10⁶ dyne = 2 × 10⁶ × 10⁻⁵ N = 20 N. The trap is forgetting that both mass AND length factors must be converted simultaneously.
2The SI unit of surface tension is N/m. Expressed purely in terms of SI base units, the unit of surface tension is:
kg·s⁻²
kg·m·s⁻²
kg·m⁻¹·s⁻²
kg·m²·s⁻²
👁 Reveal Answer
Correct answer: kg·s⁻². Surface tension = Force/Length = N/m = (kg·m·s⁻²)/m = kg·s⁻². Option B is force (newton), option C is pressure (pascal), and option D is energy (joule). The key is cancelling the length dimension correctly.
3If force (F), length (L), and time (T) are chosen as fundamental quantities in a hypothetical system, the dimensional representation of mass in this system is:
F L⁻¹ T²
F L T⁻²
F L⁻¹ T⁻²
F⁻¹ L T²
👁 Reveal Answer
Correct answer: F L⁻¹ T². From F = ma = m × L/T², rearranging gives m = F × T²/L = F L⁻¹ T². Option B (F L T⁻²) has dimensions of energy, not mass. This tests whether students can rearrange the force equation using non-standard fundamental quantities.
4A femtosecond (fs) equals 10⁻¹⁵ s and a nanometre (nm) equals 10⁻⁹ m. The speed of light is approximately 3 × 10⁸ m/s. The distance light travels in 1 femtosecond, expressed in nanometres, is:
0.3 nm
3 nm
300 nm
3000 nm
👁 Reveal Answer
Correct answer: 300 nm. Distance = speed × time = 3 × 10⁸ m/s × 10⁻¹⁵ s = 3 × 10⁻⁷ m. Converting: 3 × 10⁻⁷ m / 10⁻⁹ m/nm = 300 nm. This equals the wavelength of near-UV light, confirming physical reasonableness.

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Frequently Asked Questions

Notes · Downloads · Revision · Important Questions
What is the difference between a fundamental unit and a derived unit?
A fundamental (base) unit is independently defined without reference to any other unit — the metre is defined by the distance light travels in 1/299,792,458 of a second. A derived unit is constructed from combinations of fundamental units through algebraic operations — velocity (m/s) combines the base units of length and time. The SI system has 7 fundamental units; all other physical quantity units are derived from these seven.
Why are mass, length, and time chosen as fundamental quantities in mechanics?
The choice is purely conventional and not unique. Any three independent mechanical quantities could serve as fundamental. For instance, if speed and time are chosen as fundamental, length becomes a derived quantity: length = speed × time. The mass-length-time triad is preferred because these quantities are intuitively distinct, easily standardised with physical artifacts or constants, and have a long metrological history.
How many base units does the SI system define and what are they?
The SI system defines 7 base units: metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. Two supplementary units also exist: radian (rad) for plane angle and steradian (sr) for solid angle, now classified as derived dimensionless units.
Is a light year a fundamental unit or a derived unit?
A light year is classified as a fundamental unit because it measures length — a single fundamental quantity. Despite containing the word year, it represents a distance of approximately 9.46 × 10¹⁵ m, not a time interval. The textbook explicitly states that light year or km is a fundamental unit as it is a unit of length. NEET exploits this naming confusion as a trap question.
What are the supplementary units in the SI system?
The SI defines 2 supplementary units: the radian (rad) for plane angle, defined as the ratio of arc length to radius, and the steradian (sr) for solid angle, defined as the ratio of intercepted spherical surface area to the square of the radius. Both are dimensionless. The 1995 CGPM decision reclassified these as derived dimensionless units, but many textbooks still list them separately.
How do you convert a derived unit from CGS to SI?
Decompose the derived unit into base-unit components, convert each base unit individually, and recombine. For example, to convert 1 erg to joules: 1 erg = 1 g·cm²·s⁻². Replace g with 10⁻³ kg and cm with 10⁻² m: 1 erg = 10⁻³ kg × (10⁻² m)² × s⁻² = 10⁻³ × 10⁻⁴ kg·m²·s⁻² = 10⁻⁷ J. Apply the correct power to each conversion factor.
Why was the definition of the kilogram changed in 2019?
Before 2019, the kilogram was defined by a platinum-iridium cylinder stored at the BIPM in France, which was susceptible to contamination and micro-wear. The 26th CGPM in 2019 redefined the kilogram by fixing the Planck constant at h = 6.62607015 × 10⁻³⁴ J·s exactly, linking mass to an unchanging fundamental constant reproducible in any laboratory worldwide. This eliminates artifact-dependent uncertainty.
What is the NEET significance of SI prefixes?
SI prefixes express very large or very small quantities using powers of ten. For NEET, the most tested prefixes are: nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), kilo (10³), mega (10⁶), and giga (10⁹). Questions may require converting between prefixed and standard forms. The most frequent trap is confusing uppercase M (mega, 10⁶) with lowercase m (milli, 10⁻³), a factor-of-10⁹ error.
Can the same physical quantity have both a fundamental unit and a practical unit?
Yes. Length is a fundamental quantity with the SI base unit metre. It can also be measured using practical units such as light year (9.46 × 10¹⁵ m), parsec (3.26 light years), angstrom (10⁻¹⁰ m), or fermi (10⁻¹⁵ m). These practical units are still classified as fundamental because they measure a single fundamental quantity. The textbook notes that practical units may or may not belong to a formal system but can always be expressed in any system.
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Fundamental Units

Derived Units

System of units

CGS system

MKS system

FPS system

S.I. system

Subtopics

Fundamental Units

Derived Units

System of units

CGS system

MKS system

FPS system

S.I. system

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