UNITS AND MEASUREMENTS
Units and Measurements deals with the fundamental and derived physical quantities used to measure various physical phenomena. It covers SI and CGS units, dimensional formulae, important physical constants, and their conversions. It also includes astronomical, practical, and atomic units used to express different measurements. Scientific measuring instruments and their uses are essential for understanding practical applications and answering important examination questions.
| Fundamental Quantity | SI Unit | CGS Unit |
| Length | Metre (m) | centimetre(cm) |
| Mass | Kilogram (kg) | gram(g) |
| Time | Second(s) | second(s) |
| Electric Current | Ampere(A) | Statampere (statA) |
| Thermodynamic Temperature | Kelvin(K) | degree Celsius(°C) |
| Amount of Substance | Mole(mol) | mole(mol) |
| Luminous Intensity | Candela(cd) | candela(cd) |
Important Derived Units, Word Formulas & Dimensions
| Physical Quantity | Word Formula | Dimensional Formula | SI Unit (Special Name) | CGS Unit | Key Exam Notes |
| Force | Mass × Acceleration | [MLT-2] | Newton | Dyne | 1 Newton = 105 dynes |
| Work / Energy | Force × Displacement | [ML2 T-2] | Joule | Erg | 1 Joule = 107 ergs |
| Power | Work Done ÷ Time Taken | [ML2 T-3] | Watt | Erg per second | 1 Horsepower = 746 Watts |
| Pressure / Stress | Force ÷ Area | [M L-1 T-2] | Pascal | Barye | 1 bar = 105 Pascals |
| Linear Momentum | Mass × Velocity | [M L T-1] | Newton-second | Gram ×× Centimetre per second | Same dimension as Impulse (Force × Time Interval) |
| Frequency | One ÷ Time Period | [M0 L0 T-1] | Hertz | Cycles per second | Reciprocal of time |
| Electric Charge | Electric Current × Time | [AT] | Coulomb | Statcoulomb | 1 Coulomb ≈≈ 3 × 109 Statcoulombs |
| Potential Difference (Voltage) | Work Done ÷ Electric Charge | [M L2 T-3 A-1] | Volt | Statvolt | 1 Statvolt = 300 Volts |
| Electric Resistance | Potential Difference ÷ Electric Current | [M L2 T-3 A-2] | Ohm | Statohm | Derived from Ohm’s Law |
| Electric Capacitance | Electric Charge ÷ Potential Difference | [M-1 L-2 T4 A2] | Farad | Statfarad | Microfarad and Picofarad are practical units |
| Magnetic Flux | Magnetic Field × Area | [M L2 T-2 A-1] | Weber | Maxwell | 1 Weber = 108 Maxwells |
| Magnetic Field Strength | Force ÷ (Electric Current × Length) | [M L0 T-2 A-1] | Tesla | Gauss | 1 Tesla = 104 Gauss |
| Inductance | (Induced Voltage × Time) ÷ Change in Current | [M L2 T-2 A-2] | Henry | Abhenry | 1 Henry = 1 Weber per Ampere |
| Surface Tension | Force ÷ Length | [M L0 T-2] | Newton per metre | Dyne per centimetre | 1 Newton per metre = 103 dynes per centimetre |
| Viscosity (Dynamic) | (Force × Distance) ÷ (Area × Velocity) | [M L-1T-1] | Pascal-second | Poise | 1 Pascal-second = 10 Poise |
Key Constants
| Physical Constant | Word Formula | Dimensional Formula | SI Unit |
| Universal Gravitational Constant | (Gravitational Force × Distance squared) ÷ (First Mass × Second Mass) | [M-1 L3 T-2] | Newton ×× metre2/kilogram2 |
| Planck’s Constant | Energy of a Photon ÷ Frequency of Radiation | [M L2 T-1] | Joule ×× second (Same as Angular Momentum) |
| Universal Gas Constant | (Pressure × Volume) ÷ (Amount of Substance in Moles × Absolute Temperature) | [M L2 T-2 K-1 mol-1] | Joule per mole per Kelvin |
Astronomical, Practical & Atomic Units
| Unit Name | Value in SI Meters / Pa | Key Exam Takeaway |
