Fundamental And Derived Quantities And Units

Edited By Vishal kumar | Updated on Jul 02, 2025 05:34 PM IST

Consider the everyday experience of driving a car. To provide a thorough description of your trip, you must utilise certain basic quantities such as time, which tells you how long it will take, and distance, which tells you how far you will travel. You will also utilise derived quantities such as speed, which combines time and distance. Measurements are very important to you since they allow you to make sound decisions and understand the day-to-day operations of all phenomena around you.

This Story also Contains

Fundamental and Derived Quantities
Fundamental and Derived Units
Solved Example Based on Fundamental and Derived Quantities
Summary

In this article, we will cover the concept of fundamental and derived quantities and units. This is the very basic concept of the chapter Physics and Measurement which is a crucial chapter in Class 11 physics. It is not only important for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, VITEEE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of one question has been asked on this concept. But no direct question was asked in NEET from this concept.

Fundamental and Derived Quantities

1) Fundamental Quantities

Those physical quantities are independent of all other quantities and cannot be expressed in terms of other basic quantities. These quantities are also called absolute /basic quantities.

Ex- Length, mass, time, electric current, temperature, amount of substance and luminous intensity.

2) Derived Quantities

Derived Quantities are products and ratios of the fundamental quantities that exist in a system of units and these quantities can be expressed in terms of other basic quantities.

Ex- Area, Density, Force, Pressure, etc.

So l = length of the square is a fundamental quantity.

But the area of square = A= l²is Derived Quantity which we get with the help of taking a square of the length.

Now we will study the fundamental and derived units.

Fundamental and Derived Units

Fundamental units: The units of fundamental or basic quantities are called fundamental units or base units.

Derived units: The units of those physical quantities which can be expressed as the combination of fundamental units are called derived units.

Now, after reading about the fundamental and derived quantities, let's look at some solved examples to better understand the concept.

Solved Example Based on Fundamental and Derived Quantities

Example 1: Which of the following is/are the examples of derived quantities?

1) Time

2) Mass

3) Current

4) Energy

Solution:

The physical quantities that depend upon the fundamental quantities are known as the derived quantities. These quantities can be expressed in terms of other basic quantities.

Energy = power/time or Force$\times$Displacement

unit of energy - Joule or N−m or kg⋅m/s−2
Dimension- M1L2T−2

Energy depends on the fundamental quantities so the energy is a derived quantity.

Hence, the answer is option (4).

Example 2: Which of the following is/are examples of fundamental quantities?

1)Time

2) Length

3) Mass

4) All of them

Solution:

The physical quantities which do not depend on any other physical quantities for their measurements are known as fundamental quantities or base quantities.

In physics, length, mass, time, electric current, temperature, amount of substance, and luminous intensity are the seven fundamental physical quantities

Hence, the answer is option (4).

Example 3:Which of the following is not a pair of fundamental quantities

1) Time and mass

2) Length and time

3) Electric current and Luminous Intensity

4) Electric current and electric field

Solution:

As we learnt in

Fundamental Quantities- Those physical quantities are independent of all other quantities and cannot be expressed in terms of other basic quantities.

Length, mass, time, electric current, temperature, amount of substance and luminous intensity all are fundamental quantities.

But The electric field is not a fundamental quantity because it depends on fundamental quantity. It is a derived quantity.

Hence, the answer is option (3).

Example 4:The heliocentric theory proposed by Nicolas Copernicus was

1) replaced by circular orbits to fit the data better

2 replaced by elliptical orbits to fit the data better

3) replaced by elliptical orbits to fit the taste of the new rulers of Italy

4) replaced by parabolic orbits to fit the data better

Solution:

The heliocentric theory is an astronomical model which was proposed by Polish astronomer Nicolaus Copernicus. In this theory, the sun is at the centre of the solar system and all the planets and heavenly bodies revolve around it.

The heliocentric theory was replaced by Kepler's theory which proposed the orbits are elliptical, which the German astronomer Johannes Kepler demonstrated in 1609.

Hence, the answer is option (2).

Example 5: Which of the following statements is true regarding fundamental and derived quantities?

