NCERT Solutions for Class 11 Physics Chapter 2 – Units and Measurements
Complete solutions, dimensional formulas, error analysis, significant figures, and free PDF for Chapter 2 Units and Measurements.
About Chapter 2 – Units and Measurements
Chapter 2, Units and Measurements, is one of the most practically important chapters in Class 11 Physics. Without a proper system of measurement, no scientific experiment or observation can be meaningfully communicated. This chapter introduces students to the International System of Units (SI), which standardises the measurement of physical quantities such as length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
Students learn about the distinction between fundamental (base) quantities and derived quantities, and how every physical quantity can be expressed in terms of a combination of base units. A core skill introduced here is dimensional analysis – a powerful tool for checking equations, deriving relations, and converting units. Understanding significant figures and the rules for rounding off results is essential for expressing measurements with appropriate precision.
The chapter also covers errors in measurement in detail, explaining the difference between systematic errors (which affect accuracy) and random errors (which affect precision). Students learn to calculate absolute error, relative error, percentage error, and how errors propagate through mathematical operations. This knowledge is indispensable for laboratory work and all of science. Mastery of this chapter ensures that students can confidently handle numerical problems across all future chapters of physics and chemistry. Practising all NCERT examples and exercise questions is strongly recommended for board examination success.
NCERT Solutions for Class 11 Physics Chapter 2 – Free PDF Download
NCERT Solutions – Chapter 2: Units and Measurements (All Exercises)
Download the complete solved PDF with all textbook exercises including numerical problems on dimensional analysis, error calculation, and unit conversion.
Important Formulas – Chapter 2: Units and Measurements
| Concept | Formula / Expression | Description |
|---|---|---|
| Absolute Error | Δa = |a_mean − aᵢ| | Magnitude of difference between individual reading and mean value |
| Mean Absolute Error | Δā = (Σ|Δaᵢ|) / n | Average of all absolute errors |
| Relative Error | δa = Δā / a_mean | Ratio of mean absolute error to mean value |
| Percentage Error | % error = (Δā / a_mean) × 100% | Relative error expressed as a percentage |
| Error in Sum/Difference | ΔZ = ΔA + ΔB | Errors add for both addition and subtraction |
| Error in Product/Quotient | ΔZ/Z = ΔA/A + ΔB/B | Relative errors add for multiplication and division |
| Error in Power | ΔZ/Z = n(ΔA/A) | For Z = Aⁿ, the relative error is multiplied by n |
| Dimensional Formula of Force | [F] = [MLT⁻²] | Derived from Newton's second law F = ma |
| Dimensional Formula of Energy | [E] = [ML²T⁻²] | Work = Force × displacement |
| Dimensional Formula of Pressure | [P] = [ML⁻¹T⁻²] | Pressure = Force / Area |
| Dimensional Formula of Power | [P] = [ML²T⁻³] | Power = Work / Time |
| Unit Conversion (SI) | n₁u₁ = n₂u₂ | Numerical value × unit = constant regardless of system |
Subtopics of Chapter 2 – Units and Measurements
2.1 Introduction to Measurement
Measurement is the process of comparing an unknown quantity with a standard. It requires both a number and a unit.
2.2 The International System of Units (SI)
SI has 7 base units: metre, kilogram, second, ampere, kelvin, mole, and candela. All other units are derived from these.
2.3 Measurement of Length
Covers methods from parallax for astronomical distances to optical microscopy for small lengths. Includes metre, light-year, and fermi.
2.4 Measurement of Mass and Time
Mass measured using balances; atomic mass unit defined. Time measured using atomic clocks (caesium standard, accurate to 10⁻¹³ s).
2.5 Accuracy, Precision, and Errors
Accuracy is closeness to true value; precision is reproducibility. Types of errors: systematic, random, and gross errors explained.
2.6 Significant Figures
Rules for counting significant figures and rounding off results. Arithmetic operations follow specific rules for significant figures.
2.7 Dimensions of Physical Quantities
Every physical quantity has a dimensional formula. Dimensions can be used to check correctness of equations and derive relations.
2.8 Dimensional Analysis and Applications
Used to verify formulas, convert units, and derive expressions. Limitations: dimensionless constants and trigonometric functions excluded.
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Quick Reference – Dimensional Formulas of Common Quantities
| Physical Quantity | SI Unit | Dimensional Formula |
|---|---|---|
| Velocity | m/s | [LT⁻¹] |
| Acceleration | m/s² | [LT⁻²] |
| Force | Newton (N) | [MLT⁻²] |
| Work / Energy | Joule (J) | [ML²T⁻²] |
| Power | Watt (W) | [ML²T⁻³] |
| Pressure | Pascal (Pa) | [ML⁻¹T⁻²] |
| Momentum | kg·m/s | [MLT⁻¹] |
| Angular Momentum | kg·m²/s | [ML²T⁻¹] |
| Electric Charge | Coulomb (C) | [AT] |
| Electric Potential | Volt (V) | [ML²T⁻³A⁻¹] |
| Resistance | Ohm (Ω) | [ML²T⁻³A⁻²] |
| Frequency | Hertz (Hz) | [T⁻¹] |
NCERT Solutions for Class 11 Physics Chapter 2: Units and Measurements – FAQs
SI units form the standard system of measurement used throughout physics. In this chapter, students learn fundamental units such as metre, kilogram, second, ampere, kelvin, mole, and candela. These units help maintain uniformity in scientific calculations and experiments. Most numerical questions in NCERT exercises require correct use of SI units before applying formulas. Students often lose marks by ignoring unit conversion. Understanding SI units also helps in higher chapters where derived units such as velocity, acceleration, force, and energy are used. A strong grasp of SI units makes problem-solving easier and improves accuracy in examinations.
Dimensional analysis is a method used to check whether a physical equation is correct. It compares the dimensions of quantities on both sides of an equation. In Class 11 Physics, this concept is important because many NCERT numerical problems involve deriving relationships between physical quantities. Dimensional analysis helps students identify errors in formulas and convert one system of units into another. It is also frequently asked in school exams and competitive entrance tests. By mastering dimensions of quantities like force, energy, momentum, and pressure, students can solve complex questions more confidently and accurately.
Significant figures represent the precision of a measured quantity. In this chapter, students learn rules for counting significant figures and performing calculations using them. Many NCERT questions involve measurements obtained from instruments, making precision important. A correct answer with the wrong number of significant figures may be considered inaccurate. Significant figures help avoid false precision in scientific measurements. Students should practice addition, subtraction, multiplication, and division rules involving significant figures. Understanding this topic improves calculation skills and helps present answers scientifically, which is essential for board examinations and competitive tests.
Measurement errors occur because no instrument can provide a perfectly accurate reading. The chapter discusses systematic errors, random errors, and least count errors. Students learn methods for reducing errors by taking repeated observations, using better instruments, and applying correction techniques. Questions based on percentage error and propagation of errors are common in examinations. Understanding measurement errors helps students appreciate the limitations of experiments and improves analytical thinking. Mastery of this topic also prepares students for practical work where accurate observations are required for obtaining reliable experimental results.
The least count is the smallest value that a measuring instrument can accurately measure. In NCERT exercises, students encounter instruments such as vernier calipers and screw gauges where least count plays a significant role. Knowing the least count helps determine measurement precision and estimate errors. Questions often involve calculating dimensions using instrument readings. Understanding least count also helps students interpret experimental data correctly. This concept develops practical skills and forms the basis of laboratory measurements. A clear understanding ensures greater accuracy while solving numerical problems and conducting experiments.




