NCERT Class 11 Physics Chapter 2 Notes Units and Measurement - Download PDF

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NCERT Class 11 Physics Chapter 2 Notes Units and Measurement - Download PDF

Edited By Vishal kumar | Updated on Jan 30, 2024 03:02 PM IST

Revision Notes for CBSE Class 11 Physics Chapter 2 Units and Measurements - Free PDF Download

Welcome to Units and Measurements class 11 notes, a valuable resource for developing a solid understanding of fundamental physics principles. These class 11 physics chapter 2 notes, written by Careers360 subject matter experts, delve into key concepts, theories, and formulas, allowing for a thorough understanding of the chapter's core principles. Whether you aim for academic excellence or are preparing for competitive exams, these Units and Measurements notes class 11 will help you enhance your learning experience, resolve questions, and solidify key concepts.

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These CBSE class 11 physics ch 2 notes, written by Careers360's subject experts in an understandable language and in a systematic format, allow for efficient revision. Also, the availability of the ch 2 physics class 11 notes in PDF format, which is free, allows students to use them whenever and wherever they want.

Physical Quantity

A physical quantity is something we can measure, and it helps us understand and describe different things that happen in the world through rules. Examples of physical quantities are length, mass, time, and force.

Physical quantity (Q) = Magnitude × Unit = n × u

Types of Physical Quantity

1. Ratio (Numerical Value Only): A physical quantity has no unit when it is a ratio of two similar quantities.
Example: Relative density, refractive index, and strain are a few examples.
2. Scalar (Only Magnitude): Quantities such as length, time, work, and energy have no direction. Without specifying a direction, the magnitude can be negative, indicating a negative numerical value. Ordinary addition and subtraction laws apply to scalar quantities.
3. Vector (Magnitude and Direction): Vector quantities include displacement, velocity, acceleration, and force. Vector laws of addition, as opposed to ordinary addition laws, govern vectors.

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Fundamental Quantities and Fundamental Units

The units of quantities ( length, mass, and time) are independent of one another; no one can be changed or related to any other unit. These quantities are called fundamental quantities and their units are called fundamental units.

• Seven fundamental quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminescent intensity.

Derived Unit

Units of physical quantities derived from the seven fundamental quantities are termed "derived units." Examples include:

Volume = length ✕ breadth ✕ height = m ✕ m ✕ m = m³

Density = mass/volume = kgm⁻³

System of Units

A unit system is a comprehensive set of units that includes both fundamental and derived units for various physical quantities. Typical systems include:

• CGS system: The Gaussian system of units, also known as the CGS system, designates length, mass, and time as fundamental quantities, with corresponding units of centimetre (cm), gramme (g), and second (s).

• FPS system: Foot, pound, and second are the units of length, mass, and time in the FPS system, respectively. In this system, force is a derived quantity with the poundal as its unit.

• MKS system:- The Giorgi system, also known as the MKS system, designates length, mass, and time as fundamental quantities, with corresponding fundamental units of length (m), mass (kg), and time (s).

• S.I. system:- It is known as the International System of Units, which was accepted in 1960 and it is an extended system of units that is used throughout physics. This system has seven fundamental quantities. The quantities and units are listed in the table below.

Basic Units

 Name of Quantity Name of unit Symbol Length Meter m Mass Kilogram kg Time Second s Electric current Ampere A Thermodynamic temperature Kelvin K Amount of substance Mole mol Luminous intensity Candela cd

Supplementary Units

Some Supplementary Fundamental units

• Meter: It is the fundamental unit of length

1 kilometer(km) = 10³m

1 centimeter(cm) = 10⁻²m

1 millimeter (mm) = 10⁻³m

1 micron(μ) = 10⁻⁶m

1 nanometer (nm) = 10⁻⁹m

1 Angstrom (Å) = 10⁻¹ºm

1 fermometer = 1 fermi (fm) = 10⁻¹⁵m

• Astronomical unit (AU): 1AU is the average distance of the sun from the Earth, commonly used for measuring astronomical distances.

1 AU = 1.496 ✕ 10¹¹m ≅ 1.5 ✕ 10¹¹m

• Light Year (ly): 1 light-year is the distance travelled by light in one year.

1 light-year = (3 ✕ 10⁸ms⁻¹) ✕ (365 ✕24✕60✕60)s = 9.46 ✕ 10¹⁵m

• Parallactic second or parsec(pc): The parallactic second (pc): 1 parsec is the distance between the average radius of the Earth's orbit around the Sun and an angle of 1" (second of arc).

