Physical Quantity: Definition, Types, Formula, Examples

Physical Quantity

Edited By Vishal kumar | Updated on Jul 02, 2025 05:44 PM IST

Imagine trying to build a house without a tape measure or cook without measuring ingredients. Measurement is essential in our daily lives. Similarly, physicists need precise measurements to understand the physical world. In this chapter of physics and measurement, we will explore the fundamentals of physics and measurement, focusing on length, mass, and time. We'll discuss accuracy, precision, and the use of various instruments in scientific experiments and everyday life.

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Physical Quantity
Types of Physical Quantity
Solved Example Based on Physical Quantity
Summary

Physical Quantity

In this article, we will cover the concept of Physical quantity. This concept falls under the broader category of Physics and Measurement which is a crucial chapter in Class 11 physics. It is not only essential 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, BCECE and more. No direct question was asked about this concept In JEE and NEET but indirectly this concept is very important to learn the chapter on physics and measurement.

Physical Quantity

A quantity that can be measured and expressed in the form of laws is called a Physical quantity. A physical quantity is expressed completely by its magnitude and unit.

One physical quantity can be represented in terms of one or more units.

Amount of physical quantity (Q)=nu
n= numerical value or magnitude
u=unit

For a given amount of physical quantity

nu = constant

So, n1u1=n2u2= constant So, nα1u

So larger the unit smaller the magnitude.

Now let's understand the types of physical quantity

Types of Physical Quantity

There are mainly four main types of physical quantity which are mentioned below:

1) Scalar Quantity

The quantities having magnitude only are known as scalar quantities. It does not specify the direction.

Scalar quantity can be added or subtracted by the laws of addition or subtraction.

Examples-Distance, time, work, energy, etc

2) Vector Quantity

The quantities having both directions as well as magnitude are known as vector quantities. It has a specific direction.

Vector quantity can be added and subtracted according to vector laws of addition.

Examples - Displacement, force, velocity, acceleration, momentum, etc.

3) Tensor Quantity

Scalar and vector are special cases of a tensor. Tensors are represented in the multi-dimensional array, i.e., in different directions, tensors will have different magnitudes.

If a tensor has only magnitude and no direction, it is called a scalar (a tensor of rank zero).
If a tensor has magnitude and one direction, it is called a vector (a tensor of rank one).

Examples are stress, The moment of inertia, coefficient of viscosity.

4) Ratio Quantity

When a physical quantity is the ratio of two similar quantities.

eg. Relative density = density of object density of water at 4∘C

Solved Example Based on Physical Quantity

Example 1: A metallic sphere floats in an immiscible mixture of water (density 103 kg/m3) and a liquid (density 8×103 kg/m3 ) such that its 23 part is in water and 13 part in the liquid. The density of metal is-

1) 50003 kg/m3 2) 100003 kg/m3 3) 5000 kg/m3 4) 2000 kg/m3

Solution:

weight of sphere = upthrust from water + upthrust from liquid

v =(23v×103×g)+(v3×8×103×g) or ρ=100003 kg/m3

Hence, the answer is option (2).

Example 2: What is true for the ratio of physical quantity-

1) It is the ratio of two similar quantity

2) It has no unit

3) An example is the relative density

4) All of the above

Solution:

Ratio Quantity -

When a physical quantity is the ratio of two similar quantities

- wherein

eg. Relative density = density of object density of water at 4∘C

Ratio is a physical quantity which is the ratio of two similar quantities. It is unit-less

Hence, the answer is the option 4.

Example 3: Statement 1: A tensor quantity not completely specified even by magnitude and direction.

Statement 2: stress and moment of inertia are tensor quantities

which of the above statements is/are true?

1) only 1

2) only 2

3) both

4) none

Solution:

Tensor Quantity - Which are not completely specified even by magnitude and direction.

example: moment of inertia, co-efficient of viscosity

Hence, the correct option is 3.

Example 4: For a physical quantity which of the following relation is true? [n- numerical value, u - unit ]

1) nαu2
2) nαu
3) n∝u
4) n∝1u

Solution:

For any physical quantity

Q = n u =constant

So, n α1/u

Hence, the answer is the option (4).

Example 5: Which one of these groups shows the scalar physical quantity-

1) Displacement, speed, work

2) Current, force, work

3) (correct)mass, charge, volume, electric potential

4) Charge, electric field, speed, work

Solution:

Scalar Quantity can be added or subtracted by the laws of addition or subtraction. It does not specify the direction.

Ex- displacement, force and electric field are vector quantities.

Hence, the correct option is 3.

