The trap that costs marks on this topic: confusing units with dimensions. Radian and steradian have unit names — but they are dimensionless. NEET distractors exploit exactly this confusion.
Fundamental units are the seven SI base units — metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). These are independently defined and cannot be expressed in terms of each other (NCERT Class 11 Physics Chapter 1, page 2).
Two supplementary units — radian (plane angle) and steradian (solid angle) — were historically listed alongside the base units. After the 1995 CGPM decision, they are classified as derived, dimensionless units. A radian is arc-length divided by radius (length/length = dimensionless). A steradian is surface-area divided by radius-squared (length²/length² = dimensionless). They carry unit names purely for convenience — they have no dimensions.
Derived units are built from the fundamental units through multiplication, division, or exponentiation. Examples: newton (kg·m·s⁻²), joule (kg·m²·s⁻²), pascal (kg·m⁻¹·s⁻²), watt (kg·m²·s⁻³).
The distinction matters for NEET because:
Watch-out: "dimensionless" does not mean "unitless." Radian is dimensionless but has a unit name. This is the single distinction NEET tests on this topic.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
Which of the following is a DERIVED unit in the SI system?
Answer: B. B is correct. The newton is built from base units: 1 N = 1 kg·m·s⁻², the force that gives 1 kg an acceleration of 1 m/s². It is defined through a relation (F = ma), which is what makes a unit derived rather than base.
Why A is wrong: A is wrong because the kelvin is one of the seven SI base units, the unit of thermodynamic temperature. It is not expressed in terms of any other unit.
Why C is wrong: C is wrong because the candela is an SI base unit, the unit of luminous intensity. Its name sounds unusual, which is why it is easy to mistake for a derived unit.
Why D is wrong: D is wrong because the ampere is an SI base unit, the unit of electric current. The coulomb is the derived one (1 C = 1 A·s), not the ampere.
Which of the following is NOT an SI base unit?
Answer: D. Radian is a supplementary/derived unit for plane angle. It is dimensionless and not one of the seven SI base units (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A is wrong because ampere is the SI base unit for electric current.
Why B is wrong: B is wrong because candela is the SI base unit for luminous intensity.
Why C is wrong: C is wrong because mole is the SI base unit for amount of substance.
Which of the following pairs are both dimensionless quantities?
Answer: A. Plane angle (radian = arc/radius) and solid angle (steradian = area/radius²) are both ratios of like quantities and therefore dimensionless (NCERT Class 11 Physics Chapter 1, page 2).
Why B is wrong: B is wrong because electric charge has dimensions [AT] (ampere × time) and is not dimensionless.
Why C is wrong: C is wrong because luminous intensity has dimensions — it is an SI base quantity with unit candela.
Why D is wrong: D is wrong because although refractive index is dimensionless — it is a ratio of two speeds — electric current is an SI BASE quantity with dimension [A]. A pair qualifies only if both members are dimensionless.
The SI unit of force is the newton. Express 1 newton in terms of fundamental SI units.
Answer: C. Force = mass × acceleration. Acceleration = m/s². So 1 N = 1 kg·m·s⁻² (NCERT Class 11 Physics Chapter 1, page 7).
Why A is wrong: A is wrong because kg·m·s⁻¹ is the unit of momentum (mass × velocity), not force. The time exponent should be −2 (from acceleration), not −1.
Why B is wrong: B is wrong because kg·m²·s⁻² is the unit of energy (joule), not force. The length exponent should be 1 (from acceleration = m/s²), not 2.
Why D is wrong: D is wrong because kg·m⁻¹·s⁻² is the unit of pressure (pascal = force/area). The length exponent is negative here, whereas force has a positive length exponent.
The SI unit of pressure is the pascal. Which of the following correctly expresses 1 pascal in terms of base SI units?
Answer: D. Pressure = Force/Area = (kg·m·s⁻²)/m² = kg·m⁻¹·s⁻². The length exponent drops from +1 to −1 after dividing by m² (NCERT Class 11 Physics Chapter 1, page 7).
Why A is wrong: A is wrong because kg·m·s⁻² is the unit of force (newton), not pressure. Pressure requires dividing force by area (m²), which changes the length exponent.
Why B is wrong: B is wrong because kg·m⁻²·s⁻¹ has incorrect exponents for both length and time. The time exponent for pressure is −2 (from force), not −1.
Why C is wrong: C is wrong because kg·m²·s⁻² is the unit of energy (joule). This has an extra m³ compared to pressure.
Which of the following statements about radian and steradian is correct?
Answer: B. Radian (plane angle = arc/radius) and steradian (solid angle = area/r²) are ratios of like quantities, making them dimensionless. However, they do carry unit names (rad, sr) for clarity in physical equations (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A is wrong because neither radian nor steradian has dimensions — they are ratios of quantities with the same dimensions, yielding M⁰L⁰T⁰. Having a unit name does not imply having dimensions (trap: confusing 'has a unit' with 'has dimensions').