1) Force is a fundamental quantity, and length is a derived quantity.
2) Length is a fundamental quantity, and velocity is a derived quantity.
3) Time is a derived quantity, and acceleration is a fundamental quantity.
4) Mass is a derived quantity, and temperature is a fundamental quantity.

Solution:

length is a fundamental quantity, and velocity is a derived quantity. Length is a basic physical quantity, while velocity is derived from length divided by time (displacement per unit time).

Hence, the answer is option (2).

Summary

Fundamental quantities, as the name implies, are those basic physical quantities that can't be broken down into simpler forms. These are length, mass, time, electric current, temperature, amount of substance, and luminous intensity, whose units include meter, kilogram and second. Derived quantities are formed by combining the basic physical quantities via physical laws. speed, which is the ratio of distance over time, acceleration, defined as the rate of change in velocity with time; force that mass times acceleration, measured in newtons or meters per second squared. Understanding the difference between fundamental and derived quantities helps deliver an accurate measurement and description of physical phenomena in day-to-day activities as well as in scientific experiments.

Frequently Asked Questions (FAQs)

1. What are fundamental quantities?

Fundamental quantities are basic physical measurements. They can not be broken down into simpler forms. Some examples are length, mass, and time.

2. What are derived quantities?

Derived quantities are combined from the basic Fundamental quantities and are obtained, for instance, speed= distance/time and force=mass x acceleration.

3. Give one example of a fundamental unit.

Yes, one fundamental unit is a meter which is used to measure the length.

4. Give an example of a derived unit.

An example is the newton, the unit of force which is a derived quantity since it can be obtained from mass × acceleration.

5. Why have fundamental quantities been chosen?

Since all physical measurements involve some combination of base quantities, they are the building blocks for all of them; as such, they have been chosen to provide a foundation for understanding and describing the physical world.

6. What is the difference between fundamental and derived quantities in physics?

Fundamental quantities are basic physical quantities that cannot be expressed in terms of other quantities. They form the foundation of measurement in physics. Derived quantities, on the other hand, are quantities that can be expressed in terms of fundamental quantities. For example, length is a fundamental quantity, while velocity (distance/time) is a derived quantity.

7. What is the difference between mass and weight, and why is this distinction important?

Mass is a fundamental quantity that represents the amount of matter in an object, while weight is a derived quantity that represents the force of gravity on an object. Mass is constant regardless of location, but weight can vary depending on the strength of the gravitational field. This distinction is crucial for understanding motion, especially in environments with different gravitational strengths, like on different planets or in space.

8. Why is it important to distinguish between scalar and vector quantities?

Distinguishing between scalar and vector quantities is crucial because they behave differently in calculations and have different physical meanings. Scalar quantities (like mass or temperature) have only magnitude, while vector quantities (like velocity or force) have both magnitude and direction. This distinction affects how these quantities are measured, represented, and manipulated in physical equations and problem-solving.

9. What is the significance of dimensionless quantities in physics?

Dimensionless quantities, which have no physical dimension, are significant because they often represent universal relationships or ratios that are independent of the specific system of units used. Examples include the fine-structure constant in quantum electrodynamics or the Reynolds number in fluid dynamics. These quantities can reveal fundamental aspects of physical systems and laws.

10. How does the choice of reference frame affect measurements in physics?

The choice of reference frame can significantly affect measurements, especially those involving motion. Quantities like velocity and acceleration are relative and depend on the chosen frame of reference. Understanding this concept is crucial for correctly interpreting and applying physical laws, particularly in areas like classical mechanics and special relativity.

11. Why do we need standardized units in physics?

Standardized units are essential in physics for several reasons: they allow for consistent measurements across different locations and times, enable clear communication of scientific results, facilitate comparison of data, and ensure reproducibility of experiments. Without standardized units, it would be challenging to collaborate and share scientific findings globally.

12. How many fundamental quantities are there in the SI system, and what are they?

In the International System of Units (SI), there are seven fundamental quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity. These form the basis for all other measurements in physics and other sciences.

13. Can you explain why the kilogram was redefined in 2019?

The kilogram was redefined in 2019 to improve its long-term stability and accuracy. Previously, it was defined by a physical artifact (a platinum-iridium cylinder) which could change over time due to environmental factors. The new definition is based on the Planck constant, a fundamental constant of nature, making it more stable and universally reproducible.

