NDA Physics · Free notes
Units, Measurement and Dimensions — NDA Physics
Units, Measurement and Dimensions is NDA Physics's most reliable scoring chapter — about 14 PYQs across 2017–2025, and roughly three-quarters of them are EASY one-line recall. Almost every question reduces to a fixed fact: a light year is a unit of DISTANCE (asked four separate times), 1 dyne = 10⁻⁵ N, H stands for Henry, 1 kWh = 3.6×10⁶ J, strain is dimensionless. The handful of MODERATE/HARD items just apply one tool — the dimensional formula [M^a L^b T^c] — to find the dimension of G or to identify an unknown quantity (thrust/impulse turns out to be frequency). The chapter teaches in one continuous arc, all inside a single subtopic: first the foundations (physical quantity, unit, the seven SI base units, fundamental vs derived); then the named SI derived units (Newton, Pascal, Joule, Watt, Henry — and the fact that stress and pressure share a unit); the special units of length/distance (light year, ångström, nanometre) and of energy/power (joule, kWh, the force-vs-energy trap); unit-system conversion (CGS ↔ SI, the dyne); and finally the dimensional method itself — writing dimensional formulas, spotting dimensionless quantities, identifying a quantity from its dimensions, and reading least count / precision off an instrument. Memorise the reference tables, learn the one dimensional-analysis recipe, and this chapter is near-free marks.
The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.
Subtopic notes
Formula & revision sheet
6 formulas · 3 reference tables · 13 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
6 formulas · 3 reference tables · 13 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (6)
- Units of energy and power — joule, kWh, and the force trap · Kilowatt-hour to joules
- Unit-system conversion — CGS to SI (the dyne) · CGS force unit to SI
- Dimensional formulas — writing [M^a L^b T^c] · Dimension of the gravitational constant G
- Dimensionless quantities — strain, angle, refractive index · Strain is a pure ratio
- Identifying a quantity from its units or dimensions · Thrust ÷ impulse is a frequency
- Measurement — precision, accuracy and least count · Least count of a metre scale
Reference tables (3)
Physical quantities, units, and the seven SI base units7 rows
| Base quantity | SI unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | KQ NDA 2025 match-list — Temperature → Kelvin, Mass → Kilogram (weight is a force → Newton, pressure → Pascal). |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
SI derived units named after scientists6 rows
| Unit (symbol) | Quantity | In base units |
|---|---|---|
| Newton (N) | Force | kg·m/s² |
| Pascal (Pa) | Pressure, stress | N/m² = kg/(m·s²) |
| Joule (J) | Work, energy | N·m = kg·m²/s² |
| Watt (W) | Power | J/s = kg·m²/s³ |
| Hertz (Hz) | Frequency | s⁻¹ |
| Henry (H) | Inductance | kg·m²/(s²·A²)Q NDA 2017 — the symbol H stands for Henry (after Joseph Henry), NOT Hertz. |
Units of length and distance — light year, ångström, nanometre5 rows
| Unit | Measures | Value |
|---|---|---|
| Light year (ly) | Distance (astronomical) | 9.46 × 10¹⁵ mQ Asked 4× (2017, 2018, 2021) — light year is DISTANCE, never time, never light intensity. |
| Astronomical unit (AU) | Distance (Earth–Sun) | 1.496 × 10¹¹ m |
| Parsec (pc) | Distance (astronomical) | 3.086 × 10¹⁶ m ≈ 3.26 ly |
| Nanometre (nm) | Length (atomic-scale) | 10⁻⁹ m |
| Ångström (Å) | Length (atomic-scale) | 10⁻¹⁰ mQ NDA 2018 — 1 nm = 10 Å (since nm is 10⁻⁹ m and Å is 10⁻¹⁰ m). |
Watch out for (13)
- Mass is kilogram; weight is a force (newton)→ Physical quantities, units, and the seven SI base units
- H is Henry, not Hertz→ SI derived units named after scientists
- Stress and pressure share a unit→ SI derived units named after scientists
- Light year is DISTANCE, not time→ Units of length and distance — light year, ångström, nanometre
- 1 nm = 10 Å (not 0.1 Å)→ Units of length and distance — light year, ångström, nanometre
- kg·m/s² is force, not energy→ Units of energy and power — joule, kWh, and the force trap
- 1 kWh = 3.6 × 10⁶ J, not 3600→ Units of energy and power — joule, kWh, and the force trap
- 1 dyne = 10⁻⁵ N (not 10⁻³ N)→ Unit-system conversion — CGS to SI (the dyne)
- G carries a NEGATIVE mass power: M⁻¹→ Dimensional formulas — writing [M^a L^b T^c]
- Strain is dimensionless; stress is NOT→ Dimensionless quantities — strain, angle, refractive index
- Impulse is force × TIME, not force→ Identifying a quantity from its units or dimensions
- Precision is set by the least count→ Measurement — precision, accuracy and least count
- Precision ≠ accuracy→ Measurement — precision, accuracy and least count
PYQ weightage by concept
9 concepts · 14 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
9 concepts · 14 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Units of length and distance — light year, ångström, nanometre | 4 | 29% |
| SI derived units named after scientists | 2 | 14% |
| Units of energy and power — joule, kWh, and the force trap | 2 | 14% |
| Physical quantities, units, and the seven SI base units | 1 | 7% |
| Unit-system conversion — CGS to SI (the dyne) | 1 | 7% |
| Dimensional formulas — writing [M^a L^b T^c] | 1 | 7% |
| Dimensionless quantities — strain, angle, refractive index | 1 | 7% |
| Identifying a quantity from its units or dimensions | 1 | 7% |
| Measurement — precision, accuracy and least count | 1 | 7% |
Test yourself on a real paper
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