NCERT Solutions Class 11 Physics Chapter 1 Units and Measurements

The Class 11 Physics NCERT Solutions Chapter 1 Units and Measurements will help students prepare for Boards, JEE Main, JEE Advanced, NEET, CUET and NDA in 2026-27. Every back-exercise question is solved with full working, so students can check each unit conversion, dimensional check, significant-figure count, and error calculation step by step.

This is the first chapter of the NCERT textbook, and it sets up the measurement skills used across all later chapters.

• CBSE Weightage: 4 to 6 marks, usually one short answer plus one numerical on dimensions or errors.
• Questions solved: all Exercise 1.1 onward, covering unit conversion, dimensional analysis, significant figures, and error analysis.
• Key formulas: percentage error, combination of errors, dimensional formulae of common quantities.

Each solution in this Class 11 Physics NCERT Solutions Chapter 1 Units and Measurements compilation is curated by subject experts, based on the 2026-27 NCERT textbook, and refined against the last five years of CBSE Board, JEE Main and NEET papers.

SI Base Units and the International System of Units

Measurement starts with a fixed set of standards. The chapter builds the whole subject on the seven SI base units. Every other unit in physics, called a derived unit, is made by combining these seven. Getting the base units right is the first step in solving any numerical in this chapter.

The NCERT questions here ask students to write a physical quantity in SI units and to convert between systems. A common task is changing a value from the CGS system to the SI system, or the reverse. Always convert every quantity to SI before you substitute numbers. The solved answers show the conversion factor on its own line, so no step is skipped. This habit prevents the most frequent mark loss in the chapter.

Dimensional Analysis and the Principle of Homogeneity

The dimensional formula of a quantity shows how it is built from mass (M), length (L), and time (T). For example, force has the dimensional formula [M L T^-2] and energy has [M L² T^-2]. The chapter uses these formulas for three jobs, and the NCERT solutions cover all three.

• Checking an equation: by the principle of homogeneity, every term on both sides must have the same dimensions.
• Deriving a relation: guess how one quantity depends on others, then match dimensions to find the powers.
• Converting units: use the dimensional formula to move a value from one system to another.

Several NCERT numericals, such as Exercise 1.6, ask students to check whether a given formula is dimensionally correct. The method is simple: write the dimensions of each term and compare. A dimensionally correct equation may still be physically wrong, but a dimensionally wrong equation is always wrong. The solutions state this limit clearly so students do not over-trust the method in the exam.

Significant Figures and Rounding Rules in Measurement

Significant figures are the digits in a measured value that carry real meaning. They tell the reader how precise a measurement is. The chapter gives a fixed set of rules, and the NCERT answers apply them to every calculation so the final answer is never written with false precision.

• All non-zero digits are significant.
• Zeros between non-zero digits are significant.
• Leading zeros are not significant; trailing zeros after a decimal point are significant.
• In multiplication or division, the answer keeps as many significant figures as the least precise value.
• In addition or subtraction, the answer keeps as many decimal places as the least precise value.

Questions such as Exercise 1.9 and the rounding problems test these rules directly. Round only at the last step, never in the middle of a calculation, because early rounding builds up error. The Class 11 Physics NCERT Solutions Chapter 1 Units and Measurements show the full-precision working first and round the boxed answer at the end, exactly as CBSE expects.

Error Analysis: Absolute, Relative and Percentage Error

No measurement is exact, so the chapter teaches students to state the error in every result. Three ideas do most of the work, and the NCERT solutions use them in every error numerical.

• Absolute error: the size of the difference between a measured value and the true value, written as Δa.
• Relative error: the absolute error divided by the true value, Δa/a.
• Percentage error: the relative error written as a percent, (Δa/a) × 100%.

When two measured quantities are combined, the errors combine by fixed rules. The table below is the one students use most in the exam.

Numericals like Exercise 1.10 give the readings of a physical quantity and ask for the percentage error in a result. For a quantity raised to a power, multiply its relative error by that power before adding. This single step is the most common slip in the chapter, so the solved answers show it on a separate line.

Measurement of Length, Mass, Time and Order of Magnitude

The chapter also covers how very large and very small quantities are measured. These methods appear in short-answer questions and in fill-in-the-blank exercises like Exercise 1.1. The NCERT solutions explain each method with the reasoning a student can reproduce in the exam.

• Length: the parallax method measures the distance to a far object, such as a star, using the shift in its apparent position from two points.
• Mass: large masses use a physical balance; atomic masses use the unified atomic mass unit (u).
• Time: an atomic clock, based on the vibration of a caesium atom, gives the modern standard of the second.

The order of magnitude of a number is the power of ten nearest to it. Writing a value in this form lets students compare sizes quickly, from the radius of an atom to the distance of a galaxy. To find the order of magnitude, write the number in scientific notation and round the coefficient to the nearest power of ten. This tool makes estimation questions fast and is a favourite in objective papers for JEE Main and NEET.

Exercise-wise Breakdown for Class 11 Physics Chapter 1 Units and Measurements

The NCERT back-exercise splits into clear groups. Use this map to plan which answers to practise first for the 2026-27 boards. Every group links to the full solved set.

Solving the groups in this order builds the skills in the same sequence the chapter teaches them. Start with unit conversion, then dimensions, then errors, because each group uses the one before it.

Common Mistakes Students Make in the Units and Measurements Chapter

These slips happen while writing or calculating the answer, not because the concept is unclear. Each one costs 1 to 3 marks in the CBSE paper, so the solved answers point them out at the exact step.

Student Feedback on the Units and Measurements Chapter

Practice Questions for Class 11 Physics Chapter 1 Units and Measurements

Once the solved answers are clear, test yourself on the full question set. The practice page has every NCERT question with a step-by-step Solution and an Expert Solution behind a click.

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