14. How does the choice of units affect the form of physical equations?

The choice of units can affect the form of physical equations by introducing or eliminating numerical constants. For example, in Newton's second law, F = ma in SI units, but if we use different units, we might need a constant: F = kma. This is why physicists often use "natural units" where fundamental constants are set to 1, simplifying equations.

15. Why is the speed of light considered a fundamental constant?

The speed of light in vacuum (c) is considered a fundamental constant because it is invariant across all inertial reference frames and plays a crucial role in many physical laws. It's not just about light; it represents the maximum speed at which any information or matter can travel in the universe. Its constancy is a cornerstone of modern physics, particularly in special relativity.

16. What is dimensional analysis, and why is it useful in physics?

Dimensional analysis is a method used to check the consistency of equations and to derive relationships between physical quantities. It's based on the principle that all terms in a physically meaningful equation must have the same dimensions. This technique is useful for verifying equations, converting units, and even predicting the form of unknown relationships between quantities.

17. How does the principle of homogeneity apply to physical equations?

The principle of homogeneity states that all terms in a physically meaningful equation must have the same dimensions. This principle is a powerful tool for checking the validity of equations and for dimensional analysis. If an equation violates this principle, it indicates an error in the formulation or understanding of the physical relationship being described.

18. How does the concept of significant figures relate to measurement uncertainty?

Significant figures (or sig figs) are digits in a measurement that carry meaning and indicate the precision of the measurement. They are directly related to measurement uncertainty because they show how precisely a quantity is known. The last significant figure in a measurement implies the uncertainty in that digit. For example, 5.37 cm implies that the measurement is certain to 0.01 cm.

19. Why is it important to understand the concept of derived dimensions in physics?

Derived dimensions are combinations of fundamental dimensions that represent more complex physical quantities. Understanding these helps in analyzing the relationships between different physical quantities and in checking the consistency of equations. It's a powerful tool in dimensional analysis and in developing intuition about how different physical quantities are related.

20. Why do we use scientific notation in physics, and how does it relate to significant figures?

Scientific notation is used in physics to express very large or very small numbers concisely and to easily perform calculations with such numbers. It also helps in clearly showing the number of significant figures in a measurement. For example, 5.00 × 10^3 m clearly shows three significant figures, whereas writing 5000 m might lead to ambiguity about the precision of the measurement.

21. How does the concept of precision differ from accuracy in measurements?

Precision refers to the consistency or reproducibility of measurements, while accuracy refers to how close a measurement is to the true value. A set of measurements can be precise (close to each other) but inaccurate (far from the true value), or accurate but imprecise. Understanding this difference is crucial for evaluating experimental results and measurement techniques.

22. How does the uncertainty principle relate to the limits of measurement in physics?

The uncertainty principle, formulated by Heisenberg, states that there's a fundamental limit to the precision with which certain pairs of physical properties can be determined simultaneously. This principle sets a theoretical limit on measurement precision at the quantum scale, affecting our understanding of the nature of reality and the process of measurement itself.

23. Why is it important to understand the concept of orders of magnitude in physics?

Understanding orders of magnitude is crucial for grasping the scale of physical phenomena, making quick estimates, and comparing vastly different quantities. It helps in simplifying complex problems, identifying dominant factors in a system, and developing intuition about physical processes across different scales, from subatomic particles to cosmic structures.

24. Why is it important to consider significant figures in calculations involving measurements?

Considering significant figures in calculations is important because it reflects the precision of the original measurements and prevents overstating the accuracy of results. It ensures that the final answer doesn't imply more precision than is justified by the input data, maintaining the integrity of scientific calculations and conclusions.

25. Why is it important to understand the limitations of measurement in physics?

Understanding the limitations of measurement is crucial because all measurements have some degree of uncertainty. This awareness helps in interpreting experimental results, estimating errors, and recognizing the practical limits of applying theoretical models to real-world situations. It also underscores the importance of continual improvement in measurement techniques and technologies.

26. How does the concept of measurement uncertainty relate to the scientific method?

Measurement uncertainty is a crucial aspect of the scientific method. It acknowledges that all measurements have limitations and helps in assessing the reliability of experimental results. Understanding and reporting uncertainties allows for meaningful comparisons between theory and experiment, and between different experiments. It's essential for drawing valid conclusions and for the progress of scientific knowledge.

