Which of the following is NOT a derived unit?
Mole
Understanding Base and Derived Units in Physics
In the International System of Units (SI), physical quantities are measured using specific units. These units are broadly classified into two categories: base units and derived units.
What are SI Base Units?
SI base units are the fundamental units from which all other units can be derived. There are seven defined SI base units:
- Metre (m) for length
- Kilogram (kg) for mass
- Second (s) for time
- Ampere (A) for electric current
- Kelvin (K) for thermodynamic temperature
- Mole (mol) for amount of substance
- Candela (cd) for luminous intensity
These base units are considered independent of each other.
What are Derived Units?
Derived units are units of measurement that are obtained by combining the base units through multiplication or division. For example, the unit for speed is metres per second (m/s), which is derived from the base units of length (metre) and time (second).
Many physical quantities like force (Newton, N), energy (Joule, J), power (Watt, W), pressure (Pascal, Pa), etc., have derived units.
Analyzing the Given Options
We are asked to identify the option that is NOT a derived unit. Let's examine each option based on our understanding of base and derived units:
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Volt: The Volt (V) is the SI derived unit of electric potential difference or electromotive force. It is defined as one joule per coulomb (\(1\text{ V} = 1\text{ J/C}\)). Both Joule (J) and Coulomb (C) are derived units (\(1\text{ J} = 1\text{ kg} \cdot \text{m}^2/\text{s}^2\), \(1\text{ C} = 1\text{ A} \cdot \text{s}\)). Since Volt is defined in terms of other derived units (which are themselves derived from base units), Volt is a derived unit.
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Mole: The Mole (mol) is the SI unit for the amount of substance. As listed above, the mole is one of the seven fundamental SI base units. It is not derived from other units; it is a foundational unit.
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Radian: The Radian (rad) is the SI unit for measuring plane angles. It is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. Dimensionally, it is the ratio of arc length to radius, i.e., \(m/m\), making it a dimensionless unit. Historically, radian and steradian were considered supplementary units in SI, but in 1995, they were classified as derived units. While dimensionless, it is a unit derived from the ratio of two lengths.
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Lumen: The Lumen (lm) is the SI derived unit of luminous flux. It is defined in terms of the candela (cd), which is a base unit, and the steradian (sr), which is the SI derived unit of solid angle. One lumen is equal to one candela times one steradian (\(1\text{ lm} = 1\text{ cd} \cdot \text{sr}\)). Since it is a combination of a base unit and a derived unit, Lumen is a derived unit.
Conclusion on Derived Units
Based on the analysis:
- Volt is a derived unit.
- Mole is a base unit.
- Radian is a derived unit (specifically, a dimensionless derived unit).
- Lumen is a derived unit.
The question asks which option is NOT a derived unit. The Mole is a base unit, and therefore it is not a derived unit.
| Unit | Symbol | Classification | Notes |
|---|---|---|---|
| Volt | V | Derived Unit | Unit of electric potential difference |
| Mole | mol | Base Unit | Unit of amount of substance |
| Radian | rad | Derived Unit | Unit of plane angle (dimensionless) |
| Lumen | lm | Derived Unit | Unit of luminous flux |
Therefore, the unit that is NOT a derived unit among the given options is the Mole.
Revision Table: SI Units Classification
| Feature | Base Units | Derived Units |
|---|---|---|
| Definition | Fundamental, independent units | Combinations of base units |
| Number in SI | Seven | Infinite (as needed) |
| Examples | Metre, Kilogram, Second, Ampere, Kelvin, Mole, Candela | Newton, Joule, Watt, Volt, Pascal, Lumen, Radian, Steradian, etc. |
Additional Information on Units
Understanding the distinction between base and derived units is crucial for dimensional analysis in physics and other sciences. Dimensional analysis helps check the consistency of equations and understand the relationships between different physical quantities.
While radian and steradian are dimensionless derived units, they are sometimes given special names and symbols (rad and sr) because they represent distinct physical quantities (plane angle and solid angle) that are important in many applications.
The definition of the mole is related to Avogadro's number (\(N_A\)), which is defined as \(6.02214076 \times 10^{23}\) entities per mole. One mole of any substance contains exactly \(N_A\) elementary entities (like atoms, molecules, ions, etc.).
The correct option is the one that is a base unit, as base units are not derived units.
Important Questions from Units, Dimensions and Measurements
Unit of pressure is:
One mile is approximately equivalent to _______ kilometres.
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