CBSE · Class 11 · Physics · Chapter 2

Units and
Measurement

Complete chapter resources for CBSE Class 11 Physics — topic breakdown, SI units, dimensional analysis, error formulas, sample questions, previous year board questions, and instant AI question paper generation.

4Topics
6–8Board marks
8Sample questions
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Key Formulas — Chapter 2
  • Mean absolute error: Δa_mean = (Σ|Δa_i|) / n
  • Relative error: δa = Δa_mean / a_mean
  • Percentage error: = (Δa_mean / a_mean) × 100%
  • Error in product Z = AB: ΔZ/Z = ΔA/A + ΔB/B
  • Error in power Z = Aⁿ: ΔZ/Z = n · (ΔA/A)
  • Dimensions of velocity: [M⁰ L¹ T⁻¹]
Chapter Overview

What this chapter covers

Chapter 2 of NCERT Class 11 Physics establishes the language of measurement that underpins every other chapter in the syllabus. It introduces the International System of Units (SI) — the seven base units (metre, kilogram, second, ampere, kelvin, mole, candela) and the derived units built from them — along with the conventions for expressing very large and very small quantities using scientific notation and SI prefixes such as nano, micro, kilo, and mega.

A central skill developed in this chapter is dimensional analysis: expressing physical quantities as products of the base dimensions M (mass), L (length), and T (time). Dimensional analysis is used to verify the correctness of physics formulae, to derive relationships between physical quantities, and to convert units from one system to another. Students must also master significant figures — the rules for counting them in a measurement and rounding correctly when combining measurements through addition, subtraction, multiplication, or division.

The chapter closes with a rigorous treatment of errors in measurement. Students learn to calculate mean absolute error, relative (fractional) error, and percentage error from a set of repeated readings, and to propagate errors through arithmetic combinations of measured quantities. Board questions in this section often ask students to find the maximum percentage error in a derived quantity such as density, acceleration, or kinetic energy when the errors in the constituent measurements are given.

Topics

What's inside Chapter 2

As per NCERT Class 11 Physics (CBSE syllabus)

Topic 1
Physical Quantities & SI Units
Fundamental and derived quantities. The seven SI base units and their symbols. Supplementary units (radian, steradian). SI prefixes from yocto (10⁻²⁴) to yotta (10²⁴). Conversion between unit systems (CGS, FPS, SI).
Topic 2
Dimensional Analysis
Writing dimensional formulae using [M], [L], [T], [A], [K], [mol], [cd]. Checking dimensional homogeneity of equations. Deriving formulae by dimensional methods. Limitations of dimensional analysis.
Topic 3
Significant Figures & Rounding
Rules for counting significant figures in measured values. Rounding rules for arithmetic operations: least decimal places for addition/subtraction; least significant figures for multiplication/division. Order-of-magnitude estimates.
Topic 4
Errors in Measurement
Systematic vs. random errors. Absolute, relative, and percentage error. Mean absolute error from repeated readings. Error propagation in sums, differences, products, quotients, and powers of measured quantities.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Ch 1 · Physical World
Scope of physics, fundamental forces, nature of physical laws
Class 10 · Science
Basic SI units, scalar and vector quantities, scientific notation
Chapter 2 Units and
Measurement
Leads to
Ch 3 · Motion in a Straight Line
Kinematic formulae verified by dimensional analysis; error in v, a
All of Class 11 & 12 Physics
Every numerical question uses SI units, significant figures, and error rules
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 11 Physics board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Assertion–Reason 1 1–2 SI unit identification, dimensional formula, significant figures count
Very Short Answer 2 1 State the dimensional formula of a derived quantity; convert units
Short Answer 3 1 Dimensional analysis to check or derive a formula; significant figures in a calculation
Long Answer / Numerical 4–5 1 Error propagation — find maximum percentage error in a derived quantity
Total (approximate) 6–8 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 11 Physics Chapter 2. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
Which of the following is NOT a fundamental (base) SI unit? (a) Kilogram (b) Ampere (c) Newton (d) Kelvin
Q2 Easy 2 marks Short Answer
Write the dimensional formula of (i) pressure and (ii) power. State the SI unit of each.
Q3 Medium 2 marks Short Answer
The period of oscillation of a simple pendulum is given by T = 2π√(l/g). Using dimensional analysis, verify whether this formula is dimensionally correct.
Q4 Medium 3 marks Short Answer
The resistance R of a wire is given by R = ρl/A, where ρ is resistivity, l is length, and A is cross-sectional area. Derive the dimensional formula of resistivity ρ and state its SI unit.
Q5 Medium 3 marks Short Answer
Five students measure the diameter of a sphere and record: 2.42 cm, 2.45 cm, 2.41 cm, 2.44 cm, 2.43 cm. Find (i) the mean diameter, (ii) mean absolute error, and (iii) percentage error.
Q6 Hard 4 marks Numerical
The kinetic energy of a body is measured as E = ½mv², where mass m = (5.0 ± 0.2) kg and velocity v = (12.0 ± 0.5) m s⁻¹. Calculate the kinetic energy and the maximum percentage error in E. Express the result with the correct number of significant figures.
Q7 Hard 4 marks Numerical
Using the method of dimensions, derive the formula for the time period T of a simple pendulum assuming it depends on mass m of the bob, length l of the string, and acceleration due to gravity g.
Q8 Hard 5 marks Word Problem
The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in measuring mass and length are 2% and 3% respectively: (i) What is the maximum percentage error in the measurement of density? (ii) If the measured mass is 2.50 kg and the side is 0.20 m, calculate the density and express it with the correct number of significant figures. (iii) State two ways to minimise systematic errors in such experiments.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 11 Physics board papers — Units and Measurement chapter.