• Kilogram: It is the unit of mass.

1 metric ton = 10³kg

1 quintal = 10²kg

1 gram = 10⁻³kg

1miligram = 10⁻³g = 10⁻⁶kg

To measure the mass of an atom or molecule we use a unified atomic mass unit(u) defined as 1/12th mass of an atom of the carbon-12 isotope.

1u = 1.66 ✕ 10⁻²⁷kg

• Second(s): It is the unit of time.

1 millisecond (ms) = 10⁻³s

1 microsecond (*s) = 10⁻⁶s

1 nanosecond (ns) = 10⁻⁹s

1 picosecond (ps) = 10⁻¹²s

Shake is the unit of time used in microscopic physics

1 shake = 10⁻⁸s

Significant Figures

Significant figures in a physical quantity's measured value indicate the number of digits in which we have confidence. The greater the number of significant figures obtained in a measurement, the greater the measurement's accuracy. The opposite is also true.

When counting the number of significant figures in a given measured quantity, the following rules apply.

(1) Non-zero digits: A number's non-zero digits are all considered significant.

For example, 41.3 contains three significant figures, 147.6 contains four significant figures, and 12.123 contains five significant figures.

(2) Between non-zero digits, a zero: Significant is a zero between two non-zero digits.

For example, 5.03 contains three significant figures, 5.404 contains four significant figures, and 6.004 contains four significant figures.

(3) Leading zeros: Leading zeros (zeroes to the left of the first non-zero digit) are ignored.

For example, the number 0.583 has three significant figures, the number 0.045 has two significant figures, and the number 0.003 has one significant figure.

(4) Trailing zeros: Trailing zeros are considered significant (zeroes to the right of the last non-zero digit).

For example, 4.250 has four significant figures, 434.00 has five significant figures, and 243.000 has six significant figures.

(5) Exponential notation: The numerical portion of exponential notation indicates the number of significant figures.

For example, 1.32 10*10-2 has three significant figures, while 1.32*104 has three significant figures.

Rounding Off

When rounding off measurements, the following rules are followed:

• If the digit to be dropped is less than 5, the preceding digit is not affected.

For example, 7.82 is rounded to 7.8, and 3.94 is rounded to 3.9.

• If the digit to be dropped is greater than 5, the digit before it is increased by one.

For example, 6.87 is rounded to 6.9, and 12.78 is rounded to 12.8.

• If the digit to be dropped is 5 followed by a non-zero digit, the preceding digit is increased by one.

For example, 16.351 is rounded to 16.4, and 6.758 is rounded to 6.8.

• If the dropped digit is 5 or 5 followed by zeros and the preceding digit is even, it is dropped.

For example, 3.250 becomes 3.2, and 12.650 becomes 12.6.

• If the digit to be dropped is 5 or 5 followed by zeros and the preceding digit is odd, the digit to be dropped is increased by one.

For example, 3.750 is rounded to 3.8, and 16.150 is rounded to 16.2.

Errors of Measurement

The measuring process is essentially a comparison process. Despite our best efforts, the measured value of a quantity is always slightly different from its true value. This difference in the true value of a quantity is referred to as measurement error.

(1) Absolute error: Absolute error is the magnitude of the difference between the true value of the measured quantity and the individual measured value.

Assume that a physical quantity has n measurements. Let a1, a2, a3,... a be the measured value. These values' arithmetic mean is

If the true value of a quantity is unknown, it is usually assumed to be am. Absolute errors in the measured values of the quantity are, by definition,

The absolute errors can be positive in some cases and negative in others.

(2) Mean absolute error: It is the arithmetic mean of the magnitudes of absolute errors in all of the quantity's measurements.

(3) Relative Error or Fractional Error: The ratio of the mean absolute error to the true value of the measured quantity is known as relative or fractional error.

==mean absolute error/mean value

(4) Percentage Error: If the fractional error is multiplied by 100, it is known as a percentage error.

Propagation of Errors

(1) Error in sum of the quantities: Suppose x = a + b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the sum of a and b.

The maximum absolute error in x is Δx = ±(Δa+Δb)

• Percentage error in the value of x is

(2) Error in difference of the quantities: Suppose x = a – b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the difference of a and b.

The maximum absolute error in x is Δx = ±(Δa+Δb)

• Percentage error in the value of x is

(3) Error in product of quantities : Suppose x = a * b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the product of a and b.

The maximum fractional error in x is

• Percentage error in the value of x = (percentage error in a) + (percentage error in b)

(4) Error in division of quantities : Suppose x=a/b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the division of a and b.

