The trap that costs marks on SI Units questions is simpler than you think: confusing a unit name with a dimension. Radian and steradian both have names — they appear in tables, they have abbreviations — but they are dimensionless. They are ratios: arc length divided by radius (radian), surface area divided by radius squared (steradian). NEET distractors exploit this by offering "radian has dimension of length" or "steradian has dimension of area."
The SI system, as defined by the CGPM (NCERT Class 11 Physics Chapter 1, page 2), rests on seven base quantities with seven base units: length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole), and luminous intensity (candela). Every other unit — newton, joule, pascal, watt — is derived from these seven by multiplication, division, or exponentiation. No additional independent quantities are needed.
Two supplementary quantities — plane angle and solid angle — were historically listed alongside the base quantities but were reclassified as dimensionless derived quantities. Their units (radian and steradian) remain in use for clarity, but they carry no independent dimension. This is where the confusion sits: having a unit name does not mean having a dimension.
For NEET, anchor on these facts:
Watch out for distractors that list radian or steradian as "having dimensions" or that claim there are nine base quantities. There are seven.
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 NOT an SI base unit?
Answer: A. Newton is the SI unit of force, which is a derived quantity (kg·m·s⁻²). The seven SI base units are metre, kilogram, second, ampere, kelvin, mole, and candela (NCERT Class 11 Physics Chapter 1, page 2).
Why B is wrong: B (candela) is the SI base unit for luminous intensity — it is one of the seven base units.
Why C is wrong: C (ampere) is the SI base unit for electric current — it is one of the seven base units, not a derived unit.
Why D is wrong: D (kelvin) is the SI base unit for thermodynamic temperature — it is one of the seven base units.
Every SI base unit is now defined by fixing the numerical value of a specific physical constant — for example, the second fixes the caesium hyperfine frequency, and the kilogram fixes the Planck constant. Given this pattern, which statement about the modern definition of the mole is correct?
Answer: A. NCERT states: "One mole contains exactly 6.02214076×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant." Just as the second fixes the caesium frequency and the kilogram fixes the Planck constant, the mole fixes the Avogadro constant — each of the seven base units is defined this same way, by pinning down one constant's numerical value (NCERT Class 11 Physics Chapter 1, page 2).
Why B is wrong: B is wrong because none of the seven modern SI base units — including the mole — is defined via a physical prototype any longer. A reference-artifact definition describes the OLD (pre-2019) kilogram standard, not the current mole definition, which fixes the Avogadro constant instead. (trap: confusing the mole with the historical prototype-based approach to the kilogram)
Why C is wrong: C is wrong because each base unit's modern definition fixes its OWN constant independently — the mole's definition fixes the Avogadro constant on its own, without needing the Planck constant (used for the kilogram) to appear in the same defining statement. (trap: assuming the constants are chained together in one combined definition)
Why D is wrong: D is wrong because amount of substance is precisely one of the seven SI base quantities, measured independently by counting elementary entities (in units of mole) — NCERT lists it alongside length, mass, and the others as a base quantity. (trap: assuming only mechanical quantities like mass or length can be 'base' quantities)
How many base quantities are there in the International System of Units (SI)?
Answer: A. The SI system defines exactly seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity (NCERT Class 11 Physics Chapter 1, page 2). The number 9 is a common trap — it comes from the historical listing that included two supplementary quantities (plane angle and solid angle), which are now classified as dimensionless derived quantities.
Why B is wrong: B (5) undercounts — this omits two of the seven base quantities.
Why C is wrong: C (9) is the trap answer. It includes the two supplementary quantities (plane angle and solid angle), which were reclassified as dimensionless derived quantities and are NOT base quantities (trap: unit vs dimension confusion for radian/steradian).
Why D is wrong: D (6) undercounts by one — all seven base quantities are distinct and independently defined.
Plane angle (radian) and solid angle (steradian) are:
Answer: B. Radian is arc length ÷ radius (length ÷ length = dimensionless). Steradian is surface area ÷ radius² (length² ÷ length² = dimensionless). Both are classified as dimensionless derived quantities in the current SI. They have unit names for convenience but no independent dimension (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A is wrong because both quantities are ratios of like dimensions — arc/radius for radian, area/r² for steradian — so both are dimensionless, not dimensional (trap: confusing 'has a unit name' with 'has dimensions').
Why C is wrong: C is wrong because base quantities are the seven independently defined quantities (length, mass, time, etc.). Plane angle and solid angle were reclassified from supplementary to derived status.
Why D is wrong: D is wrong on two counts: (i) the 'supplementary' label is historical and no longer current, and (ii) neither quantity has the dimension of length — both are dimensionless ratios.
The SI unit of luminous intensity is:
Answer: D. Candela (cd) is the SI base unit for luminous intensity. Lumen is the derived SI unit of luminous flux (cd·sr). Lux is luminous flux per unit area (lm/m²). Watt is the unit of power (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A (lumen) is the SI derived unit of luminous flux, not luminous intensity. Lumen = candela × steradian.
Why B is wrong: B (lux) is the SI derived unit of illuminance (lumen per square metre), not luminous intensity.
Why C is wrong: C (watt) is the SI derived unit of power (joule per second). It measures energy transfer rate, not luminous intensity.
Which of the following statements about SI base units is correct?
