PRELIMS

01. Units and Measurements

1. Definition & Characteristics of Units

The chosen standard used for measuring a physical quantity is called a unit.

A standard unit should be:

1. Well-defined.
2. Easy to reproduce.
3. Easy to compare.
4. Independent of changes in physical conditions.
5. Internationally accepted.

2. System of Units

Units depend on choice. Each choice of units leads to a new system (set) of units. The internationally accepted systems are:

1. CGS system (Centimetre, Gram, Second)
2. MKS System (Metre, Kilogram, Second)
3. FPS System (Foot, Pound, Second)
4. SI Units (International System of Units)

3. SI Fundamental & Supplementary Units

In SI Units, there are seven fundamental units:

• Length: SI Unit: metre. Symbol: m
• Mass: SI Unit: kilogram. Symbol: kg
• Time: SI Unit: second. Symbol: s
• Electric Current: SI Unit: ampere. Symbol: A
• Temperature: SI Unit: kelvin. Symbol: K
• Luminous intensity: SI Unit: candela. Symbol: Cd
• Amount of substance: SI Unit: mole. Symbol: mol

Supplementary Units:

• Radian [rad]: Used for measuring plane angle.
• Steradian [sr]: Used for measuring solid angle.

3A. 2019 Redefinition of SI Base Units (Fixed via Fundamental Constants)

Since 20 May 2019, all seven SI base units are defined by fixing the numerical values of fundamental physical constants (rather than physical artefacts). This was adopted by the General Conference on Weights and Measures (CGPM) in Nov 2018.

• Kilogram: Defined by fixing the Planck constant ( ) = J·s. Earlier based on the International Prototype Kilogram (a platinum-iridium cylinder kept in Paris).
• Metre: Defined by fixing the speed of light ( ) = m/s.
• Second: Defined by fixing the caesium-133 hyperfine transition frequency = Hz.
• Ampere: Defined by fixing the value of the elementary charge ( ).
• Kelvin: Defined by fixing the Boltzmann constant ( ).
• Mole: Defined by fixing the Avogadro constant ( ) = per mole.
• Candela: Defined by fixing the luminous efficacy of monochromatic radiation of frequency Hz.
• Significance: Makes the SI system universally reproducible in any lab without reliance on a physical artefact; the metre was similarly redefined via in 1983, and the second via the caesium standard in 1967.

3B. Errors, Significant Figures & Dimensional Analysis

• Measurement Errors:
  • Systematic errors: Errors that occur in a definite pattern (instrumental, personal, or environmental); can be reduced by improved technique.
  • Random errors: Irregular, unpredictable errors; reduced by taking multiple readings and averaging.
  • Absolute error: Magnitude of the difference between the true value and the measured value.
  • Relative/Percentage error: Absolute error expressed as a fraction/percentage of the true value.
• Significant Figures: Digits in a measurement that are reliably known plus one estimated digit; indicate the precision of a measurement.
• Dimensional Analysis: Expressing a physical quantity in terms of the powers of the fundamental dimensions (Mass , Length , Time , etc.).
  • Used to check the correctness of an equation (principle of homogeneity — dimensions must match on both sides), derive relations between quantities, and convert units from one system to another.
  • Limitation: Cannot determine dimensionless constants in a formula.

4. Derived Units

All units which are defined or expressed in terms of fundamental units are called derived units.

• Force: CGS Unit: dyne. SI Unit: newton. Relation:
• Work: CGS Unit: erg. SI Unit: joule. Relation:

5. Practical Units of Measurement

I. Units of Length

• Light year (ly): Distance travelled by light in one year in vacuum.
• Astronomical Unit (A.U.): Mean distance between Earth and Sun.
• Parsec: .
• Nautical mile (seamile): .
• Micron: .

II. Units of Mass

• Quintal: .
• Metric ton: .
• Atomic mass unit (amu) or Dalton: .
• Slug: .
• Chandrasekhar limit: .

III. Units of Time

• Solar day: .
• Year: .
• Lunar month: .
• Tropical year: The year in which a total solar eclipse occurs.
• Leap year: The year in which February has 29 days.

6. Prefixes used in Metric System

• : Prefix: deci. Symbol: d. Multiplier: . Prefix: deca. Symbol: da
• : Prefix: centi. Symbol: c. Multiplier: . Prefix: hecto. Symbol: h
• : Prefix: milli. Symbol: m. Multiplier: . Prefix: kilo. Symbol: k
• : Prefix: micro. Symbol: . Multiplier: . Prefix: mega. Symbol: M
• : Prefix: nano. Symbol: n. Multiplier: . Prefix: giga. Symbol: G
• : Prefix: pico. Symbol: p. Multiplier: . Prefix: tera. Symbol: T
• : Prefix: femto. Symbol: f. Multiplier: . Prefix: peta. Symbol: P
• : Prefix: atto. Symbol: a. Multiplier: . Prefix: exa. Symbol: E
• : Prefix: zepto. Symbol: z. Multiplier: . Prefix: zetta. Symbol: Z
• : Prefix: yocto. Symbol: y. Multiplier: . Prefix: yotta. Symbol: Y

6A. New SI Prefixes (2022) — Ronna, Quetta, Ronto, Quecto

In November 2022, the General Conference on Weights and Measures (CGPM) approved four new SI prefixes — the first addition since 1991 — to keep pace with the growth of "big data".

• : Ronna (R)
• : Quetta (Q)
• : Ronto (r)
• : Quecto (q)
• Context: Driven by the need to express extremely large data quantities (e.g., global internet traffic in bytes) and extremely small quantities in metrology; these extend the metric prefix scale beyond yotta/yocto ( ).

UPSC Relevance

• Direct Facts: Definitions of light-year vs. parsec (common trap).
• Practical Units: Chandrasekhar limit (linked to astrophysics/supernovae).
• Systems: Significance of SI units in international scientific communication.
• 2019 Redefinition: Kilogram now fixed via Planck constant instead of a physical artefact — a recurring current-affairs-linked fact.
• 2022 New Prefixes: Ronna, Quetta, Ronto, Quecto — newest addition to the metric system, a live current-affairs trap.
• Confused Pair: Accuracy (closeness to true value) vs. Precision (closeness among repeated measurements) — commonly tested distinction.