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

NCERT Notes for Class 11 Physics Chapter 1: Download PDF

The NCERT Notes for Class 11 Physics Chapter 1 Units and Measurements can also be downloaded in PDF format and revised probably and easily by students. These are well-organised notes that contain major formulas, solved examples, as well as important points which can be useful in exam preparation. The PDF format makes sure that you will have the ability to study anywhere at any time without inconvenience.

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Class 11 Physics Chapter 1 Units and Measurements Notes

The Units and Measurements Class 11 Notes simplify the way students learn the concepts of Units and Measurements in a simple and clear way. They state the principles of measurement, important figures, and dimensional analysis in a simplified manner. These NCERT Notes for Class 11 Physics Chapter 1 are prepared according to the syllabus of NCERT and are given in brief, easily revised points and this way the students can remember and understand the topics best.

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.

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 Quantities and Derived Units:

• 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.
• 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

The International 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

Supplementary Units

Practical Units

Practical units of length:

1 kilometer(km) = 10³m

1 centimeter(cm) = 10⁻²m

1 millimetre (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).

Practical units 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 the mass of an atom of the carbon-12 isotope.

1u = 1.66 ✕ 10⁻²⁷kg

Practical units of time:

1 millisecond (ms) = 10⁻³s

1 microsecond (*s) = 10⁻⁶s

1 nanosecond (ns) = 10⁻⁹s

1 picosecond (ps) = 10⁻¹²s

A shake is the unit of time used in microscopic physics

1 shake = 10⁻⁸s

Significant Figures:-

The figures of a number that expresses a magnitude to a specified degree of accuracy.

1) All non-zero digits are significant

For example-

42.3 -Three significant figures

238.4 -four significant figures

33.123 -five significant figures

2) Zero becomes a significant figure if it exists between two non-zero digits

For example-

2.09 - Three significant figures

8.206 -four significant figures

6.002 -four significant figures

3) For leading zero(s), the zero(s) to the left of the first non-zero digits are not significant.

For example-

0.543 - three significant figures

0.069 - two significant figures

0.002 -one significant figure

4) The trailing zero(s) in a number without a decimal point are not significant. But if the decimal point is there, then they will be counted in significant figures.

For example-

4.330- four significant figures

433.00- five significant figures

343.000- six significant figures

5) Exponential digits in scientific notation are not significant.

For example- 1.32 X 10^-2 -three significant figures

• Rounding Off:-

Rounding off figures during calculation helps to make the calculation of big numbers easier. While rounding off measurements, we use the following rules by convention:

(1) If the digit to be dropped is less than 5, then the preceding digit is left unchanged.

Example: x=7.82 is rounded off to 7.8, again x=3.94 is rounded off to 3.9.

(2) If the digit to be dropped is more than 5, then the preceding digit is raised by one.

Example: x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded off to 12.8.

(3) If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.

Example: x = 16.351 is rounded off to 16.4, again x = 6.758 is rounded off to 6.8.

(4) If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is left unchanged if it is even.

Example: x = 3.250 becomes 3.2 on rounding off, again x = 12.650 becomes 12.6 on rounding off.

(5) If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one if it is odd.

Example: x = 3.750 is rounded off to 3.8, again x = 16.150 is rounded off to 16.2.

Significant Figures in Calculation:-

1. Rules for addition and subtraction-

The result of an addition or subtraction in the number having different precisions should be reported to the same number of decimal places as are present in the number having the least number of decimal places.

For example:-

1) 33.3+3.11+0.313=36.723, but here the answer should be reported to one decimal place as the 33.3 has the least number of decimal places (i.e only one decimal place), therefore the final answer=36.7

2) 3.1421+0.241+0.09=3.4731 but here the answer should be reported to two decimal places as the 0.09 is having the least number of the decimal place(i.e two decimal places), therefore the final answer=3.47

2 Rules for multiplication and division-

The answer to a multiplication or division is rounded off to the same number of significant figures as is possessed by the least precise term used in the calculation:-

For example:-

1) 142.06 x 0.23=32.6738 but here the least precise term is 0.23 which has only two significant figures, so the answer will be 33.

Dimensions of Physical Quantities

All derived physical quantities can be expressed using the seven base quantities as discussed at the beginning of this chapter. Hence, these quantities are also referred to as the seven dimensions of the physical world. They are represented by using square brackets. Thus, the seven dimensions of the physical world are represented as follows.

