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] |