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# Learn the Derivations in Physics Class 11 CBSE PDF 11 in a Simple and Easy Way

## Derivations in Physics Class 11 CBSE PDF 11

Physics is one of the most fascinating subjects that deals with the study of nature and its phenomena. It helps us to understand the fundamental laws and principles that govern the physical world. Physics also develops our logical thinking and problem-solving skills, which are essential for any career path.

## derivations in physics class 11 cbse pdf 11

However, physics can also be challenging and intimidating for many students, especially when it comes to solving numerical problems and deriving formulas. That's why it is important to have a good grasp of the concepts and derivations in physics class 11 CBSE.

## Introduction

In this article, we will provide you with a comprehensive guide on how to master the derivations in physics class 11 CBSE. We will cover the following topics:

• What are derivations in physics?

• Why are derivations important for class 11 CBSE students?

• Chapter-wise derivations in physics class 11 CBSE

By the end of this article, you will have a clear understanding of the derivations in physics class 11 CBSE and how to use them effectively for your exams.

## What are derivations in physics?

A derivation in physics is a logical process of obtaining a formula or an equation from some basic principles or assumptions. For example, we can derive the formula for the area of a circle by using the definition of pi and the concept of circumference.

A derivation usually involves the following steps:

• Identify the given data and the required formula or equation.

• Write down the relevant definitions, laws, principles, or postulates that apply to the problem.

• Use algebraic manipulation, trigonometry, calculus, or other mathematical tools to simplify and rearrange the expressions.

• Eliminate any unnecessary variables or constants and obtain the final result.

A derivation can be written in different ways depending on the level of detail and explanation required. However, it is always advisable to write each step clearly and logically, with proper symbols and units.

## Why are derivations important for class 11 CBSE students?

Derivations are important for class 11 CBSE students for several reasons:

• They help to understand the concepts and principles behind the formulas and equations. By deriving a formula, you can see how it is related to other concepts and how it is derived from some basic assumptions. This will enhance your conceptual clarity and logical thinking.

• They help to solve numerical problems and application-based questions. By knowing the derivations, you can easily apply the formulas and equations to different situations and scenarios. You can also modify or adapt the derivations to suit the given data or conditions.

• They help to score well in the exams. Derivations are an integral part of the CBSE class 11 physics syllabus and they carry a significant weightage in the exams. You can expect to get direct or indirect questions based on the derivations in both theory and practical exams. Therefore, by mastering the derivations, you can boost your marks and confidence.

If you are looking for a reliable and convenient source of CBSE class 11 physics notes with derivations, you can visit the website of Toppers CBSE. Toppers CBSE is a leading online platform that provides high-quality notes, solutions, sample papers, previous year papers, and other study materials for CBSE students.

Toppers CBSE has prepared the CBSE class 11 physics notes with derivations by following the NCERT syllabus and the latest CBSE guidelines. The notes cover all the topics and chapters of the class 11 physics syllabus, along with the step-by-step explanation of the derivations. The notes also include diagrams, graphs, tables, examples, and tips to make the learning process easier and more effective.

To download the CBSE class 11 physics notes with derivations from Toppers CBSE, you need to follow these simple steps:

• Click on the tab "CBSE CLASS 11 NOTES" on the homepage.

• Select "CBSE Class 11 PHYSICS NOTES" from the drop-down menu.

• You will see a list of all the chapters of the class 11 physics syllabus along with their links.

• You will be redirected to a new page where you can view or download the notes in PDF format.

You can also order the printed version of the notes from Toppers CBSE by filling up an online form and paying a nominal fee.

## Chapter-wise derivations in physics class 11 CBSE

In this section, we will provide you with a brief overview of some of the important derivations in physics class 11 CBSE for each chapter. However, we recommend you to refer to the detailed notes from Toppers CBSE for a complete understanding of the derivations.

### Chapter 1: Physical World

This chapter introduces you to the scope and excitement of physics, as well as some of its fundamental concepts and methods. It also discusses some of the major domains and frontiers of physics research.

#### Derivation of dimensional formula of physical quantities

A dimensional formula is an expression that shows how a physical quantity depends on the basic dimensions of mass (M), length (L), time (T), electric current (A), temperature (K), amount of substance (mol), and luminous intensity (cd).

To derive the dimensional formula of a physical quantity, we need to use its definition or relation with other physical quantities whose dimensions are known. For example, let us derive the dimensional formula of force.

We know that force is defined as the product of mass and acceleration. Therefore,

F = ma

where F is force, m is mass, and a is acceleration.

We also know that mass has dimension M, and acceleration has dimension LT, where L is length and T is time.

Therefore,

[F] = [m][a]

where [ ] denotes dimension.

[F] = M(LT)

[F] = MLT

This is the dimensional formula of force.

#### Derivation of dimensional analysis and its applications

Dimensional analysis is a technique that uses the dimensions of physical quantities to check the correctness of equations, to convert units, and to derive new relations.

To derive a relation using dimensional analysis, we need to use the principle of homogeneity of dimensions. This principle states that in any valid equation, both sides must have the same dimensions.

For example, let us derive a relation for the time period (T) of a simple pendulum in terms of its length (l) and acceleration due to gravity (g).

We assume that the time period of the simple pendulum depends only on its length and the acceleration due to gravity. Therefore,

T = k(l/g)

where T is the time period, l is the length, g is the acceleration due to gravity, and k is a constant of proportionality.

To find the value of k, we need to use dimensional analysis. We know that the dimensions of time period are T, length are L, and acceleration are LT. Therefore,

[T] = [k][l/g]

T = k(L/LT)

T = kT

Comparing both sides, we get

k = 1

Therefore,

T = (l/g)

This is the relation for the time period of a simple pendulum derived using dimensional analysis.

### Chapter 2: Units and Measurements

This chapter deals with the basic concepts of units and measurements, such as the international system of units, fundamental and derived units, dimensional analysis, error analysis, and significant figures.

#### Derivation of error analysis and propagation of errors

Error analysis is a method of estimating the uncertainty or inaccuracy in a measurement or a calculation. Propagation of errors is a technique of finding the error in a result obtained from a combination of measured quantities.

To derive the formula for propagation of errors, we need to use the concept of differentiation and approximation. For example, let us find the error in the area of a rectangle whose length (l) and breadth (b) are measured with some errors (l and b).

We know that the area (A) of a rectangle is given by

A = lb

We can write this as a function of l and b as

f(l,b) = lb

We can differentiate this function with respect to l and b as

df/dl = b

df/db = l

We can multiply both sides by l and b respectively and add them to get

(df/dl)l + (df/db)b = bl + lb

This is an approximation for the change in f due to the changes in l and b. We can write this as

f bl + lb

We can divide both sides by f to get the relative error in f as

(f/f) (bl + lb)/(lb)

(f/f) (l/l) + (b/b)

This is the formula for propagation of errors for multiplication or division. Similarly, we can derive the formula for propagation of errors for addition or subtraction as

(f/f) (l + b) 71b2f0854b