27. How does the concept of dimensionality in physics extend beyond the usual three spatial dimensions?

While we commonly deal with three spatial dimensions and one time dimension, many modern physical theories involve additional dimensions. Understanding higher-dimensional spaces is crucial in string theory and other attempts to unify fundamental forces. This concept challenges our intuitive understanding of space and time and is essential for exploring the most fundamental aspects of the universe.

28. How does the concept of base units relate to derived units?

Base units are the units of the seven fundamental quantities in the SI system. Derived units are formed by combining base units according to the algebraic relations of the corresponding quantities. For instance, the unit of force (newton) is derived from the base units of mass (kg), length (m), and time (s) as kg⋅m/s^2.

29. What is the importance of understanding unit conversions in physics?

Understanding unit conversions is crucial in physics for several reasons: it allows comparison of measurements made in different systems, helps in solving complex problems that involve multiple units, prevents errors in calculations, and is essential for interpreting and applying physical laws and equations correctly in various contexts.

30. What is the significance of the Planck units in fundamental physics?

Planck units are a set of natural units based on fundamental physical constants. They are significant because they provide a scale at which quantum gravitational effects are expected to become important. Planck units also simplify certain physical equations by eliminating constants, potentially revealing deeper relationships between physical quantities.

31. How does the concept of physical constants relate to the fundamental and derived quantities?

Physical constants are quantities that have a fixed numerical value in nature. Some, like the speed of light, are related to fundamental quantities and play a role in defining units. Others, like the gravitational constant, relate different fundamental quantities. Understanding these constants is crucial for grasping the interconnections between various physical quantities and laws.

32. How does the concept of base quantities in the SI system differ from other systems of units?

The SI system defines seven base quantities, each with its corresponding unit. This approach differs from some other systems, like the CGS system, which uses fewer base units. The SI system's approach provides a more comprehensive foundation for scientific measurements, allowing for greater consistency and ease of conversion between different quantities.

33. What is the relationship between units and dimensions in physics?

Units are specific measures used to quantify physical quantities, while dimensions represent the nature of the quantity regardless of the unit system. For example, length can be measured in meters or feet (units), but its dimension is always [L]. Understanding this relationship is crucial for dimensional analysis and for grasping the fundamental nature of physical quantities.

34. How does the concept of derived units simplify the expression of complex physical relationships?

Derived units, formed by combining base units, simplify the expression of complex physical relationships by encapsulating multiple fundamental quantities into a single unit. For example, using the unit of newton (N) for force is simpler than always writing kg⋅m/s^2. This simplification makes equations more manageable and helps in understanding the relationships between different physical quantities.

35. How does the concept of dimensional homogeneity help in deriving physical relationships?

Dimensional homogeneity, which requires all terms in an equation to have the same dimensions, can be used to derive or check physical relationships. By analyzing the dimensions of known quantities involved in a physical process, one can often deduce the form of the equation relating these quantities, even without knowing the exact relationship.

36. What is the significance of the recent redefinition of the SI base units?

The recent redefinition of SI base units, completed in 2019, linked all units to fundamental constants of nature rather than physical artifacts or specific experimental setups. This change makes the definitions more stable and universal, ensures long-term consistency of measurements, and allows for more precise measurements as measurement technologies improve.

37. How does the concept of coherent units in the SI system contribute to simplifying calculations?

Coherent units in the SI system are derived units that can be expressed as products of powers of base units without any numerical factors. This coherence simplifies calculations by eliminating the need for conversion factors between related quantities. For example, 1 N = 1 kg⋅m/s^2, without any additional numerical factor.

38. Why is it important to distinguish between intensive and extensive properties in physics?

Distinguishing between intensive properties (independent of system size, like temperature or density) and extensive properties (dependent on system size, like mass or volume) is crucial for understanding how physical quantities behave when systems are combined or divided. This distinction affects how these properties are measured, calculated, and applied in various physical contexts.

39. How does the concept of measurement standards relate to the reproducibility of scientific experiments?

Measurement standards ensure that units are defined and realized consistently across the world. This consistency is crucial for the reproducibility of scientific experiments, as it allows researchers in different locations to make comparable measurements. Without agreed-upon standards, it would be difficult to verify results or build upon previous research.