[M] for mass
[L] for length
[T] for time
[A] for electric current
[K] for thermodynamic temperature
[cd] for luminous intensity
[mol] for amount of substance

The dependence of all other physical quantities on these base quantities can be expressed in terms of their dimensions.
For example, the speed v, of a moving object is given by the relation v= Distance Time
Therefore, the dimension of speed can be given as

[v]=[L][T^-1]=[LT⁻¹]

Thus, the dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity.

Dimensional Formulae and Dimensional Equations

The expression of a physical quantity in terms of its dimensions is called its dimensional formula. For example, the dimensional formula of force is [MLT⁻²] and that for acceleration is [M⁰LT⁻²]. Dimensional formula for density is [ML⁻³ T⁰].
The table given in the formulae chart at the end of this chapter gives the dimensional formulae for some physical quantities.
An equation which contains a physical quantity on one side and its dimensional formula on the other side is called the dimensional equation of that quantity. Dimensional equations for a few physical quantities are given below.
Speed [V]=[M⁰L⁻¹]
Area [A]=[M⁰L²T⁰]
Force [F]=[MLT⁻²] etc.
The physical quantities having the same derived units have the same dimensions.

Dimensional Analysis and Its Applications

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

1. 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 be n₁ and n₂ in two different systems and the corresponding units be u₁ and u₂.

   As we know, the measure of a physical quantity is constant, i.e., nu=constant.

   $
   n_1\left[u_1\right]=n_2\left[u_2\right]
   $

   
   If the dimension of a quantity in one system is $\left[M_1^a L_1^b T_1^c\right]$ and in another system, dimension is $\left[M_2^a L_2^b T_2^c\right]$, then

   $
   n_2=n_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c
   $

Using this formula, we can convert the numerical value of a physical quantity from one system of units to another system.

2. To check the correctness of an equation:

• It is based on the principle of homogeneity. According to this principle, both sides of an equation must be the same.

L.H.S = R.H.S

• It also states that only those physical quantities can be added or subtracted which have the same dimensions.
• If the dimension of each term on both sides is the same, then the equation is dimensionally correct; otherwise not.
• A dimensionally correct equation may or may not be physically correct.

Limitations:

• Cannot give numerical constants (like 1/2,π, etc.).
• Not applicable to equations involving logarithms, trigonometric or exponential functions.
• Works only for dimensionally homogeneous equations.

Class 11 Physics Chapter 1 Units and Measurements: Previous Year Question and Answer

Q1:

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is:

(a) $164 \pm 3 \mathrm{~cm}^2$
(b) $163.62 \pm 2.6 \mathrm{~cm}^2$
(c) $163.6 \pm 2.6 \mathrm{~cm}^2$
(d) $163.62 \pm 3 \mathrm{~cm}^2$${\mathrm{}}^{}$

Answer:

Given :

$
\begin{gathered}
l=16.2 \mathrm{~cm}, \text { and } \Delta l=0.1 \\
b=10.1 \mathrm{~cm}, \Delta b=0.1 \\
l=16.1 \pm 0.1 \text { and } b=10.1 \pm 0.1
\end{gathered}
$

$
\begin{array}{lc}
\text { Now, area (a) } \quad & =l \times b \\
= & 16.2 \times 10.1 \\
= & 163.62 \mathrm{~cm}^2 \\
= & 164 \mathrm{~cm}^2
\end{array}
$

(by rounding off the answer of the area in 3 significant numbers)

$
\begin{gathered}
\Delta \frac{A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b} \\
=\frac{0.1}{16.2}+\frac{0.1}{10.1} \\
\frac{\Delta A}{164}=\left(\frac{10.1 \times 0.1+16.2 \times 0.1}{16.2 \times 10.1}\right)
\end{gathered}
$

Thus, $\Delta A=2.64 \mathrm{~cm}^2$
We get $\Delta A=3 \mathrm{~cm}^2$
(by rounding off the answer of $\Delta A$ in 1 significant number)
Thus, $\Delta A=(164 \pm 3) \mathrm{cm}^2$
Hence, the correct answer is option (a).

Q2:

Which of the following are not units of time?

a) second

b) parsec

c) year

d) light year

Answer:

Parsec and Light year
Explanation: Parsec & Light year are units to measure distance, while second \& Year are units to measure time.

