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What are fundamental and derived units?

Class 11 PhysicsNCERT chapter: Units and Measurementsइसे हिंदी में पढ़ें

Exam-ready answer

The units of the fundamental or base quantities are called fundamental or base units. In SI there are seven: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). Units of all other physical quantities, expressed as combinations of base units, are derived units, for example the newton, N = kg m s⁻².

Explanation

Measuring a physical quantity means comparing it with an internationally accepted reference standard called a unit. The number of physical quantities is very large, but only a limited number of units is needed. A small set of quantities is chosen as fundamental or base quantities, and their units are the fundamental or base units. All other quantities can be expressed in terms of these. The complete set of base and derived units is called a system of units.

The International System of Units (SI) has seven base quantities: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol) and luminous intensity (candela, cd). Each base unit is defined independently. SI also defines two dimensionless units for angles: the radian (rad) for plane angle and the steradian (sr) for solid angle.

Derived units are obtained from base units through the defining relation of the quantity. Speed = distance/time, so its unit is m s⁻¹. Acceleration has unit m s⁻². Force = mass × acceleration, so its unit is kg m s⁻², named the newton (N). Work = force × displacement gives kg m² s⁻², the joule (J). Density = mass/volume gives kg m⁻³. Some derived units carry special names, such as the newton, joule, watt and pascal.

Points to remember

  1. Fundamental (base) units: units of base quantities, defined independently of other units.
  2. Seven SI base units: m, kg, s, A, K, mol, cd.
  3. Derived units: units of other physical quantities expressed as combinations of base units, e.g. m s⁻¹, kg m⁻³.
  4. Force: 1 N = 1 kg m s⁻²; work and energy: 1 J = 1 kg m² s⁻².
  5. Radian (plane angle) and steradian (solid angle) are dimensionless SI units; the full set of base and derived units forms a system of units.

Exam tip

Write the definition of both terms, then a two-column table of the seven base quantities with their SI units and symbols. For derived units, show at least one derivation step, for example force = ma gives kg m s⁻² = N.

Questions students also ask

Why is the kilogram a base unit while the newton is derived?
Mass is chosen as a base quantity, so its unit, the kilogram, is defined independently. Force is defined by F = ma, so its unit is obtained by combining base units: kg × m s⁻² = kg m s⁻², which is given the special name newton.
What are the rules for writing SI unit symbols?
Unit symbols are written without a full stop and do not take a plural form, such as 10 kg, not 10 kgs. Symbols of units named after scientists use a capital letter, like N and K, but the full unit name is written in lowercase, like newton and kelvin.
What is the SI unit of pressure in base units?
Pressure = force/area. Its SI unit is N m⁻², named the pascal (Pa). Since 1 N = 1 kg m s⁻², one pascal in base units is 1 kg m⁻¹ s⁻².

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