Units, Dimensions and Measurement
~9 min read
- SI units: 7 fundamental: metre (m, length), kilogram (kg, mass), second (s, time), ampere (A, current), kelvin (K, temp), mole (mol, amount), candela (cd, luminous intensity).
- Dimensions: Each physical quantity = combination of fundamental units. Used to derive formulas and check consistency.
- Errors: Random, systematic, parallax. Mean absolute error, relative error, percentage error.
Measurement is the basis of physics. SI units provide a global standard. Dimensional analysis derives and checks equations. NDA tests SI base units, dimensions of common quantities, and measuring instruments.
SI System and Base Units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Supplementary: radian (rad, plane angle), steradian (sr, solid angle).
Derived Units and Dimensions
| Quantity | Unit | Dimensions |
|---|---|---|
| Force | newton (N) | [MLT⁻²] |
| Energy/Work | joule (J) | [ML²T⁻²] |
| Power | watt (W) | [ML²T⁻³] |
| Pressure | pascal (Pa) | [ML⁻¹T⁻²] |
| Frequency | hertz (Hz) | [T⁻¹] |
| Charge | coulomb (C) | [AT] |
| Voltage | volt (V) | [ML²T⁻³A⁻¹] |
| Resistance | ohm (Ω) | [ML²T⁻³A⁻²] |
Measuring Instruments
- Vernier Calipers: Measures up to 0.01 cm. Main scale + vernier scale.
- Screw Gauge (Micrometer): Measures up to 0.001 cm. Pitch / number of divisions.
- Spherometer: Measures radius of curvature of spherical surfaces.
- Ammeter, Voltmeter: For electrical quantities.
- Stop watch, atomic clock: Time.
Errors in Measurement
- Systematic errors: Same direction repeatedly (zero error, instrument error).
- Random errors: Unpredictable variations. Reduced by averaging.
- Parallax error: Apparent shift due to wrong viewing angle.
- Mean absolute error Δa = (|Δa₁| + |Δa₂| + ...)/n.
- Relative error = Δa / a.
- Percentage error = (Δa / a) × 100%.
NDA PYQ Examples
Q: The SI unit of work is:
(a) Newton (b) Joule (c) Watt (d) Pascal
Answer: (b) Joule = 1 N·m.
Q: Which is NOT a fundamental SI unit?
(a) Kilogram (b) Newton (c) Mole (d) Kelvin
Answer: (b) Newton — that's a derived unit.
Q: Dimensions of force are:
(a) [MLT⁻¹] (b) [MLT⁻²] (c) [ML²T⁻²] (d) [ML⁻¹T⁻²]
Answer: (b) [MLT⁻²].
Drill Units, Dimensions and Measurement for NDA
NDA-pattern items on Units, Dimensions and Measurement with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
How is the metre defined now?
Since 1983, the metre is defined as the distance light travels in vacuum in 1/299,792,458 of a second. Earlier defined by a platinum-iridium bar in Paris.
What is dimensional analysis used for?
To check whether equations are dimensionally consistent (both sides must have same dimensions). Also to derive relationships between quantities and convert units between systems.
What is the difference between accuracy and precision?
Accuracy = how close a measurement is to the true value. Precision = how close repeated measurements are to each other. A measurement can be precise but inaccurate (consistent but wrong), or accurate but imprecise (right on average but scattered).
What does parallax mean?
Apparent displacement of an object when viewed from different angles. To minimise parallax error in instruments, the line of sight should be perpendicular to the scale.
Why use SI units?
Globally standardised, decimal-based (easy conversion), self-consistent, defined by reproducible physical constants. All scientific literature uses SI.