Units and Measurement

Unit and Measurement is the very first chapter of the class 11 curriculum. This chapter is the foundation of physics in which we study about the unit of physical quantity and measurement. Natural laws are explained in a unique way in Physics. This explanation includes a quantitative description, comparison, and measurement of various Physical Quantities. We must first create a standard unit of measurement before we can measure or compare a physical quantity. The weight of a lion is more than that of a goat. However, how many times have you done that before? Prashant towers over Robin, but by how much? To answer such questions, we'll need to build a unit. We can calculate that the lion's weight is 200 times that of a goat if the mass is the unit. If we take the length as a unit, we can easily conclude that Robin is 2 times the unit taller than Prashant.

We need a universally acquired standard called a Unit to measure any quantity or compare two quantities. Any physical quantity is measured using a number and a specific unit.

Topics of Unit and Measurement

Given below is the complete list of topics for the chapter unit and measurement class 11, which starts from the introduction and ends with the exercise.

1. Introduction

Physics relies on measurements to describe natural phenomena quantitatively. Understanding Fundamental And Derived Quantities And Units is essential for precise scientific studies.

2. The International System of Units (SI)

The System Of Units provides a standardized set of units for measuring physical quantities, ensuring consistency and clarity in scientific communication globally.

• Practical Units

3. Measurement of Length

Unit of Length is measured using instruments like rulers, Vernier callipers, and micrometres, depending on the precision required. Advanced methods include laser techniques and astronomical measurements.

4. Measurement of Mass

Mass is measured using balances like beam balances and electronic balances. For microscopic entities, techniques like mass spectrometry are employed.

• Unit of Mass
• Difference Between Pound and Kilogram

5. Measurement of Time

Time measurement uses devices ranging from mechanical clocks to atomic clocks, ensuring extreme precision for both everyday use and scientific research.

6. Accuracy, Precision of Instruments, and Errors in Measurement

In Accuracy Precision Measurement accuracy refers to how close a measurement is to the true value, while precision indicates repeatability. Errors arise due to limitations of instruments or human factors.

• Errors Of Measurements

7. Significant Figures

Significant figures in a measurement include all known digits plus one estimated digit, representing the precision of a measured quantity.

• Error Significant Figures Rounding Off

8. Dimensions of Physical Quantities

Dimensions Of Physical Quantities express the dependence of a physical quantity on the basic quantities (mass, length, time, etc.) and are helpful in analyzing equations.

9. Dimensional Formulae and Dimensional Equations

A dimensional formula represents a physical quantity in terms of basic dimensions, while dimensional equations relate multiple quantities through Dimensional Analysis.

• Dimensionless Quantities

10. Dimensional Analysis and Its Applications

Dimensional analysis is used to check the correctness of equations, derive relations among quantities, and convert units across different systems.

• Applications Of Dimensional Analysis

Note: Approximately 4% of questions come from the topic in JEE Mains and NEET.

Important Terms and Formula of Unit and Measurement

Unit

The measurement of a physical quantity involves comparing it with a standard reference, which is an internationally accepted unit.

• A comprehensive set of these units, including both base and derived units, is referred to as a system of units.
• Traditional systems of units include CGS, FPS, and MKS systems:
  • In the CGS system, the fundamental units are the centimetre (cm), gram (g), and second (s).
  • In the FPS system, the fundamental units are the foot (ft), pound (lb), and second (s).
  • In the MKS system, the fundamental units are the meter (m), kilogram (kg), and second (s).

SI System of Units (International System of Units)

• Currently accepted internationally for measurement is the SI system of units.
• Some Rules to be followed with standard symbols

1. Conversion within the system is easy because it is a decimal system unit.

2. It has 7 base units and 2 supplementary units

Measurement of Length

• Large distances are measured using the parallax method.
• The parallax angle is given by:

Parallax angle $=\frac{\text { Basis }}{\text { Distance }}$

• Conversion Factor

$1^{\circ}=1.745 \times 10^{-2} \mathrm{rad}$ and $1^{\prime \prime}=4.85 \times 10^{-6} \mathrm{rad}$

• Very small distances, such as the size of a molecule, are measured using instruments like:

1. Optical microscope
2. Electron microscope
3. Tunneling microscope

Important Distance Units and Values:

• Astronomical Unit (AU):