Board 20222 marks
Write the dimensional formula of (a) angular momentum and (b) surface tension. Which of these has the same dimensions as Planck's constant? (CBSE All India 2022)
Board 20233 marks
The period T of a tuning fork depends on its length l, density ρ, and Young's modulus Y. Using dimensional analysis, derive a formula for T. (CBSE Delhi 2023)
Board 20203 marks
In an experiment, the refractive index n of glass is measured using n = sin(A+D)/2 ÷ sin(A/2). The measured values are A = (60 ± 1)° and D = (40 ± 1)°. Find the error in the measurement of n. (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Units and Measurement carry in the CBSE Class 11 Physics board exam? +
Units and Measurement typically carries 6–8 marks in the CBSE Class 11 Physics board exam, usually spread across 1–2 short-answer questions and one reasoning or application question. Dimensional analysis and error calculation are the most frequently tested sub-topics.
What are the seven base SI units students must know for Class 11 Physics? +
The seven SI base units are: metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. Students are often asked to state which unit corresponds to which physical quantity.
How do I use dimensional analysis to check the correctness of a physics formula? +
Write the dimensional formula of each quantity on both sides of the equation. If the dimensions on the left-hand side equal those on the right-hand side, the formula is dimensionally consistent. For example, for v = u + at: [LT⁻¹] = [LT⁻¹] + [LT⁻²][T] = [LT⁻¹]. Note that dimensional analysis cannot verify dimensionless constants or distinguish between formulae that share the same dimensions.
What is the difference between absolute error, relative error, and percentage error? +
Absolute error is the magnitude of the difference between a measured value and the true (mean) value: Δa = |a_mean − a_i|. Relative (fractional) error is the ratio of mean absolute error to the mean value: Δa/a_mean. Percentage error is relative error expressed as a percentage: (Δa/a_mean) × 100%. Board questions frequently ask students to compute these three from a set of repeated measurements.
How do I generate a custom question paper for Units and Measurement using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 11 Physics, select Chapter 2 (Units and Measurement), set your preferred question-type mix (MCQ, short answer, numerical) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.