The maximum fractional error in x is

• Percentage error in the value of x = (percentage error in a) + (percentage error in b)

(5) Error in quantity raised to some power: Let x= an/bm

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x

The maximum fractional error in x is

• The percentage error in the value of x = n (the percentage error in the value of a) + m (the percentage error in the value of b).

Dimensional Analysis

The dimensions of a physical quantity are calculated by raising the fundamental units to the powers that are needed to derive its derived units.

The length, mass, and time are denoted by [L], [M], and [T] respectively.

Uses of Dimensional Equations

• To convert units of one system into units of another system: The product of a physical quantity's numerical value and its corresponding unit is a constant. Let the numerical value of a physical quantity p are n₁ and n₂ in two different systems and the corresponding units are u₁ and u₂, then

If the dimensions of the physical quantity are a in mass, b in length, and c in time, then its dimensional formula will be . If the fundamental units in one system are M₁, L₁, and T₁

Similarly, if the fundamental units in the second system are M₂, L₂, and T₂, then

According to eqn (i), we have

Using this formula we can convert the numerical value of a physical quantity from one system of units into the other system.

• To check the correctness of an equation: All terms on both sides of a physical equation must have the same dimensions. This is known as the dimension homogeneity principle.Both sides are the same.

• To establish the relationship among various physical quantities: If we know the factors on which a given physical quantity may possibly depend then, using dimensions, we can find a formula relating the quantity with those factors.

How to Use Units and Measurements Notes Class 11 Effectively

• Actively read: Don't just read the Units and Measurements class 11 notes passively; actively engage with the content. Take notes, highlight key points, and ask yourself questions as you read.
• Create a Study Plan: Create a study schedule that includes regular study time for units and measurements. The key to mastering the concepts is consistency.
• First, grasp the fundamental concepts: Before moving on to more complex topics, ensure a solid understanding of fundamental concepts such as SI units, conversion factors, significant figures, and dimensional analysis.
• Regular practice: Solve problems involving unit conversions, significant figures, and dimensional analysis. The more you practise, the more comfortable you will be applying these concepts.
• Use Supplemental Resources: To gain different perspectives on the concepts, supplement your ch 2 physics class 11 notes with other resources such as textbooks, online tutorials, or videos. This can help you understand more.
• Create Flashcards: Make flashcards of CBSE class 11 physics ch 2 notes for important terms, formulas, and rules. Use them for quick reviews and self-evaluation. Regularly quiz yourself to reinforce memory.
• Review and Reflect: Review what you've learned and reflect on your progress on a regular basis. Determine which areas require additional attention and revisit those topics.

Significance of NCERT Class 11 Physics Chapter 2 Notes

Units and Measurement NCERT Class 11 chapter 2 notes are really helpful as it helps you to get a brief of the chapter as well, as it is a more convenient way to recognize things more precisely. Also, this NCERT Class 11 Physics chapter 2 notes are used in covering each and every highlight of the chapter. NCERT Class 11 Physics chapter 2 notes guide you on the right path to just stick on it and to achieve a perfectly good score in the CBSE board examination. NCERT Class 11 Physics chapter 2 notes can be helpful in offline.

NCERT Class 12 Notes Chapter-Wise

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Subject Wise NCERT Solutions

 NCERT Books for Class 11 NCERT Syllabus for Class 11

1. Is physics class 12 chapter 2 notes pdf important for JEE?

Yes, Physics Class 12 Chapter 2 notes in PDF format are essential for JEE preparation, offering a concise and targeted resource for effective revision and problem-solving strategies.

2. What are the main topics covered in units and measurement?

The main topics covered in Units and Measurements include introduction to measurement, units of measurement, accuracy, precision, significant figures, dimensional analysis, unit conversions, measurement of physical quantities, dimensional formulas and equations and dimensional analysis and its applications.

3. Define the accuracy from NCERT notes for Class 11 Physics chapter 2.

From the NCERT Class 11 Physics chapter 2 notes, Accuracy is defined as‘’  The degree to which an observed value happens to agree with the true value of a quantity (or the closeness of measured value to the true value) is referred to as accuracy".

4. What do you mean by precision?

The precision of an observed value which informs us at what resolution the quantity is measured. Thus, measured values that are really close to each other (and may or may not be close to the true value) are precise values.

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Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Reporter

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.

2 Jobs Available
Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.

2 Jobs Available
Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.

2 Jobs Available
Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.

4 Jobs Available

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.

4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
3 Jobs Available
Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.

2 Jobs Available