$
1 \mathrm{AU}=1.496 \times 10^{11} \mathrm{~m}
$

• Light-year (ly):

$
1 \mathrm{ly}=9.46 \times 10^{15} \mathrm{~m}
$

• Parsec:

$
1 \text { parsec }=3.08 \times 10^{16} \mathrm{~m}
$
Reference Distance and Size

- Size of a proton:

$
10^{-15} \mathrm{~m}
$

- Radius of Earth:

$
10^7 \mathrm{~m}
$

- Distance to the boundary of the observable universe:

$
10^{26} \mathrm{~m}
$

Error in Measurement

$\begin{aligned} & \text { Absolute error }=\frac{\Sigma\left(\left|a_j-a_{\text {mean }}\right|\right)}{n} \\ & \text { Relative error }=\frac{\Delta a_{\text {mean }}}{a_{\text {mean }}} \\ & \text { Percentage error }=\frac{\Delta a_{\text {mean }}}{a_{\text {mean }}} \times 100\end{aligned}$

Combination of error

$
\begin{aligned}
&\text { Sum and difference }\\
&\Delta Z=\Delta A+\Delta B
\end{aligned}
$

$
\begin{aligned}
&\text { Product or Quotient }\\
&\frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}
\end{aligned}
$

$$
\text { If } X=\frac{A^s B^b}{C^6} \text { then } \% \frac{\Delta X}{X}=a\left(\% \frac{\Delta A}{A}\right)+b\left(\% \frac{\Delta B}{B}\right)+c\left(\% \frac{\Delta C}{C}\right)
$$

Dimensional Formulae and SI Units of Various Physical Quantity

\[
\begin{array}{|c|c|c|c|c|}
\hline
\textbf{S. No.} & \textbf{Physical Quantity} & \textbf{Relation with Other Quantities} & \textbf{Dimensional Formula} & \textbf{SI Unit} \\
\hline
1 & \text{Gravitational constant } G & \frac{\text{Force} \times (\text{Distance})^2}{\text{Mass} \times \text{Mass}} & [M^{-1}L^3T^{-2}] & \mathrm{N \, m^2 \, kg^{-2}} \\
\hline
2 & \text{Stress} & \frac{\text{Force}}{\text{Area}} & [ML^{-1}T^{-2}] & \mathrm{N \, m^{-2}} \\
\hline
3 & \text{Coefficient of Elasticity} & \frac{\text{Stress}}{\text{Strain}} & [ML^{-1}T^{-2}] & \mathrm{N \, m^{-2}} \\
\hline
4 & \text{Surface Tension} & \frac{\text{Force}}{\text{Length}} & [MT^{-2}] & \mathrm{N \, m^{-1}} \\
\hline
5 & \text{Coefficient of Viscosity} & \frac{\text{Force} \times \text{Distance}}{\text{Area} \times \text{Velocity}} & [ML^{-1}T^{-1}] & \mathrm{N \, m^{-2}}, \, \mathrm{Pa}, \, \mathrm{decaPoise} \\
\hline
6 & \text{Planck's Constant } h & \frac{\text{Energy}}{\text{Frequency}} & [ML^2T^{-1}] & \mathrm{J \, s} \\
\hline
7 & \text{Velocity Gradient} & \frac{\text{Velocity}}{\text{Distance}} & [T^{-1}] & \mathrm{s^{-1}} \\
\hline
8 & \text{Pressure Gradient} & \frac{\text{Pressure}}{\text{Distance}} & [ML^{-2}T^{-2}] & \mathrm{Pa \, m^{-1}} \\
\hline
\end{array}
\]

Unit and Measurement in Different Exams

Unit and measurement are not only important for board exams but also for different exam which are given in the table below along with preparation tips and area in which student should focus.

Importance of Units and Measurement Class 11

The topic is crucial to understand since there will be no uniformity in measurement without a standard unit system. The only way to verify the correctness of any hypothesis is to use measurements. As a result, understanding Units and Measurements is critical because it deals with a comparison tool. Though it is a part of the school curriculum, namely the Physics syllabus for class 11, it is used in our daily lives. A review of the subjects covered in the following class XI Physics chapter will give you an idea of what to expect.

NCERT Notes Subject Wise Link:

• NCERT notes Class 11 Maths
• NCERT notes Class 11 Physics
• NCERT notes Class 11 Chemistry
• NCERT notes Class 11 Biology