A system of units is a complete, self-consistent set of units built from a chosen set of base quantities. The confusion that costs marks on NEET: treating radian and steradian as if they carry dimensions, when they are dimensionless ratios that merely have unit names.
What NCERT says. A system of units selects a small number of base (fundamental) quantities — length, mass, time, electric current, temperature, amount of substance, luminous intensity — and defines one unit for each. Every other unit is derived from these seven by multiplication, division, or exponentiation. The four historically important systems are CGS (centimetre–gram–second), FPS (foot–pound–second), MKS (metre–kilogram–second), and the modern SI, which extends MKS with four more base quantities (NCERT Class 11 Physics Chapter 1, page 2).
The SI supplementary-unit trap. Before 1995, radian and steradian were classified as "supplementary units" — a third category alongside base and derived. The 20th CGPM (1995) abolished that category and reclassified both as derived units. They remain dimensionless: radian = arc length ÷ radius (length ÷ length), steradian = subtended area ÷ radius² (length² ÷ length²). NEET distractors exploit the fact that these quantities have named units, tempting you to assign them dimensions they do not possess.
How NEET tests this. The typical question presents plane angle and solid angle side by side and asks about their dimensional status. Distractors include "plane angle has dimensions of length" or "solid angle has dimensions of area." The correct answer: both are dimensionless; both have units (rad, sr) but zero dimensional formula.
Watch-out. When a question says "supplementary units," it is testing whether you know the historical label and its modern reclassification — not whether you assign dimensions. Dimensionless means [M⁰ L⁰ T⁰].
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 a base quantity in the SI system?
Answer: D. Force is a derived quantity (force = mass × acceleration, SI unit newton = kg·m·s⁻²). The seven SI base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A (electric current) IS one of the seven SI base quantities — its base unit is the ampere.
Why B is wrong: B (luminous intensity) IS one of the seven SI base quantities — its base unit is the candela.
Why C is wrong: C (amount of substance) IS one of the seven SI base quantities — its base unit is the mole.
The SI unit of density is kg/m³ and the CGS unit is g/cm³. Using the base-unit conversions 1 kg = 10³ g and 1 m = 10² cm, express 1 kg/m³ in g/cm³.
Answer: C. 1 kg/m³ = 1 kg · m⁻³. Converting kg → g gives a factor of 10³ (1 kg = 10³ g), and converting m⁻³ → cm⁻³ gives a factor of 10⁻⁶ (since 1 m = 10² cm, m⁻³ = (10² cm)⁻³ = 10⁻⁶ cm⁻³). Multiplying the two conversion factors: 10³ × 10⁻⁶ = 10⁻³. So 1 kg/m³ = 10⁻³ g/cm³ — consistent with water's density, 1000 kg/m³ = 1 g/cm³ (NCERT Class 11 Physics, Chapter 1, pages 1–2).
Why A is wrong: Forgetting to convert kg→g (treating 1 kg as 1 g) while correctly cubing the length factor (10⁻⁶) gives only 10⁻⁶ g/cm³ — the mass conversion factor (10³) is missing.
Why B is wrong: Converting the length factor only once instead of cubing it (10³ × 10⁻² = 10, treating m³ → cm³ as a single linear step of 10² rather than (10²)³ = 10⁶) gives 10 g/cm³ — this drops two of the three length-conversion factors.
Why D is wrong: Inverting the mass conversion (using 10⁻³ instead of 10³ for kg→g) while correctly cubing the length factor gives 10⁻³ × 10⁻⁶ = 10⁻⁹ g/cm³ — the mass factor is applied backwards.
In the CGS system, the base units of length, mass, and time are respectively:
Answer: C. CGS stands for centimetre–gram–second. These are its three base units (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A describes the MKS (metre–kilogram–second) system, not the CGS system.
Why B is wrong: B describes the FPS (foot–pound–second) system, not the CGS system.
Why D is wrong: D mixes CGS length (centimetre) with MKS mass (kilogram) — a hybrid that does not correspond to any standard system.
Plane angle (radian) and solid angle (steradian) are:
Answer: B. Radian = arc/radius (length/length) and steradian = area/radius² (length²/length²), so both are dimensionless ratios [M⁰ L⁰ T⁰]. They do carry named units (rad, sr) for clarity (NCERT Class 11 Physics Chapter 1, page 2). The trap is confusing "has a unit name" with "has dimensions" (trap: unit vs dimension confusion for radian/steradian).
Why A is wrong: A is wrong — having a named unit does not imply having dimensions. Radian and steradian are ratios of like quantities, yielding [M⁰ L⁰ T⁰] (trap: assuming named unit → dimensional).
Why C is wrong: C is wrong — both plane and solid angle are dimensionless. There is no asymmetry between them; radian is length/length and steradian is length²/length² (trap: partial recall suggesting only one is dimensionless).
Why D is wrong: D is wrong — radian and steradian ARE named units, adopted by the SI. They simply lack dimensions despite having names.