Why C is wrong: C is wrong because radian is also dimensionless, just like steradian. Both are defined as ratios of like quantities.
Why D is wrong: D is wrong because while both are dimensionless, they DO have unit names — radian (rad) and steradian (sr). 'Dimensionless' ≠ 'unitless'.
A student claims: "Since radian and steradian have different unit symbols (rad and sr), they must have different dimensions." What is wrong with this claim?
Answer: A. The student confuses units with dimensions. Radian = arc/radius (length/length = dimensionless). Steradian = area/radius² (length²/length² = dimensionless). Different unit names, same (null) dimensions (NCERT Class 11 Physics Chapter 1, page 2).
Why B is wrong: B is wrong because radian and steradian do have different unit symbols (rad vs sr). The issue is not the symbols — it's the incorrect inference from different symbols to different dimensions.
Why C is wrong: C is wrong because steradian is not a fundamental unit. It is a derived, dimensionless unit classified alongside radian as a supplementary unit.
Why D is wrong: D is wrong because radian does not have dimensions of length. It is arc-length divided by radius (both in metres), giving a dimensionless ratio.
The energy stored in a capacitor is given by E = ½CV², where C is capacitance (unit: farad) and V is voltage (unit: volt). Express the farad in terms of fundamental SI units.
Given: 1 volt = 1 kg·m²·s⁻³·A⁻¹; 1 joule = 1 kg·m²·s⁻².
Answer: C. From E = ½CV², we get C = E/V² (dimensionally). Farad = joule/volt² = (kg·m²·s⁻²)/(kg·m²·s⁻³·A⁻¹)² = (kg·m²·s⁻²)/(kg²·m⁴·s⁻⁶·A⁻²) = kg⁻¹·m⁻²·s⁴·A². This requires two steps: squaring the volt expression, then dividing.
Why A is wrong: A is wrong because the time exponent is s² instead of s⁴. This comes from writing the volt as joule per ampere (kg·m²·s⁻²·A⁻¹) and dropping the per-second: a volt is a joule per coulomb, and a coulomb is an ampere-second.
Why B is wrong: B is wrong because kg·m²·s⁻⁴·A⁻² has all exponents with the wrong sign compared to the correct answer. This results from inverting the fraction (computing V²/E instead of E/V²).
Why D is wrong: D is wrong because kg·m²·s⁻²·A⁻² is the unit of energy divided by A² — it omits the division by V² entirely, effectively just appending A⁻² to the joule.
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Pattern: Derive the SI base-unit expression for a derived quantity (aligned with the unit-vs-dimension conceptual theme of this lesson).
Given
The power dissipated in a resistor is P = V²/R, where V is voltage and R is resistance.• 1 watt (P) = 1 kg·m²·s⁻³• 1 volt (V) = 1 kg·m²·s⁻³·A⁻¹
Required
Express the ohm (unit of resistance R) in terms of fundamental SI units.
Concept
From P = V²/R, we get R = V²/P. Since both watt and volt are already expressed in base units, we can derive the ohm by algebraic substitution.
Formula
R = V²/P (dimensional relationship)
Substitution
ohm = (kg·m²·s⁻³·A⁻¹)² / (kg·m²·s⁻³)
Numerator (V²): kg²·m⁴·s⁻⁶·A⁻²
Denominator (P): kg·m²·s⁻³
Calculation
ohm = kg²·m⁴·s⁻⁶·A⁻² / (kg·m²·s⁻³)
Divide each base unit:• kg: 2 − 1 = 1• m: 4 − 2 = 2• s: −6 − (−3) = −3• A: −2 − 0 = −2
ohm = kg·m²·s⁻³·A⁻²
Note: the exponents in the given volt and watt expressions are exact definitions, not measured values — they do not carry uncertainty.
Final answer
1 ohm = 1 kg·m²·s⁻³·A⁻²
Common trap
The common error is mishandling the squaring step — students sometimes square only the numerical coefficient or forget to square every base-unit exponent in the volt expression. For instance, forgetting to square the A⁻¹ term yields A⁻¹ instead of A⁻² in the final answer.
Similar NEET-style question
"Express the henry (unit of inductance) in terms of fundamental SI units, given that the energy stored in an inductor is E = ½LI²."
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Although the number of physical quantities is large, only a limited number of units is needed because all physical quantities are inter-related. The chosen quantities are called fundamental (base) quantities; the rest are derived from them.
-- NCERT Class 11 Physics, Ch. 1, p. 1More in Units and Measurements: 9 exam traps and mistakes · 3 formulas · 9 question patterns from its other lessons.
No question in our NEET 2020–2025 set targets this topic directly.
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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