| Light Year | 9.46 × 10¹⁵ m | Distance traveled by light in vacuum in 1 year (Unit of distance, NOT time) |
| Parsec (Parallactic Second) | 3.26 Light Years ≈ 3.08 × 10¹⁶ m | Largest practical unit of astronomical distance |
| Astronomical Unit (AU) | 1.496 × 10¹¹ m | Mean distance between Earth and Sun |
| Angstrom (Å) | 10⁻¹⁰ m = 0.1 nm | Used for wavelength of light and atomic radii |
| Fermi / Femtometer (fm) | 10⁻¹⁵ m | Used to express nuclear radius |
| Nautical Mile | 1852 meters (1.852 km) | Used in sea and air navigation |
| Knot | 1 Nautical mile per hour | Unit of speed in maritime and air navigation |
| Bar | 10⁵ Pa | Unit of atmospheric pressure |
| Torr | 1 mm of Hg ≈ 133.3 Pa | Unit of pressure in vacuum |
| Atmosphere (atm) | 1.013 × 10⁵ Pa = 760 torr | Standard sea-level atmospheric pressure |
Scientific Measuring Instruments & Their Uses
| Altimeter | Measures altitude / height above sea level (used in aircraft) |
| Ammeter | Measures electric current in a circuit (connected in series) |
| Voltmeter | Measures electric potential difference (connected in parallel) |
| Galvanometer | Detects presence and direction of minute electric currents |
| Anemometer | Measures wind speed and direction |
| Barometer | Measures atmospheric pressure (invented by Torricelli) |
| Hydrometer | Measures relative density / specific gravity of liquids |
| Hygrometer | Measures humidity / moisture content of the atmosphere |
| Lactometer | Tests the purity and relative density of milk |
| Pyrometer | Measures very high temperatures non-contact (e.g., Sun/furnaces) |
| Sphygmomanometer | Measures human blood pressure (normal: 120/80 mmHg) |
| Stethoscope | Listens to heart and lung sounds (works on multiple reflection) |
| Sonar | Detects underwater objects/depth using ultrasonic waves |
| Radar | Detects direction, range, and speed of aircraft using radio waves |
| Fathometer | Measures depth of ocean / sea water |
| Sextant | Measures angular distance between two visible objects (navigation) |
| Odometer | Measures total distance traveled by a wheeled vehicle |
| Speedometer | Measures instantaneous speed of a vehicle |
| Tacheometer | Measures rotational speed of a shaft or disk (in RPM) |
PREVIOUS YEAR QUESTION
- Which of the following pairs of physical quantities has the same SI unit and dimensional formula? (RRB NTPC (Graduate 2024))
(a) Force and Pressure
(b) Work and Torque
(c) Momentum and Force
(d) Power and Energy
Correct Answer: (b) Work and Torque
- What is the SI unit of “Luminous Intensity”, one of the seven fundamental base quantities? (RRB ALP 2025)
(a) Lumen
(b) Lux
(c) Candela
(d) Watt per steradian
Correct Answer: (c) Candela (cd)
- The unit “Dioptre” (D) is used to measure which property of an optical lens? (RRB ALP 2025)
(a) Focal length
(b) Power of a lens
(c) Magnification
(d) Radius of curvature
Correct Answer: (b) Power of a lens
- Which device is used to measure very high temperatures (such as inside blast furnaces or the surface of the Sun) without physical contact? (RRB NTPC (Graduate 2025)
(a) Pyrometer
(b) Bolometer
(c) Manometer
(d) Hygrometer
Correct Answer: (a) Pyrometer
- What are the two supplementary units recognized in the SI system, and what do they measure? (RRB NTPC (UG 2025))
(a) Radian (Plane angle) and Steradian (Solid angle)
(b) Degree and Candela
(c) Newton and Joule
(d) Pascal and Bar
Correct Answer: (a) Radian (Plane angle) and Steradian (Solid angle)