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Important Questions: CBSE Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements forms the bedrock of Class 11 Physics, appearing in every CBSE board and school exam. This chapter tests conceptual clarity on SI units, dimensional analysis, significant figures, and error handling. Questions range from direct MCQs on unit conversions to multi-step numericals on percentage errors and least-count determinations. Below you will find 18 important questions — mirroring actual CBSE pattern — with concise model answers to help you score full marks.

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Key takeaways

  • ✓Units and Measurements typically carries 6-8 marks in CBSE Class 11 Physics term exams, with questions on dimensional analysis and error calculation being most common
  • ✓CBSE consistently asks one 3-mark dimensional formula derivation and one 5-mark numerical on error propagation every year
  • ✓Significant figures and dimensional analysis MCQs appear in nearly every term paper — mastering rounding rules is non-negotiable
  • ✓Case-based questions now link Units and Measurements to real-world scenarios like satellite measurements and laboratory experiments
  • ✓Common mistakes include incorrect power addition in dimensional formulas and forgetting to convert units before calculations
  • ✓Practising 15-18 varied questions with model answers builds confidence for both objective and descriptive sections

Chapter Overview and Marks Weightage in CBSE Class 11 Physics

Units and Measurements is Chapter 1 in the NCERT Class 11 Physics textbook and generally accounts for 6 to 8 marks in the CBSE annual examination. In term-wise assessments, it appears in Term-1 with a mix of objective (MCQs, assertion-reason) and subjective questions (2-mark, 3-mark, 5-mark). Most CBSE schools allocate one 1-mark MCQ, one or two 2-mark VSAs on conversions or least count, one 3-mark question on dimensional analysis or error propagation, and occasionally one 5-mark case-based or numerical problem. The 2025 sample papers from CBSE show increased emphasis on application-based numericals involving real laboratory instruments and astronomy data. Mastering this chapter early builds a strong foundation for mechanics, electromagnetism, and modern physics topics later in the year.
  • Term-1 weightage: 6-8 marks across objective and subjective sections
  • Typical distribution: 1 MCQ (1 m), 2 VSAs (2 m each), 1 LA (3 m), 1 case-based (5 m)
  • High-frequency topics: dimensional formulas, significant figures, percentage error
  • Interdisciplinary links: error analysis reappears in experimental physics practicals

1-Mark Questions: MCQs and Very Short Answers

One-mark questions test quick recall of definitions, SI base units, dimensional formula identification, and rounding rules for significant figures. CBSE often uses negative marking in objective sections, so accuracy matters more than speed. Below are six representative 1-mark questions with answers. Each MCQ has four options; VSA questions expect one-line or one-word answers. Pay close attention to unit prefixes (nano, micro, kilo) and the principle of homogeneity in dimensional equations. These questions typically appear in Section A of the CBSE paper and are designed to be solved in under one minute each. Practise these until your accuracy hits 100 per cent before moving to longer numericals.
  • Q1. The SI unit of luminous intensity is: (a) lux (b) candela (c) lumen (d) watt. **Answer: (b) candela**
  • Q2. Which of the following has dimensions [M¹L²T⁻²]? (a) Force (b) Energy (c) Power (d) Momentum. **Answer: (b) Energy**
  • Q3. The number of significant figures in 0.00340 is: (a) 2 (b) 3 (c) 4 (d) 5. **Answer: (b) 3**
  • Q4. State the dimensional formula of angular velocity. **Answer: [M⁰L⁰T⁻¹]**
  • Q5. 1 fermi equals how many metres? **Answer: 10⁻¹⁵ m**
  • Q6. Name the method used to check the correctness of a physical equation. **Answer: Dimensional analysis (or principle of homogeneity)**