Summary

In short, all of physics is based on measurement. Basic physical quantities, like length, mass, and time, are quantified in standard units, meters, kilograms, and seconds. Accuracy is a relative measure of diversity or error relative to the true value of the measure and precision is a measure of variation of the repeated measurements. To take these measurements, we will need some tools like rulers, balances, and clocks. Measurements serve in physics to provide the basis for laws, check hypotheses, and serve as the ground for technological discoveries. The principles of measurement are applicable even in day-to-day activities through scientific research for reproduction and reliability of results.

Frequently Asked Questions (FAQs)

1. What is a physical quantity?

A physical quantity is any property of a physical system that can be measured or calculated. It consists of a numerical value and a unit of measurement. For example, length, mass, time, and temperature are all physical quantities.

2. How do physical quantities differ from mathematical concepts?

Physical quantities are measurable properties of the physical world, while mathematical concepts are abstract ideas. Physical quantities always have units and can be directly or indirectly measured, whereas mathematical concepts like numbers or geometric shapes don't necessarily correspond to physical measurements.

3. Why are units important for physical quantities?

Units are crucial for physical quantities because they provide context and allow for meaningful comparisons. Without units, a number alone doesn't convey complete information. For instance, saying an object's mass is "5" is meaningless without specifying whether it's 5 grams, 5 kilograms, or 5 pounds.

4. How does the concept of physical quantities relate to the scientific method?

Physical quantities are fundamental to the scientific method as they allow for objective, quantitative measurements and observations. They enable scientists to formulate hypotheses, design experiments, collect data, and draw conclusions based on measurable evidence rather than subjective impressions.

5. What is the SI system, and why is it important for physical quantities?

The SI (Système International) system is a standardized system of units used worldwide for scientific and everyday measurements. It's important because it provides a consistent framework for expressing physical quantities, facilitating communication and collaboration in science and engineering across different countries and cultures.

6. What is dimensional analysis, and how is it useful in physics?

Dimensional analysis is a method of analyzing the relationships between different physical quantities by identifying their fundamental dimensions. It's useful for checking the consistency of equations, converting between unit systems, and even deriving relationships between physical quantities without detailed calculations.

7. What is the importance of choosing appropriate units when working with physical quantities?

Choosing appropriate units is crucial for clear communication, avoiding errors, and simplifying calculations. For instance, using astronomical units for distances in the solar system or electron volts for particle physics energies can make numbers more manageable and calculations more intuitive.

8. What is the role of significant figures in reporting physical quantities?

Significant figures indicate the precision of a measurement. They reflect the number of digits that are known with certainty plus one estimated digit. Using the correct number of significant figures is important to accurately represent the precision of measurements and calculations in scientific communication.

9. How do physical quantities help in understanding the concept of irreversibility in physics?

Irreversibility in physics is often associated with the increase of certain physical quantities, most notably entropy. Understanding how these quantities change over time is key to grasping concepts like the arrow of time and the second law of thermodynamics.

10. What is the difference between base and derived physical quantities?

Base quantities are fundamental quantities that cannot be expressed in terms of other quantities. Examples include length, mass, and time. Derived quantities are formed by combining base quantities. For instance, velocity (distance/time) and force (mass × acceleration) are derived quantities.

11. Can physical quantities be negative?

Yes, some physical quantities can be negative. The sign often indicates direction or a change relative to a reference point. For example, velocity can be positive or negative depending on the direction of motion, and temperature can be negative on certain scales like Celsius.

12. How do scalar and vector quantities differ?

Scalar quantities have only magnitude and are fully described by a single number and unit (e.g., mass, temperature). Vector quantities have both magnitude and direction and require multiple components to be fully described (e.g., velocity, force). Understanding this distinction is crucial for correctly analyzing and solving physics problems.

13. Can all physical quantities be directly measured?

No, not all physical quantities can be directly measured. Some, like length or mass, can be measured directly with appropriate instruments. Others, like energy or electric field strength, are often measured indirectly by measuring related quantities and then calculating the desired quantity using known relationships.

14. How do physical constants differ from variables in physics equations?

Physical constants are quantities that have a fixed value in nature, such as the speed of light or Planck's constant. Variables, on the other hand, can take on different values depending on the specific situation or system being studied. Constants provide a foundation for many physical laws and equations.

15. What is the significance of dimensionless numbers in physics?

Dimensionless numbers, formed by combining different physical quantities, often indicate the relative importance of different physical effects. For example, the Reynolds number in fluid dynamics compares inertial forces to viscous forces. These numbers are useful in scaling experiments and understanding complex systems.

16. How do physical quantities help in understanding the concept of feedback in systems?

Feedback in physical systems often involves the change in one quantity affecting another, which in turn influences the first. Quantifying these relationships helps in analyzing system stability, oscillations, and control mechanisms in fields ranging from electronics to climate science.

17. What is the significance of threshold values in physical quantities?

Threshold values of physical quantities often mark important transitions in system behavior. Examples include the critical temperature for superconductivity or the activation energy for chemical reactions. Recognizing these thresholds is key to understanding and predicting system behavior.