Hence, the answers are options (b) and (d).

Q3:

If momentum (P), area (A), and time (T) are taken to be fundamental quantities, then energy has the dimensional formula

(a) $\left(P^1 A^{-1} T^1\right)$
(b) $\left(P^2 A^1 T^1\right)$
(c) $\left(P^1 A^{-1 / 2} T^1\right)$
(d) $\left(P^1 A^{1 / 2} T^{-1}\right)$

Answer:
Explanation: Let us consider $\left[P^a A^b T^c\right]$ the formula for energy for fundamental quantities $\mathrm{P}, \mathrm{A}, \mathrm{~T}$. Thus, the dimensional formula of-

$
\begin{gathered}
\text { Energy }(\mathrm{E})=\left[P^a A^b T^c\right] \\
\text { Momentum }(\mathrm{P})=\left[M L T^{-1}\right] \\
\operatorname{Area}(\mathrm{A})=\left[L^2\right] \\
\operatorname{Time}(\mathrm{T})=\left[T^1\right]
\end{gathered}
$

Now, $E=f . s$
Thus, $\left[P^1 A^{1 / 2} T^{-1}\right]$ is the dimensional formula of energy.
Hence, the answer is option (d).

Importance of Units and Measurements Class 11 Notes

Units and Measurements Class 11 Notes are very important because it is the basics of learning Physics. These notes make the important concepts such as SI units, significant figures, and dimensional analysis easy to comprehend and use. They are explained briefly with solved examples, and assist students to develop accuracy, build fundamentals, and also prepare for the board exams, as it is in JEE/NEET.

Origin of Physics Concepts

• All physics calculations are based on Units and measurements. Without a standard unit system, it is impossible to compare such physical entities as length, mass, and time.

Precision with Numerical Problems

• The notes Class 11 Physics Units and Measurement are used to assist students in solving numerical questions with accurate precision, which is very important in CBSE board exams, JEE and NEET.

Learning SI Units and Conversions

• These notes describe the International System of Units (SI units), dimensional formula, and unit conversions, which are important to higher physics and engineering exams and problem-solving.

Significant Figures and Analysis of Error.

• This chapter also emphasises the importance of important figures, errors and approximations in real-life measurements, and so the students are more assured in their approach to experiments and questions in the lab.

Connection of Theory and Experiments

• Units and Measurement provides an intermediate between theoretical physics and the actual experiment since it instructs the correct approach to recording, calculating, and analysing the physical data.

Boosts Exam Preparation

• Properly organised NCERT Class 11 Physics Notes on Units and Measurement are handy both in last-minute revision and in enabling students to have a higher score in the exams.

Competitive Exam Relevance

• The chapter is commonly referred to in JEE Main, NEET and Olympiad tests. The ability to master these notes will enhance the speed and accuracy of a student in solving problems during competitive exams.

How to Use NCERT Class 11 Physics Chapter 1 Notes Effectively?

The NCERT Notes for Class 11 Physics Chapter 1 are a powerful tool to build a strong base in physics. Using them effectively helps students revise faster, avoid confusion, and improve accuracy in problem-solving. Here’s how to make the most of these notes:

Quick Revision: After going through the textbook in the definitions, formulae, and other important concepts can be remembered easily by reading the booknotes.

Highlight Key Points: Mark important formulas, SI units, and dimensional relations for last-minute exam prep.

Practice with Examples: Practice the solved examples in the notes to enable the strengthening of the numerical-solving.

Error Analysis Focus: You should focus on areas such as errors and significant figures that are also common in the boards and JEE/NEET.

Daily Short Review: Revise a small portion daily so concepts stay fresh without feeling overwhelming.

Link with Real Life: Relate measurement techniques and units to practical examples (like GPS, speedometers, lab instruments) for better retention.

Self-Testing: To test your understanding, close the notes and see how much of the formulae you should know or how many problems you should be able to solve on your own.

NCERT Class 11 Notes Chapter-Wise

The NCERT Class 11 Notes (Chapter-wise) provide simplified explanations, key formulas, and important concepts for every chapter of Physics, Chemistry, Biology, and Mathematics. These notes help students in quick revision, last-minute preparation, and building strong fundamentals for school exams as well as competitive exams like JEE and NEET.

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