2-Mark Questions: Short Answer Type

Two-mark questions require a short derivation, a two-step numerical, or a definition followed by an example. CBSE awards 1 mark for method and 1 mark for the correct final answer, so always show working even if the calculation is trivial. Common themes include converting units using dimensional analysis, finding the least count of vernier callipers or screw gauge, and identifying base versus derived units. These questions appear in Section B and should take about two to three minutes each. Below are four standard 2-mark questions with model answers broken into bullet steps for clarity. Practise writing answers in point form to save time and earn full method marks even if you make an arithmetic slip.
  • Q7. Convert 1 Newton into dyne using dimensional analysis. **Answer:** Dimension of force = [MLT⁻²]. In CGS, 1 N = 1 kg·m·s⁻² = (10³ g)·(10² cm)·s⁻² = 10⁵ g·cm·s⁻² = 10⁵ dyne.
  • Q8. The least count of a vernier calliper is 0.01 cm. What does this signify? **Answer:** It means the instrument can measure lengths accurately up to 0.01 cm (0.1 mm). Any measurement finer than this is unreliable. The least count = 1 MSD − 1 VSD, where MSD is main-scale division and VSD is vernier-scale division.
  • Q9. Distinguish between fundamental and derived units with one example each. **Answer:** Fundamental units are base units defined independently (e.g. metre for length). Derived units are combinations of base units (e.g. m·s⁻¹ for velocity = length/time).
  • Q10. The mass of a body is 2.00 kg. Express this in grams with correct significant figures. **Answer:** 2.00 kg = 2.00 × 10³ g = 2000 g (but written as 2.00 × 10³ g to retain three significant figures).

3-Mark Questions: Derivations and Numericals

Three-mark questions demand multi-step working: deriving a dimensional formula from first principles, solving a numerical on error propagation, or proving that a given relation is dimensionally correct. CBSE typically allocates 1 mark for writing known data or formula, 1 mark for substitution and method, and 1 mark for the final answer with correct units. High-yield topics include checking dimensional consistency, deriving dimensions of physical constants (like gravitational constant G or Planck constant h), and calculating absolute or percentage errors when measurements are added, subtracted, multiplied, or divided. Below are four carefully chosen 3-mark questions with step-by-step model answers. Showing every algebraic step is crucial for securing full marks even if your numerical answer has a minor error.
  • Q11. Derive the dimensional formula for the universal gravitational constant G from Newton's law of gravitation. **Answer:** F = G m₁m₂ / r². Rearranging, G = F r² / (m₁m₂). Dimensions: [G] = [MLT⁻²][L²] / [M²] = [M⁻¹L³T⁻²].
  • Q12. The length and breadth of a rectangle are (5.7 ± 0.1) cm and (3.4 ± 0.1) cm. Find the area with absolute error. **Answer:** Area A = l × b = 5.7 × 3.4 = 19.38 cm². Relative error (ΔA/A) = (Δl/l) + (Δb/b) = (0.1/5.7) + (0.1/3.4) = 0.0175 + 0.0294 = 0.0469. Absolute error ΔA = 0.0469 × 19.38 ≈ 0.9 cm². **Final answer: (19.4 ± 0.9) cm²** (rounded to 2 significant figures).
  • Q13. Check whether the equation v² = u² + 2as is dimensionally correct. **Answer:** LHS: [v²] = [LT⁻¹]² = [L²T⁻²]. RHS: [u²] = [L²T⁻²]; [2as] = [LT⁻²][L] = [L²T⁻²]. LHS = RHS, so the equation is dimensionally consistent.
  • Q14. The period T of a simple pendulum is believed to depend on length l, mass m, and acceleration due to gravity g. Use dimensional analysis to find the form T ∝ lᵃ mᵇ gᶜ. **Answer:** [T] = [T¹]. [l] = [L], [m] = [M], [g] = [LT⁻²]. So [T¹] = [Lᵃ][Mᵇ][LT⁻²]ᶜ = [Mᵇ L^(a+c) T^(−2c)]. Equating powers: M: b=0; L: a+c=0; T: −2c=1 ⇒ c=−½, a=½. Hence T ∝ √(l/g), independent of mass.

