Units and Measurements — Study Notes
Overview
Units and Measurements forms the foundation of all quantitative sciences and appears regularly in the General Science section of Railway Group D exams. Expect 1–2 direct questions on SI units, fundamental quantities, or unit conversions, often embedded in questions on motion, electricity, or heat. Mastery of this topic ensures you can quickly identify correct units in multi-step problems and avoid silly mistakes that cost marks.
The key challenge is memorizing the seven fundamental quantities and their SI units, plus recognizing how derived units (like newton, joule, watt) are constructed from these fundamentals. Unlike abstract reasoning topics, this is pure fact-recall with occasional conversion calculations. Get the basics locked in—symbols, full names, and the distinction between fundamental and derived—and you'll handle every exam variant confidently.
Key Concepts
- **Physical Quantity**: Any measurable property of matter or phenomenon (length, mass, time, temperature). Every physical quantity = numerical value × unit.
- **Fundamental Quantities**: Seven base quantities that cannot be expressed in terms of other quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity.
- **Derived Quantities**: All other quantities formed by mathematical combinations of fundamental quantities (area = length², velocity = length/time, force = mass × acceleration).
- **SI System**: International System of Units (Système International), globally accepted since 1960. All scientific and engineering work uses SI for consistency.
- **Unit Symbol Rules**: Always lowercase (m, kg, s) unless named after a person (N for Newton, J for Joule, W for Watt). Never pluralize symbols (5 kg not 5 kgs). Leave space between number and unit (10 m not 10m).
- **Dimensional Analysis**: Checking if both sides of an equation have the same fundamental dimensions (e.g., velocity has dimension LT⁻¹). Useful for verifying formulas and converting units.
Formulas / Key Facts
### Seven Fundamental Quantities and SI Units
1. **Length** — metre (m). Definition: distance light travels in vacuum in 1/299,792,458 second. 2. **Mass** — kilogram (kg). Definition: mass of the international prototype kilogram (a platinum-iridium cylinder in Paris). 3. **Time** — second (s). Definition: duration of 9,192,631,770 periods of radiation from caesium-133 atom. 4. **Electric Current** — ampere (A). Definition: current producing a specified force between two parallel conductors. 5. **Temperature** — kelvin (K). Definition: 1/273.16 of the thermodynamic temperature of water's triple point. Note: °C = K − 273.15. 6. **Amount of Substance** — mole (mol). Definition: amount containing as many entities as there are atoms in 0.012 kg of carbon-12 (Avogadro's number ≈ 6.022 × 10²³). 7. **Luminous Intensity** — candela (cd). Definition: luminous intensity in a given direction of a source emitting monochromatic radiation of frequency 540 × 10¹² Hz.