18. How do physical quantities help in understanding the concept of emergent properties in complex systems?

Emergent properties in complex systems are often described by new physical quantities that arise from the collective behavior of simpler components. For example, temperature emerges from the average kinetic energy of particles. Understanding these emergent quantities is crucial in fields like statistical mechanics and complexity science.

19. What is the significance of invariant quantities in physics?

Invariant quantities remain unchanged under certain transformations or in different reference frames. For example, the speed of light is invariant in special relativity. These invariants often reveal deep principles about the nature of space, time, and physical laws.

20. What is the importance of dimensionless ratios in comparing different physical systems?

Dimensionless ratios, formed by combining different physical quantities, allow for meaningful comparisons between systems of different scales. For example, the Reynolds number in fluid dynamics allows for comparison of flow behavior in pipes of different sizes or with different fluids. These ratios are crucial in scaling laws and similarity principles.

21. What is meant by the term "intensive" and "extensive" physical quantities?

Intensive quantities are independent of the system's size or amount of material, such as temperature or density. Extensive quantities depend on the system's size, like mass or volume. Understanding this distinction is important for analyzing systems and their properties in thermodynamics and other areas of physics.

22. What is the importance of operational definitions in physics?

Operational definitions specify how a physical quantity is measured or determined. They are crucial because they ensure that different researchers can reproduce measurements consistently. For example, the operational definition of time might involve counting oscillations of a cesium atom in an atomic clock.

23. How do physical quantities help in formulating physical laws?

Physical quantities allow scientists to express relationships between different aspects of nature mathematically. By identifying patterns and correlations between measured quantities, physicists can formulate laws that describe natural phenomena. For instance, Newton's Second Law (F = ma) relates force, mass, and acceleration.

24. What is the difference between fundamental and derived units?

Fundamental units (also called base units) are the basic units of measurement in a system, like meters for length or seconds for time in the SI system. Derived units are formed by combining fundamental units, such as meters per second for velocity or joules for energy.

25. How do prefixes modify physical quantities?

Prefixes in the metric system modify the scale of a unit by factors of 10. For example, "kilo-" means 1000 times the base unit (e.g., 1 kilometer = 1000 meters), while "milli-" means 1/1000 of the base unit (e.g., 1 millimeter = 0.001 meters). This system allows for convenient expression of very large or very small quantities.

26. What is the concept of dimensionless quantities in physics?

Dimensionless quantities are pure numbers without units. They often arise as ratios of quantities with the same dimensions, causing the units to cancel out. Examples include efficiency (expressed as a percentage) or the fine-structure constant in quantum mechanics. These quantities can be particularly important in describing universal relationships.

27. How does uncertainty relate to physical quantities?

Uncertainty is inherent in all physical measurements due to limitations in measuring instruments and procedures. It's typically expressed as a range around the measured value within which the true value is expected to lie. Understanding and properly reporting uncertainties is crucial for assessing the reliability of scientific results.

28. What is the difference between accuracy and precision in measuring physical quantities?

Accuracy refers to how close a measurement is to the true value, while precision refers to how consistently a measurement can be reproduced. A measurement can be precise (giving consistent results) without being accurate (if it's consistently off from the true value). Both are important considerations in scientific measurements.

29. How do physical quantities help in dimensional homogeneity?

Dimensional homogeneity is the principle that all terms in a physical equation must have the same dimensions. This concept, based on physical quantities, helps in checking the validity of equations and can even guide in deriving new relationships between quantities.

30. What is the role of physical quantities in scientific modeling?

Physical quantities are essential in creating scientific models as they allow for quantitative predictions and comparisons with experimental data. Models express relationships between relevant physical quantities, enabling scientists to describe, explain, and predict natural phenomena.

31. How do physical quantities contribute to the concept of conservation laws in physics?

Conservation laws state that certain physical quantities remain constant in closed systems over time. These laws, such as conservation of energy or momentum, are fundamental principles in physics and are expressed in terms of physical quantities that can be measured and tracked.

32. How do physical quantities relate to the concept of physical intuition?

Physical intuition involves developing a feel for how physical quantities relate to each other and behave in different situations. By working with physical quantities and observing their relationships, physicists can build intuition that guides their understanding and problem-solving abilities.

33. How do physical quantities help in understanding the limits of physical theories?

Physical quantities often reveal the limits of theories by reaching extreme values or unexpected behaviors. For example, the speed of light as a maximum velocity in special relativity, or the breakdown of classical physics at atomic scales, leading to quantum mechanics. These limits are often expressed in terms of specific values or ranges of physical quantities.

