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# Unit and Dimensions Formula Last updated date: 27th Nov 2023
Total views: 21k
Views today: 0.21k     ## Introduction Units and Measurement

The process of measurement is required to measure or compare physical quantities in day-to-day life. Thus, to measure each of the standard quantities, we choose certain units for them that are accepted worldwide. Other similar quantities can also be expressed in terms of these units and can be measured accordingly. The physical quantities are measured in terms of the unit and are known as a standard of that physical quantity. Thus to express any measurement done, we need the numerical value (n) and the unit (μ) of it.

Measured physical quantity = Numerical value x Unit

For example, the Length of any given rod = 6 m

where 6 is a numerical value and m (meter) is a unit of length.

### Fundamental and Derived Physical Quantities

Fundamental quantities are those elementary physical quantities that do not require any other physical quantity to express them. In other words, these cannot be resolved further in terms of any other physical quantity. Thus fundamental quantities are known as basic physical quantities. The units used to express these fundamental physical quantities are called fundamental units.

Mass, Length, and Time expressed in kilogram, meter and second respectively are fundamental units. All those physical quantities which can be expressed in terms of basic physical quantities or are derived from the combination of two or more fundamental quantities are termed as the derived physical quantities. For example, units of velocity, force are m/s and kgm/s2 respectively and they are examples of derived units.

## Unit of Fundamental and Supplementary Physical Quantities in SI System

### Definitions of Fundamental Units

There are seven fundamental units of SI. These have been defined as

• 1 meter is defined as the distance that contains 1650763.73 wavelengths of orange-red light of atom Kr-8.

• 1 kilogram is defined in terms of a cylindrical prototype of mass made of platinum and iridium alloys of height 39 mm and diameter 39 mm. Also, it can be defined as a mass of 5.0188 x 1025 atoms of carbon-12.

• 1 second is defined as the time in which a cesium atom vibrates 9192631770 times in an atomic clock.

• 1 kelvin is defined as the temperature at which (1/273.16) is part of the thermodynamics temperature of the triple point of water.

• 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’ when the source is at the melting point of platinum (1760°C).

• 1 ampere is the current which is maintained in two straight parallel conductors of infinite length and almost negligible cross-section area placed one meter apart in a vacuum and producing force of a force 2 x 10-7 N per meter length between them.

• 1 mole is defined as the amount of substance of a system that contains as many as elementary entities ( atoms, molecules, ions, electrons or group of particles, as this and atoms in 0.012 kg of carbon isotope 6C12.

### System of Units

Earlier there were three different systems of units that were used in different countries. These were CGS, FPS, and MKS systems. But nowadays, the whole world is adopting the international SI system of units. In this system of units, seven quantities are taken as the base quantities.

In CGS System Centimeter, Gram and Second are used for expressing length, mass, and time respectively. In the FPS System. Foot, pound, and second are used to express the quantities length, mass, and time respectively. While in MKS System, Length is expressed in meters, mass is expressed in kilograms and time is in seconds.

In the Standard units system Length, mass, time, electric current, thermodynamic temperature, Amount of substance, and luminous intensity are expressed in units: meter, kilogram, second, ampere, kelvin, mole, and candela respectively.

### Dimensions and Dimensional Formula

Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity. Dimensional formula of any physical quantity is an expression that represents how and which of the base quantities are included in that quantity. It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e( ).

E.g: the Dimension formula of mass is: (M)

The equation obtained by equating a physical quantity with its dimensional formula is called a dimensional equation.

When a physical quantity X depends on base dimensions M(Mass), L(Length), and T(Time), Temperature, current electricity, luminous intensity, and amount of substance with respective powers a, b and c, its dimensional formula is represented as  \[M^{a} L^{b} T^{c}\].

• The dimensional formula of Velocity is \[M^{0} L T^{-1}\]

• Dimensional formula of Volume is \[M^{0} L^{3} T^{0}\]

• The dimensional formula of Force is \[M L T^{-2}\]

• Dimensional formula of Area is \[M^{0} L^{2} T^{0}\]

• The dimensional formula of Density is \[M L^{-3} T^{0}\]

 Physical Quantity Dimensional Equation Force (F) F = \[M L T^{-2}\] Power (P) P = \[M L^{2} T^{-3}\] Velocity (v) v  = \[M L T^{-1}\] Density (D) D =  \[M L^{3} T^{0}\] Energy (E) E =  \[M L^{2} T^{-2}\] Pressure (P) P = \[M L^{-1} T^{-2}\] Time Period of wave T = \[M^{0} L^{0} T^{-1}\]

### Tips for the JEE Preparation

The chapter Units and dimensions are very important. It will be easier to be thorough in the chapter once you complete the syllabus. Once you complete the syllabus you will be well aware of the formulas and the chapter becomes much easier for you to understand rather than just mugging the formulas.

What the students should understand is the importance of each chapter and the topics and learn the concepts and then proceed further. When there is clarity things will fall in the right place and everything becomes very simple.