40. What is the role of prefixes in the SI system, and how do they relate to orders of magnitude?

Prefixes in the SI system (like kilo-, milli-, mega-, etc.) allow for convenient expression of very large or very small quantities without resorting to scientific notation. They directly relate to orders of magnitude, with each prefix representing a power of 10. Understanding these prefixes is crucial for working across different scales in physics and for quickly estimating the relative sizes of quantities.

41. How does the concept of physical dimensions help in understanding the nature of physical quantities?

Physical dimensions provide insight into the fundamental nature of quantities, independent of the units used to measure them. By analyzing dimensions, we can understand how different quantities relate to each other and verify the consistency of physical equations. This concept is particularly useful in fields like fluid dynamics and heat transfer, where dimensional analysis can reveal important physical relationships.

42. Why is it important to understand the difference between exact and measured quantities in physics?

Distinguishing between exact quantities (like the number of objects) and measured quantities (like length or mass) is crucial because it affects how we treat these values in calculations. Exact quantities have no uncertainty, while measured quantities always have some level of uncertainty. This distinction is important for proper error analysis and for understanding the limitations of physical models and theories.

43. How does the concept of unit systems reflect the historical development of physics?

The evolution of unit systems reflects the historical development of physics and measurement technology. From ancient units based on human body parts to the modern SI system based on fundamental constants, this evolution shows how our understanding of the physical world has deepened. It also reflects the increasing need for precision and universality in scientific measurements as physics has advanced.

44. What is the significance of dimensionless physical constants, and how do they relate to fundamental theories?

Dimensionless physical constants, like the fine-structure constant, are significant because their values are independent of the unit system used. These constants often appear in fundamental theories and can provide insights into the underlying structure of the universe. Their study is crucial in attempts to unify different branches of physics and in understanding the fundamental nature of reality.

45. How does the choice of units affect the numerical values in physical equations, and why is this important to understand?

The choice of units can significantly affect the numerical values in physical equations. For example, using different units can introduce or eliminate numerical constants in equations. Understanding this is crucial for correctly interpreting and applying physical laws across different unit systems, and for avoiding errors in calculations and data analysis.

46. What is the significance of universal physical constants, and how do they relate to fundamental and derived quantities?

Universal physical constants, like the speed of light or Planck's constant, are quantities that are believed to be the same throughout the universe. They often relate fundamental quantities to each other and play crucial roles in defining derived quantities. Understanding these constants is essential for grasping the fundamental laws of physics and the interconnectedness of different physical phenomena.

47. How does the concept of base quantities in physics relate to our fundamental understanding of the universe?

Base quantities in physics represent the most basic measurable aspects of the universe that we currently recognize. They reflect our fundamental understanding of the physical world and form the foundation upon which more complex physical concepts are built. As our understanding of the universe evolves, so too might our definition of what constitutes a base quantity.

48. Why is it important to understand the concept of coupling constants in physics, and how do they relate to fundamental interactions?

Coupling constants describe the strength of interactions between particles in fundamental physics. Understanding these constants is crucial for grasping how the basic forces of nature operate. They play a key role in quantum field theories and are essential for calculations in particle physics. The study of these constants and their possible variation over time or space is an active area of research in fundamental physics.

49. How does the concept of natural units relate to the fundamental constants of physics?

Natural units are systems of measurement based on fundamental physical constants, such as the speed of light or Planck's constant, set to unity. This approach simplifies many physical equations by eliminating these constants from the equations. Understanding natural units is important for theoretical physics, especially in areas like quantum mechanics and relativity, where it can reveal deeper relationships between physical quantities.

50. What is the significance of the Planck scale in relation to fundamental physical quantities?

The Planck scale represents the scale at which quantum effects of gravity become significant. It's derived from fundamental constants and represents the smallest meaningful scale in physics with our current understanding. Studying phenomena at this scale is crucial for attempts to unify quantum mechanics and general relativity, potentially leading to a more fundamental understanding of space, time, and matter.

51. Why is it important to understand the limitations of our current system of fundamental quantities and units?

Understanding the limitations of our current