Before the 20th CGPM resolution in 1995, radian and steradian were classified as:
Answer: A. Radian and steradian were historically classified as "supplementary units" — a third category separate from base and derived. The 20th CGPM (1995) abolished this category and reclassified them as derived units (NCERT Class 11 Physics Chapter 1, page 2).
Why B is wrong: B is wrong for the pre-1995 era — they were reclassified as derived units AFTER 1995, not before. The question asks about the pre-1995 category.
Why C is wrong: C is wrong — radian and steradian were never classified as base units. The SI has exactly seven base units, none of which is an angle.
Why D is wrong: D is wrong — fundamental constants (like the speed of light) define the magnitude of SI units since 2019, but radian/steradian are units, not constants.
In the CGS system, energy is measured in ergs. One joule is equal to:
Answer: D. D is correct. 1 J = 1 kg·m²·s⁻². Converting each base unit: 1 kg = 10³ g and 1 m² = 10⁴ cm², so 1 J = 10³ × 10⁴ g·cm²·s⁻² = 10⁷ erg.
Why A is wrong: A is wrong because 10⁵ is the conversion for FORCE, 1 N = 10⁵ dyne. Energy carries an extra factor of length, and a metre is 10² cm, so the factor is 10⁷.
Why B is wrong: B is wrong because 10³ converts only the mass, kilograms to grams, and leaves the metres squared unconverted.
Why C is wrong: C is wrong because 10⁻⁷ is the conversion the other way round: 1 erg = 10⁻⁷ J. The joule is the larger unit.
Which of the following pairs of physical quantities have different dimensional formulas?
Answer: B. Force = [M L T⁻²] while impulse = force × time = [M L T⁻¹]. They differ in the exponent of T. Work and energy share [M L² T⁻²]; pressure and stress share [M L⁻¹ T⁻²]; angular velocity and frequency share [T⁻¹] (NCERT Class 11 Physics Chapter 1, page 2).
Why A is wrong: A is wrong — work = force × displacement = [M L² T⁻²] and energy = [M L² T⁻²]. They have identical dimensions.
Why C is wrong: C is wrong — angular velocity = angle/time = [T⁻¹] (radian is dimensionless) and frequency = 1/time = [T⁻¹]. They have identical dimensions.
Why D is wrong: D is wrong — pressure = force/area = [M L⁻¹ T⁻²] and stress = force/area = [M L⁻¹ T⁻²]. They have identical dimensions.
A student claims: "Since radian is a unit, plane angle must be a dimensional quantity." Which statement correctly identifies the flaw?
Answer: A. The flaw is the assumption that every named unit carries dimensions. Radian = arc length ÷ radius = length ÷ length = dimensionless. A unit name is a human convention for clarity; dimensional status is determined by whether the quantity reduces to base dimensions or cancels to [M⁰ L⁰ T⁰] (trap: unit vs dimension confusion for radian/steradian).
Why B is wrong: B is wrong — radian IS a recognised SI unit (currently classified as a derived unit since 1995). The issue is not recognition but dimensionlessness.
Why C is wrong: C is wrong — plane angle does NOT have dimensions of length. It is the ratio of two lengths (arc/radius), which cancels to dimensionless.
Why D is wrong: D is wrong — many derived units ARE dimensional (e.g. newton = [M L T⁻²]). The claim that 'only derived units can be dimensional' is both false and irrelevant to the flaw in the student's reasoning.
Get a structured 30-day Mechanics plan and a complete formula booklet — delivered to your inbox instantly.
Given
• Q = (intercepted area on sphere) / (radius of sphere)²• Area has dimensions [L²]• Radius has dimensions [L]
Required
• Dimensional formula of Q• Whether Q has a named SI unit
Concept
Solid angle is defined as the ratio of the surface area subtended at the centre of a sphere to the square of the sphere's radius. Since both numerator and denominator have the same dimensions, the result is dimensionless.
Formula
[Q] = [Area] / [Radius]² = [L²] / [L²]
Substitution
[Q] = L² / L² = L⁰ = [M⁰ L⁰ T⁰]
Calculation
The length dimensions cancel exactly. No arithmetic is needed — this is a dimensional cancellation. All quantities here (area, radius) are geometric definitions with exact relationships, not measured values requiring significant-figure treatment.
Final answer
Q has dimensional formula [M⁰ L⁰ T⁰] (dimensionless). Q is the solid angle, and its named SI unit is the steradian (sr).
Note: The numbers 2 (as exponents) are exact mathematical powers — they do not contribute to any significant-figure count. This problem involves no measured values.
Common trap
Students see "area" in the numerator and write [L²], then forget to divide by [L²] from the radius squared — concluding Q has dimensions of area. Others see the named unit "steradian" and assume it must carry dimensions. A named unit ≠ a dimensional unit. (Trap: unit-vs-dimension confusion for radian/steradian.)
Similar NEET-style question
"The ratio of the circumference of a circle to its diameter is π. What is the dimensional formula of π?" Answer: [M⁰ L⁰ T⁰] — it is the ratio of two lengths (circumference [L] / diameter [L]), hence dimensionless, with no named unit.
---
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. 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.
Test yourself on this topic with real past-paper questions:
Practice this topic →