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# NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements - PDF Download

JEE Mains & Advanced

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements are the best study resources. You can get to understand the main topics and to score well in your examination. This solution provides appropriate answers to the textbook questions. To get a good grip on this chapter, you can make use of the NCERT Solutions for Class 11 Physics available at our website for free in a pdf form, you can download them and use them offline.

Chapter 1 of NCERT Solutions for Class 11 Physics mainly helps understand the fundamentals of units and measurements. In our daily lives, most of the activities depend on this, and it is very important for us to learn it effectively. Everything around us depends on units and measurements, from buying milk in the morning to the pounds of bread needed for breakfast or from buying sugar for milk to the kilograms of rice needed for lunch. You can access the Physics NCERT Solutions for Class 11 to comprehend the key concepts present in this chapter.

## Topics Covered in Class 11 Chapter 2 Physics Units and Measurement

 Section Number Topic 1.1 Introduction 1.2 The International System of Units 1.3 Significant figure 1.3.1 Measurement of Length 1.3.2 Rounding off the uncertain digits 1.3.3 Rules for determining the uncertainty in the result of Arithmetic calculation 1.4 Dimensions of Physical Quantities 1.5 Dimensional Formulae and Dimensional Equations 1.6 Dimensional Analysis and Its Applications 1.6.1 Checking the Dimensional Consistency of Equations 1.6.2 Deducing Relation among the physical quantities

## Introduction

Measurement of any kind of physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard we called that standard as Unit. The result of a measurement of any physical quantity is expressed by a numerical measure accompanied by a unit. However, if the number of physical quantities appears to be very large, we use only a limited number of units for expressing all the physical quantities, since all the units are interrelated with one another. The units for the fundamental or base quantities are called fundamental or base units.

### The International System of Units

In past times, the scientists of different countries were using different systems of units for measurement. There are basically 3 such systems like CGS, the FPS (or British) system and the MKS system were in use extensively till recently.

•  In CGS(Centimeter Gram Second system) system they were centimetre, gram and second respectively

• In the FPS(foot-pound-second system of units) system they were foot, pound and second respectively.

• In MKS system they were meter, kilogram and second respectively.

### Significant figure

Following are the rules for significant figure

• All the non-zero digits are significant.

• All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.

• If the number is less than 1, the zero(s) on the right of the decimal point but to the left of the first non-zero digit are not significant.

• The terminal or trailing zero(s) in a number without a decimal point are not significant.

• The trailing zero(s) in a number with a decimal point are significant.

### Rules for Arithmetic Operations with Significant Figures

The result of a calculation involving approximate measured values of quantities (i.e. values with limited number of significant figures) must reflect the uncertainties in the original measured values. It cannot be more accurate than the original values that we measured themselves on which the result is based. In common, the final result should not have more significant figures than the original data from which it was picked up.

The given rules for arithmetic operations with significant figures ensure that the final result of a calculation is shown with the precision that is consistent with the precision of the input measured values :

•  In multiplication or division, the final result should retain as many significant figures as there are in the original result with the least significant figures.

•  In subtraction or  addition, the final result should retain as many decimal places as are there in the number with the least decimal places.

### Rounding off the Uncertain Digits

The result of calculation with approximate numbers, which contain more than one uncertain digit, should be rounded off. The rules for rounding off numbers to the appropriate significant figures are very obvious in most cases. Let's consider a number 1.746 rounded off to three significant figures is 1.75, while the number 2.743 would be 2.74. The rule by convention is that the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the digit is less than 5. But what if the number is 3.745 in which the insignificant digit is 5. Here, the old method is that if the preceding digit is even, the insignificant digit is dropped and, if it is odd, the preceding digit is raised by 1.

### Rules for Determining the Uncertainty in the Results of Arithmetic Calculations

The rules for determining the uncertainty or error in the number/measured quantity in arithmetic operations can be understood from the below examples.

(1) If the length and breadth of a thin rectangular sheet are measured, using a meter scale as 17.2 cm and 10.1 cm respectively, there are three significant figures in each measurement. It means that the length l can be written as l = 17.2 ± 0.1 cm

And breadth b can be written as b = 10.1 ± 0.1 cm

= 10.1 cm ± 1 %

(2) If a set of experimental data is specified to n significant figures, a result gained by combining the data will also be valid to n significant figures.

(3) The relative error of a value of number specified to significant figures depends not only on n but on the number itself too.

### Dimensions of Physical Quantities

The nature of all physical quantities is described by its dimensions. All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental quantities or base quantities. We can call these base quantities as the seven dimensions of the physical world, which are represented in square brackets [ ]. So , length of dimension [L], , time [T], mass [M], electric current [A], thermodynamic temperature [K], luminous intensity [cd], and amount of substance [mol].

### Dimensional Formulae and Dimensional Equations

The expression which shows how and which of the base quantities represent the dimensions of a physical quantity are known as the dimensional formula of the given physical quantity. For example, the dimensional formula of the volume is [M° L3 T°], and that of speed or velocity is [M° L T-1]. Similarly,  [M L–3 T°] that of mass density and  [M° L T–2] is the dimensional formula of acceleration.

An equation which is obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. So, the dimensional equations are the equations, which represent the dimensions of a physical quantity in terms of the base quantities.

### Dimensional Analysis and Its Applications

The recognition of concepts of dimensions, which guide the description of physical behaviour is of basic importance as only those physical quantities can be added or subtracted which have the similar dimensions. A thorough understanding of dimensional analysis helps you in deducing certain relations among different physical quantities and checking the derivation, accuracy and dimensional consistency or homogeneity of various mathematical expressions.

### Checking the Dimensional Consistency of Equations

if an equation fails this consistency test, it is proved wrong, but if it passes, it is not proved right. Thus, a dimensionally correct equation need not be actually an exact (correct) equation, but a dimensionally wrong (incorrect) or inconsistent equation must be wrong.

## Benefits of the Class 11 Physics Chapter 1 Solution

The benefits of using the NCERT Solutions for Class 11 Physics Chapter 1 are –

1. Completely solved answers for all the questions given in the NCERT textbook are freely available in PDF format.

2. Simple and easy-to-understand language is used to make learning fun for you.

3. Our Subject teacher experts prepare the solutions after conducting vast research on each concept.

4. The solutions not only help you with your exam preparation but also for various competitive exams like JEE, NEET, etc.

5. PDF format of solutions is available in chapter-wise and exercise-wise formats to help students learn the concepts in a better way.

#### Frequently Asked Questions

Question 1 : What are the topics in chapter 1 in physics class 11th?

Answer : Following are the topics in chapter 1 physics class 11th

1.1 Introduction

1.2 The International System of Units

1.3 Significant figure

1.3.1 Measurement of Length

1.3.2 Rounding off the uncertain digits

1.3.3 Rules for determining the uncertainty in the result of Arithmetic calculation

1.4 Dimensions of Physical Quantities

1.5 Dimensional Formulae and Dimensional Equations

1.6 Dimensional Analysis and Its Applications

1.6.1 Checking the Dimensional Consistency of Equations

1.6.2 Deducing Relation among the physical quantities

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