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Fundamental and derived units are standards of measurement required to measure physical quantities such as length, mass, and time. The unit of that physical quantity is the measurement standard. The unit of length, for example, is the meter, and a standard length of one meter has a precise definition. To determine how many times this standard length meter is contained in the length of a room, measure the length of an object. Measurement is the process of comparing a physical quantity to a standard quantity.
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| Table of Content |
KeyTerms: Unit, Measurement, Standard, Velocity, Physical Quantity, Length, Temperature, Ampere, Metre.
What is a Unit?
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Unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by society and in terms of which other quantities of similar nature may be measured. Fundamental units and Derived units are the two types of units. Units are governed by certain properties. They are as follows:
- The unit needs to be an appropriate size.
- The unit must have clear boundaries.
- The unit should be easily reproducible everywhere.
- The unit must remain static over time.
- The unit should not alter under the influence of physical parameters like pressure, temperature, etc.
- The unit must be simple to compare experimentally to physical quantities of a similar nature.
Units and Measurements Video Lecture
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What is Standard?
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The actual physical representation of the unit of a physical quantity is described as the standard of that physical quantity. The two major objectives of employing Standards. They help in accurate measurement. They help in accurate communication that in turn helps to precisely comprehend the information.
We need a numerical value (n) and a unit (μ) for expressing any measurement of a quantity.
| Measurement of physical quantity = Numerical value x Unit |
For example Length of a tube = 10 m
In the above example,
10 = Numerical value, and
m (meter) = Unit of length.
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System of Units
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Earlier there were three unit systems used which were CGS, FPS, and MKS systems. Nowadays, the SI system is the unit system that is being used internationally. Within the SI unit system, 7 quantities are taken as the base quantities. The list of these are:
- CGS system: This system comprises a centimeter, gram, and second which are used to express length, mass, and time respectively.
- FPS system: In this system foot, pound, and second are used to express length, mass, and time respectively.
- MKS system: In the MKS system, the quantities such as length, mass, and time are expressed in meters, kilograms, and second respectively.
- SI units: The SI units of length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity are expressed in meter, kg, second, ampere, kelvin, mole, and candela respectively.
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Fundamental Physical Quantity
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A fundamental physical quantity does not require any other physical quantity to express it.
- This determines that it cannot be resolved further in terms of any other physical quantity.
- It is also acknowledged as the basic physical quantity.
- The fundamental physical quantities have units that are known as fundamental units.
- For example: In the M.K.S. system, the physical quantities such as Mass, length, and time are expressed in kilograms, meters, and second, respectively are the fundamental units.
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Derived Physical Quantity
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All the physical quantities that can be derived or obtained from a combination of two or more fundamental quantities or can be expressed in terms of basic physical quantities are known as derived physical quantities. The units of the rest of the other physical quantities, which can be obtained from a fundamental unit, are known as derived units.
For example, units of velocity, density, and force are m/s, and kg/m3, and kg m/s2 respectively are examples of derived units.
Base Units of Measurement
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There are a total of 7 base units of measurement the details of which have been mentioned in the table below:
| Base quantity | SI unit | Symbol |
|---|---|---|
| Length | Meter | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Electric current | Ampere | A |
| Thermodynamics temperature | Kelvin | K |
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
Dimensional Formula
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Any physical quantity's dimensional formula is the formula that tells which of the fundamental units was used to measure that physical quantity.
Ways to write a dimensional formula for a physical quantity:
- The physical quantity's formula must be written down. On the left-hand side of the equation, the quantity must be.
- The right-hand side of the formula must have all of the quantities written in terms of fundamental quantities like mass, length, and time.
- Substitute M, L, and T for mass, length, and time.
- Make a list of the terms' powers.
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Characteristics of Dimensions
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The characteristics of Dimensions are as follows:
- Dimensions are independent of the unit system.
- Similar-sized quantities can be added or subtracted from each other.
- Dimensions can be calculated from physical quantity units and vice versa.
- The same dimension can be shared by two different quantities.
- The dimension of the third quantity is formed by multiplying or dividing two dimensions.