Timetable- It is very important to have a proper plan and a study strategy. Know the syllabus and make a plan in such a way that the syllabus has to be completed in a specific time so that there is enough time to practice the question papers and the mock test.

Know the Strengths and Weaknesses- While analyzing the syllabus you will come across the topics which might be easy and also difficult ones. Knowing this, devote more time to the difficult topics so that it is learned and understood clearly.

Revise the Topics- As you proceed further with the learning of the new topics it is equally important to revise the previously studied topics. So before you start any new topic, spare a few minutes to revise the topics. This will be very helpful to remember well and also easier.

Formulas- This chapter has lots of formulas and often it is a difficult task to remember those formulas thoroughly. So the best method would be to write down all the formulas in a single sheet or notes and read them out every day, this way you will be able to remember effectively. It is a known fact that when you keep reading certain things every day automatically it gets captured in your mind and it won’t get erased easily.

One more important thing to remember is to learn the formulas with understanding and just don’t memorize. Once you complete the syllabus then you can start solving the previous year's question paper. This will help you to know the exact pattern of the real exam and also the difficulty level in the exam. This will help you to prepare in those areas and be thorough with the preparation. The methods are very simple, it just helps to be focussed and the practice makes a difference.

The extensive practice of question papers will help the students to have an appropriate exam preparation with the improvement of the time management skills which is very important in exams like IIT JEE.

Solving the question papers will also help in the enhancement of speed and accuracy.

### Advantages of Studying the Real-life Examples of the Exothermic Reactions

• Science is a practical subject, especially Chemistry, that is to say, the knowledge of practical concepts of chemistry is just as important as that of its theory.

• A real-life example of Exothermic Reactions becomes rather easy to understand the theory by the real-life practical demonstration. Furthermore, it helps the students not only in understanding the concepts of Exothermic Reactions but also in remembering the same as well.

• The real-life example also makes the students understand how the everyday things that happen around are the reason for Exothermic Reactions.

## FAQs on Unit and Dimensions Formula

1. What are the limitations of  Dimension Formulas?

This can be defined as the relationship of physical quantities. We can also define the dimensional quantities which do not have a fixed value. Now let us know some of the limitations in the dimensional formulas. The formulas cannot be derived if they contain trigonometric functions, exponential functions, and log functions. This does not contain any dimensional constants in the formula. It is not possible to know the plus and minus in two points and the relations.

2. What are the four main applications of dimensions?

The four main applications of dimensions are that it helps in the conversion of the physical quantity from one system to another. It helps in checking the accuracy of the physical relation. It helps to obtain the relations among various physical quantities. Lastly, it helps in finding the dimensions of a constant in physical relation. So focussing and learning all these applications and the concepts will help in the preparation of this chapter comprehensively. Students can refer to the Vedantu NCERT solution to have a better understanding.

3. What do you understand by Dimensional analysis?

Dimensional analysis helps in quantifying the size and shape of the objects. It helps to analyze the nature of the objects involving lengths, angles, and some of the geometrical properties like flatness and straightness. The main concepts in dimensions are that it is possible to add or subtract those quantities that have the same dimensions only. We can also conclude that the two physical quantities are said to be equal if they have the same dimensions.

4. What are the advantages of preparing the chapter from Vedantu’s NCERT solutions?

The advantages of Vedantu are as below.

1. The solutions are well organized.

2. The chapter-wise solutions are very systematic and are precise.

3. Students will know the exact format of answering.

4. This is the best guide for helping the students in every step of the preparation.

5. All the solutions are prepared by experts having excellent subject knowledge.

6. The latest curriculum of the CBSE is followed accurately.

7. Students can be confident and prepare thoroughly through Vedantu’sNCERT solutions for the chapter Units and Dimensions.

8. We can say accuracy is Vedantu.

5. What are the advantages of solving the previous year's question papers?

Solving the previous year's questions paper helps the students to have an exact idea of the real exam pattern. Students should solve at least the previous 5 years question paper so that they can improve on their time management skills and also enhance their speed and accuracy. Students can analyze the questions which are repeated. These can be more focussed and prepared accurately.  It is mandatory to be perfect in all the topics but certain topics can be given little more importance. It does not mean that you can skip any of the topics. Every topic is very essential.

6. Explain a few limitations of Dimension Formulas.

This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. A formula containing more than one term which is added or subtracted likes s = ut+ ½ at2 also cannot be derived. The relation derived from this method gives no information about the dimensionless constants.

7. The ratio of the dimension Planck’s constant and that of the moment of inertia is the dimension of?

A. Velocity

B. Angular momentum

C. Time

D. Frequency

Time

8. Write some applications of Dimensional Analysis.

Following are some applications of dimensional analysis:

1. To convert a physical quantity from one system of the unit to the other.

2. To check the dimensional correctness of a given physical relation: If in a given relation, the terms of both sides have the same dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions.

3. To derive the relationship between different physical quantities: Using the principle of homogeneity of dimension the new relation among physical quantities can be derived if the dependent quantities are known.