34. What is the role of physical quantities in interdisciplinary research?

Physical quantities provide a common language for different scientific disciplines. For instance, concepts like energy and entropy are used across physics, chemistry, and biology. This shared framework of measurable quantities facilitates collaboration and the transfer of knowledge between different fields of study.

35. How do physical quantities relate to the concept of symmetry in physics?

Symmetries in physics often manifest as invariances or conservation of certain physical quantities. For example, translational symmetry in space leads to conservation of momentum, while time symmetry leads to conservation of energy. Understanding these relationships deepens our grasp of fundamental physical principles.

36. What is the significance of dimensionality in physical quantities?

The dimensionality of a physical quantity (e.g., length, area, volume) is crucial for understanding how it scales with size. This concept is important in fields like materials science, where properties may change dramatically with scale, or in astrophysics when dealing with vastly different size scales.

37. How do physical quantities help in understanding the concept of equilibrium?

Equilibrium in physics often involves the balancing of different physical quantities. For example, thermal equilibrium involves equalizing temperatures, while mechanical equilibrium involves balancing forces. Understanding these balances in terms of measurable quantities is key to analyzing stable and unstable systems.

38. What is the role of physical quantities in defining the state of a system?

The state of a physical system is typically described by a set of physical quantities. For instance, the state of an ideal gas can be defined by its pressure, volume, and temperature. These state variables allow for a complete description of the system's condition at any given time.

39. How do physical quantities relate to the concept of fields in physics?

Fields in physics, such as electric or gravitational fields, are described by physical quantities that vary in space and time. These field quantities, like electric field strength or gravitational potential, allow for the mathematical description of how forces act at a distance.

40. What is the importance of identifying intensive and extensive quantities in thermodynamics?

In thermodynamics, distinguishing between intensive (e.g., temperature, pressure) and extensive (e.g., volume, entropy) quantities is crucial for understanding how systems behave when combined or divided. This distinction is fundamental to concepts like phase transitions and equilibrium conditions.

41. How do physical quantities contribute to the development of new measurement techniques?

The need to measure new or more precise physical quantities often drives technological innovation. For instance, the quest to measure gravitational waves led to the development of incredibly sensitive laser interferometers. This interplay between theory and measurement techniques is a key driver of scientific progress.

42. What is the role of physical quantities in defining and understanding physical constants?

Physical constants, like the speed of light or Planck's constant, are expressed as specific values of physical quantities. These constants play a fundamental role in physics, often appearing in equations that describe natural phenomena and serving as cornerstones for physical theories.

43. What is the importance of understanding the relationships between different physical quantities?

Understanding the relationships between different physical quantities is fundamental to physics. These relationships, often expressed as equations, allow for predictions and explanations of natural phenomena. For example, the relationship between force, mass, and acceleration (F = ma) is a cornerstone of classical mechanics.

44. How do physical quantities relate to the concept of causality in physics?

Causality in physics often involves changes in one physical quantity leading to changes in another. Understanding these causal relationships, such as how forces cause acceleration or how temperature differences drive heat flow, is crucial for explaining and predicting physical phenomena.

45. How do physical quantities help in understanding the limits of measurement precision?

The precision of measurements is ultimately limited by fundamental physical quantities. For instance, the Heisenberg uncertainty principle sets limits on how precisely we can simultaneously measure position and momentum. Understanding these limits is crucial for interpreting experimental results and developing new measurement techniques.

46. What is the role of physical quantities in defining and understanding phase transitions?

Phase transitions are often characterized by abrupt changes in certain physical quantities, such as density or magnetization. Understanding how these quantities behave near transition points is key to studying phenomena like superconductivity, ferromagnetism, and critical phenomena in statistical physics.

47. How do physical quantities contribute to our understanding of symmetry breaking?

Symmetry breaking in physics often involves a physical quantity (called an order parameter) that changes from zero to a non-zero value. This concept is crucial in understanding phenomena like ferromagnetism, where the net magnetization serves as the order parameter, or in particle physics where symmetry breaking plays a role in explaining particle masses.

48. What is the role of physical quantities in defining and understanding quantum states?

In quantum mechanics, physical quantities are associated with operators, and the possible values a quantity can take are the eigenvalues of these operators. This framework is fundamental to understanding concepts like superposition, measurement, and the probabilistic nature of quantum mechanics.

49. How do physical quantities contribute to our understanding of the universe's evolution?

Cosmological models describe the evolution of the universe in terms of changing physical quantities such as temperature, density, and expansion rate. Understanding how these quantities evolved over time is crucial for explaining the current state of the universe and predicting its future.

50. What is the significance of coupling constants in physics?

Coupling constants are physical quantities that determine the strength of interactions between particles or fields. Examples include the fine-structure constant in electromagnetism or the gravitational constant. These quantities play a crucial role in fundamental theories and often raise questions about why they have the specific values observed in nature.