Fundamental And Derived Quantities And Units

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.

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= l² is 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.

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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 ForceDisplacement

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.