NDA Physics · Formula sheet

Units, Measurement and Dimensions formulas

6 formulas, 3 reference tables and 13 common traps for NDA Physics Units, Measurement and Dimensions, grouped by subtopic.

Full notes with worked examples

Units, Measurement and Dimensions

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Units of energy and power — joule, kWh, and the force trap

Kilowatt-hour to joules

1\,\text{kWh} = 1000\,\text{W} \times 3600\,\text{s} = 3.6 \times 10^{6}\,\text{J}

$W$ watt = joule per second (power)
kWhkilowatt-hour, the commercial unit of electrical energy

Unit-system conversion — CGS to SI (the dyne)

CGS force unit to SI

1\,\text{dyne} = 1\,\frac{\text{g·cm}}{\text{s}^2} = (10^{-3}\,\text{kg})(10^{-2}\,\text{m})\,\text{s}^{-2} = 10^{-5}\,\text{N}

dyneCGS unit of force (g·cm/s²)
$N$ SI unit of force (kg·m/s²)

Dimensional formulas — writing [M^a L^b T^c]

Dimension of the gravitational constant G

F = \frac{G m_1 m_2}{r^2} \;\Rightarrow\; [G] = \frac{[F][r^2]}{[m^2]} = \frac{(MLT^{-2})(L^2)}{M^2} = M^{-1}L^3T^{-2}

$F$ gravitational force, [MLT⁻²]
$m_1, m_2$ masses, [M] each
$r$ separation, [L]

Dimensionless quantities — strain, angle, refractive index

Strain is a pure ratio

\text{strain} = \frac{\Delta L}{L} = \frac{[L]}{[L]} = [M^0 L^0 T^0]

$\Delta L$ change in length, [L]
$L$ original length, [L]

Identifying a quantity from its units or dimensions

Thrust ÷ impulse is a frequency

\frac{\text{thrust}}{\text{impulse}} = \frac{[MLT^{-2}]}{[MLT^{-1}]} = [T^{-1}] = \text{frequency (Hz)}

thrusta force, [MLT⁻²]
impulseforce × time, [MLT⁻¹]

Measurement — precision, accuracy and least count

Least count of a metre scale

\text{LC (metre scale)} = 1\,\text{mm} = 0.1\,\text{cm} = 10^{-3}\,\text{m}

$LC$ least count — smallest readable division

Physical quantities, units, and the seven SI base units

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

The seven SI base units. Mass is the kilogram; weight is a force (newton), not a base unit — the classic match-list trap.

SI derived units named after scientists

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.

Stress and pressure share the same unit (N/m²). The symbol H is Henry (inductance); Hz is the hertz (frequency).

Units of length and distance — light year, ångström, nanometre

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).

Light year, AU and parsec all measure DISTANCE. 1 nm = 10 Å. The light-year-is-distance fact is the chapter's single highest-yield line.

Common traps

Mass is kilogram; weight is a force (newton)

In a match-list, "Weight" pairs with Newton, not kilogram — weight is the gravitational force

mg

, a derived unit. Only mass maps to the kilogram base unit. Pressure maps to the pascal, temperature to the kelvin.

H is Henry, not Hertz

The symbol H is the henry (unit of inductance, after Joseph Henry). Hertz has the symbol Hz and measures frequency. The exam offers both as distractors.

Stress and pressure share a unit

Both stress and pressure are force per unit area (N/m² = pascal). Strain, by contrast, is a pure ratio and is dimensionless — don't confuse stress (has a unit) with strain (no unit).

Light year is DISTANCE, not time

The word "year" plants the trap: a light year is the distance light covers in a year (~

9.46 \times 10^{15}

m), not a time interval and not light intensity. This exact fact is asked again and again.

1 nm = 10 Å (not 0.1 Å)

Since 1 nm

= 10^{-9}

m and 1 Å

= 10^{-10}

m, the nanometre is the larger unit:

1\,\text{nm} = 10\,\text{Å}

. Don't invert it.

kg·m/s² is force, not energy

In a "which is NOT a unit of energy" list, the planted answer is kg·m/s² — that is mass × acceleration = the newton (force). Energy is kg·m²/s² (joule). Watch the exponent on the metre.

1 kWh = 3.6 × 10⁶ J, not 3600

It's 1000 W × 3600 s =

3.6 \times 10^{6}

J. Multiplying only by 3600 (forgetting the kilo) gives

3.6 \times 10^{3}

— a factor-of-1000 error.

1 dyne = 10⁻⁵ N (not 10⁻³ N)

Both factors shrink the unit: gram → kg gives

10^{-3}

and cm → m gives

10^{-2}

. Multiply them:

10^{-3} \times 10^{-2} = 10^{-5}

. Forgetting the centimetre factor gives the wrong

10^{-3}\,\text{N}

distractor.

G carries a NEGATIVE mass power: M⁻¹

Because G = F·r²/(m₁m₂), the two masses sit in the denominator, giving

M^{-1}

— not

M^{+1}

. The full result

M^{-1}L^3T^{-2}

has

L^3

(from force's L times r²'s L²) and

T^{-2}

(from force). A sign slip on M is the planted error.

Strain is dimensionless; stress is NOT

Strain is the ratio ΔL/L (no unit). Stress is force ÷ area (N/m²). The pair is designed to be confused — only strain is dimensionless.

Impulse is force × TIME, not force

Impulse = F·t = change in momentum

[MLT^{-1}]

, one power of T less negative than force

[MLT^{-2}]

. The thrust/impulse ratio therefore leaves

T^{-1}

(frequency). Treating impulse as a plain force would wrongly make the ratio dimensionless.

Precision is set by the least count

A metre scale (LC = 1 mm) cannot honestly report below 1 mm. A value written to sub-millimetre detail (0.925 m, 29.07 cm) claims more precision than the instrument has; the reading recorded to the millimetre is the consistent one.

Precision ≠ accuracy

Precision is how finely you can read (least count); accuracy is how close you are to the true value. A finely-recorded reading can still be inaccurate, and vice versa — don't equate the two.