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Things to Remember
- Fundamental and derived units are standards of measurement required to measure physical quantities such as length, mass, and time.
- The comparison process between different quantities is termed a measurement.
- There are two types of physical quantity i.e. fundamental and derived physical quantity or units.
- Physical quantities are those that can be used to describe the laws of physics. For instance, consider the dimensions of length, mass, and time.
- The derived units can either be dimensionless or can be expressed as a product of one or more than one base unit.
- The dimensional formula of a physical quantity indicates which of the fundamental units was employed to measure it.
- The dimensional formula is based on the homogeneity principle.
- There are a total of 7 base units of measurement.
Previous Years’ Questions
- A screw gauge has the least count of 0.01 mm… [NEET – 2020]
- Dimensions of stress are… [NEET – 2020]
- Lumen is the unit of… [UPSEE – 2019]
- A quantity z, to be estimated has a dependency… [TS EAMCET – 2019]
- A student measured the diameter of a small steel ball… [NEET – 2018]
- The nearest star to our solar system is 4.3 light years… [AMUEEE – 2018]
- A physical quantity of the dimensions of length that… [NEET – 2017]
- Einstein was awarded the Nobel prize for his work in… [COMEDK UGET – 2014]
- A student measures the distance traversed… [NEET – 2010]
- A body weighs 22.42 g and has a measured volume… [WBJEE – 2010]
Sample Questions
Ques. What are physical quantities? ( 1 Mark)
Ans. The quantities which are the base quantities of measurement are termed physical quantities. They are even called fundamental quantities and their units are called fundamental units.
Ques. Define the term Ampere. ( 1 Mark)
Ans. The ampere (A) is the SI unit of the electric current. it represents a flow of 1 coulomb of electricity per second. It can also be referred to as the steady current which is produced by 1 volt applied across a resistance of 1 ohm.
Ques. What is the candela (cd)? ( 2 Marks)
Ans. The fundamental photometric value, or luminance, expresses a point light source's ability to cast light in a certain direction. Candela (cd) is the SI unit of luminous intensity. In a particular direction, 1 candela can be defined as the luminous intensity of a source that transmits monochromatic radiation of 540 × 1012 Hz frequency and that has a radiant intensity of 1/68x watt per steradian in the same direction.
Ques. What are supplementary units? (1 Mark)
Ans. Physical values without dimensions that are employed in addition to fundamental units are referred to as supplementary units.
Ques. Define these terms: 1). Measurement 2). Unit (2 Marks)
Ans. 1). The process of measurement involves comparing an object's characteristics to a standard to ascertain its attributes.
2). Any physical amount is evaluated to a fundamental unit that is arbitrarily selected and universally recognized. A number with a unit is used to represent the outcome of a measurement.
Ques. Define the S.I. (Standard International) unit of current. (1 Mark)
Ans. The ampere is the SI unit of current. One ampere is the current that produces a force of 2 x 10-7 newton per meter length when passed through two straight parallel conductors of infinite length and negligible cross-section kept at a distance of 1 meter apart in a vacuum.
Ques. What are the two main measurement systems used in the US? (2 Marks)
Ans. The two main measurement systems used in the US are:
SI, or the International system of units, or metric systems, and
United States Customary Units (The U.S. standard, British Imperial Units, or English standard).
Ques. What are the benefits of the SI unit system? ( 3 Marks)
Ans. The SI system is the unit system that is being used internationally. The advantages of the SI unit system over the rest of the unit systems have been mentioned in the list below:
- It is accepted internationally.
- It’s a rational unit system.
- It’s a metric system.
- It’s a coherent unit system.
- It uses the decimal system and hence is more user-friendly.
- It is closely related to the CGS and MKS systems of the unit.
Ques. How does a metric system quantify force? (1 Mark)
Ans. The metric system uses kilograms as the unit of force, which is represented by the sign kgf.
Ques. Differences between the fundamental unit and derived unit (5 Marks)
Ans. The difference between fundamental and derived units are tabulated below:
| Fundamental Unit | Derived Unit |
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| Examples of seven fundamental units, their abbreviation, and corresponding physical properties are as follows:
| Examples of a few derived units along with corresponding physical properties are:
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