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 Quantities & Units
| 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 | [ML²T⁻²] | Joule | Erg | 1 Joule = 10⁷ ergs |
| Power | Work Done ÷ Time Taken | [ML²T⁻³] | Watt | Erg per second | 1 Horsepower = 746 Watts |
| Pressure / Stress | Force ÷ Area | [ML⁻¹T⁻²] | Pascal | Barye | 1 bar = 10⁵ Pascals |
| Linear Momentum | Mass × Velocity | [MLT⁻¹] | Newton-second | Gram × Centimetre per second | Same dimension as Impulse (Force × Time Interval) |
| Frequency | One ÷ Time Period | [M⁰L⁰T⁻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 | [ML²T⁻³A⁻¹] | Volt | Statvolt | 1 Statvolt = 300 Volts |
| Electric Resistance | Potential Difference ÷ Electric Current | [ML²T⁻³A⁻²] | Ohm | Statohm | Derived from Ohm’s Law |
| Electric Capacitance | Electric Charge ÷ Potential Difference | [M⁻¹L⁻²T⁴A²] | Farad | Statfarad | Microfarad and Picofarad are practical units |
| Magnetic Flux | Magnetic Field × Area | [ML²T⁻²A⁻¹] | Weber | Maxwell | 1 Weber = 10⁸ Maxwells |
| Magnetic Field Strength | Force ÷ (Electric Current × Length) | [MT⁻²A⁻¹] | Tesla | Gauss | 1 Tesla = 10⁴ Gauss |
| Inductance | (Induced Voltage × Time) ÷ Change in Current | [ML²T⁻²A⁻²] | Henry | Abhenry | 1 Henry = 1 Weber per Ampere |
| Surface Tension | Force ÷ Length | [MT⁻²] | Newton per metre | Dyne per centimetre | 1 Newton per metre = 10³ dynes per centimetre |
| Viscosity (Dynamic) | (Force × Distance) ÷ (Area × Velocity) | [ML⁻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 × Distance²) ÷ (First Mass × Second Mass) | [M⁻¹L³T⁻²] | Newton × metre²/kilogram² |
| Planck’s Constant | Energy of a Photon ÷ Frequency of Radiation | [ML²T⁻¹] | Joule × second (Same as Angular Momentum) |
| Universal Gas Constant | (Pressure × Volume) ÷ (Amount of Substance in Moles × Absolute Temperature) | [ML²T⁻²K⁻¹mol⁻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) |
PYQ
1.Which of the following two quantities have the same dimensions ? SSC CGL 13/09/2024 (1st Shift)
(a) Work and torque
(b) Power and moment of inertia
(c) Work and angular displacement
(d) Power and radius of circular motion
Ans: (a) Work and torque.
2. Which of the following two quantities have the same dimensions ? SSC CGL 13/09/2024 (1st Shift)
(a) Work and torque
(b) Power and moment of inertia
(c) Work and angular displacement
(d) Power and radius of circular motion
Ans: (a) Work and torque.
3. Which of the following is NOT a unit of energy ? SSC CGL 19/09/2024 (1st Shift)
(a) Joule
(b) Calorie
(c) Newton
(d) Kilowatt hour
Ans: (c) Newton.
4. The most common rainfall measurement is the total rainfall depth during a given period, which is expressed in ________. SSC CGL 23/09/2024 (2nd Shift)
(a) Kilopascal (kPa)
(b) Millimetres (mm)
(c) Hectopascal (hPa)
(d) Millibar (mbar)
Ans: (b) Millimetres (mm).
5. Which of the following statements is NOT correct? SSC CGL 26/09/2024 (1st Shift)
(a) Light year is the unit of distance.
(b) Light year is the distance travelled by light in one year.
(c) Light year is the unit of time.
(d) Angstrom is a unit of length.
Ans: (c) Light year is the unit of time.