Answer: D. Kelvin (K) is the SI base unit for thermodynamic temperature. Gram (not kilogram) is a common error — kilogram is the SI base unit of mass. Degree Celsius is a derived scale, not the base unit. Coulomb is the unit of electric charge (A·s), not current; ampere is the base unit of current (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A is wrong because the SI base unit of mass is the kilogram (kg), not the gram. Kilogram is unique among base units in already having a prefix.
Why B is wrong: B is wrong because degree Celsius (°C) is not an SI base unit. The SI base unit of thermodynamic temperature is kelvin (K). Celsius is a derived scale offset from kelvin by 273.15.
Why C is wrong: C is wrong because coulomb (C) is the SI derived unit of electric charge (= ampere × second). The SI base unit of electric current is the ampere (A).
The unit 'pascal' is equivalent to which of the following in terms of SI base units?
Answer: A. Pascal = N/m² = (kg·m·s⁻²)/m² = kg·m⁻¹·s⁻². Option B is the newton itself (force, not pressure). Option C is the joule (energy). Option D has incorrect exponents for both length and time.
Why B is wrong: B (kg·m·s⁻²) is the dimensional decomposition of the newton (force), not the pascal (pressure). Pressure = force/area, so you need to divide by m², giving m⁻¹ instead of m¹.
Why C is wrong: C (kg·m²·s⁻²) is the dimensional decomposition of the joule (energy = force × distance). Pressure is force per unit area, not force times distance.
Why D is wrong: D (kg·m⁻²·s⁻¹) has incorrect exponents: the time exponent should be −2 (from s⁻² in newton) and the length exponent should be −1 (from m/m² = m⁻¹).
A student claims that the radian has the dimensional formula [L]. Which of the following correctly identifies the error?
Answer: B. Radian = arc length / radius = length / length = dimensionless. It has no dimensional formula — [M⁰L⁰T⁰]. The student's error is treating the numerator's dimension (length) as the radian's dimension while ignoring the denominator (also length), which cancels it out (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A doubles down on the student's error. The radian is not L² — it is a ratio where both numerator and denominator have the dimension of length, so the dimensions cancel entirely (trap: confusing a unit name with a dimension).
Why C is wrong: C confuses the radian (a dimensionless ratio) with angular velocity (rad/s, which has dimension [T⁻¹]). The radian itself carries no time dimension.
Why D is wrong: D is wrong because radian is NOT a base quantity. It was historically listed as a supplementary quantity but is now classified as a dimensionless derived quantity.
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Pattern: Plane vs solid angle dimensions — identifying dimensionless quantities (pattern anchored to NEET 2022)
Given
A physics teacher writes the following on the board:• Plane angle θ = arc length / radius• Solid angle Ω = surface area / (radius)²
A student argues that since arc length has the dimension [L] and surface area has the dimension [L²], the plane angle must have dimension [L] and the solid angle must have dimension [L²].
Required
Determine the correct dimensions of plane angle and solid angle. Identify the student's error.
Concept
A quantity's dimension depends on the complete defining expression, not just the numerator. When a quantity is defined as a ratio of two quantities with the same dimension, the dimensions cancel, yielding a dimensionless result.
Formula
Plane angle: θ = s / r, where both s and r have dimension [L].
Solid angle: Ω = A / r², where A has dimension [L²] and r² has dimension [L²].
Substitution
Plane angle: [θ] = [L] / [L] = [M⁰L⁰T⁰]
Solid angle: [Ω] = [L²] / [L²] = [M⁰L⁰T⁰]
Calculation
Both ratios yield [M⁰L⁰T⁰] — no surviving dimension of length in either case. No arithmetic beyond the dimensional cancellation is needed.
Final answer
Both plane angle and solid angle are dimensionless quantities. Their dimensions are [M⁰L⁰T⁰]. They have SI unit names (radian and steradian) for practical clarity, but these names do not confer dimensions.
The student's error: treating only the numerator's dimension as the quantity's dimension, while ignoring the denominator, which has the same dimension and cancels it completely.
Common trap
Confusing "has a unit name" with "has a dimension." Many students assume that because radian and steradian appear in tables of units — just like metre and kilogram do — they must carry independent dimensions. They do not. A unit name is a label for convenience; a dimension is a fundamental independent physical attribute. Radian and steradian are ratios of like quantities.
Similar NEET-style question
"Which of the following pairs of physical quantities are both dimensionless?
(A) Strain and refractive index
(B) Force and impulse
(C) Angle and angular velocity
(D) Solid angle and torque"
Answer: (A). Strain = ΔL/L (dimensionless ratio); refractive index = c/v (dimensionless ratio). This tests the same principle: ratios of like-dimensioned quantities yield dimensionless results.
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The SI is the internationally accepted system of units, based on seven base units: metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (thermodynamic temperature), mole (amount of substance) and candela (luminous intensity).
-- NCERT Class 11 Physics, Ch. 1, p. 2Table of seven SI base units with symbols: m (metre), kg (kilogram), s (second), A (ampere), K (kelvin), mol (mole), cd (candela). Derived units are formed from these (e.g. N for newton = kg·m·s⁻², J for joule = N·m, W for watt = J·s⁻¹).
-- NCERT Class 11 Physics, Ch. 1, p. 2More 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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