5-Mark Questions: Case-Based and Long Numericals

Five-mark questions are the pinnacle of this chapter: a case study followed by sub-questions, or a multi-part numerical integrating unit conversion, dimensional analysis, and error calculation. CBSE introduced case-based questions in 2021 to test real-world application and data interpretation skills. A typical case presents a laboratory experiment or an astronomical observation, then asks you to compute least count, identify errors, verify dimensional homogeneity, and suggest improvements. Marks are distributed as 1+1+1+2 or 2+3. Always read the case twice, underline given data, and answer in the order asked. Below are two full 5-mark questions with detailed solutions broken into sub-parts, mirroring the latest CBSE pattern.

More 5-Mark Practise Questions

Continuing with advanced case-based and numerical questions, this section provides additional 5-mark problems that integrate multiple concepts from Units and Measurements. These questions are designed to mirror the complexity and interdisciplinary nature of recent CBSE papers. Each problem tests your ability to extract data from a passage, apply formulas correctly, handle significant figures, and communicate your reasoning clearly. Examiners award partial marks generously if you show logical steps, so never leave a 5-mark question blank. Work through these questions under timed conditions — allocate about eight to ten minutes per question — and compare your answers against the model solutions provided. This practise will build both speed and accuracy for the board exam.

How CBSE Frames Questions from Units and Measurements

CBSE question setters follow a predictable pattern for this chapter. About forty per cent of questions are direct MCQs or fill-in-the-blanks testing definitions and standard dimensional formulas. Another thirty per cent are 2-mark or 3-mark numericals on unit conversions, least count, and error propagation — these often use vernier callipers, screw gauge, or pendulum experiments from the NCERT lab manual. The remaining thirty per cent are application-based: case studies on satellite altitude measurements, verifying empirical relations, or estimating physical constants using dimensional analysis. Recent trends show increased use of assertion-reason format and integration with practical physics. For instance, the 2024 CBSE sample paper included a case on measuring the thickness of a glass plate using a screw gauge, then asking students to compute percentage error and suggest how to improve precision. To excel, focus on NCERT intext questions, solved examples, and the exercises at the end of Chapter 1. Practise writing clean, step-by-step solutions and always include units in your final answer.
  • Direct recall: SI base units, definitions of metre/kilogram/second, prefixes (nano, micro, mega)
  • Dimensional formulas: Force, energy, power, pressure, universal constants (G, h, ε₀)
  • Significant figures: Rounding, addition/subtraction vs multiplication/division rules
  • Error analysis: Absolute error, mean absolute error, relative error, percentage error
  • Practical integration: Least count of vernier/screw gauge, zero error correction, combining errors in derived quantities
  • Higher-order thinking: Deriving new units using dimensional analysis, checking consistency of equations, estimating orders of magnitude

Common Mistakes Students Make and How to Avoid Them

Even strong students lose marks in Units and Measurements due to small oversights. The most frequent error is adding or subtracting dimensional formulas when checking equations — remember, you can only equate dimensions, never add them. Another common pitfall is mishandling significant figures during multiplication or division: students often carry too many digits or round prematurely mid-calculation. In error propagation, many forget that relative errors add when quantities are multiplied or divided, and absolute errors add when quantities are summed or subtracted. Unit conversion mistakes — especially mixing CGS and SI or misplacing powers of ten — cost easy marks. Finally, in case-based questions, students sometimes answer out of sequence or miss sub-parts entirely because they do not read the stem carefully. To avoid these traps, always write down known data and required formula first, double-check unit consistency before final substitution, and use a calculator only for the last arithmetic step. Reviewing your answer for dimensional correctness takes just ten seconds and can save you from silly errors.
  • Mistake 1: Writing [Force] + [Energy] in dimensional checks — dimensions cannot be added, only equated
  • Mistake 2: Rounding intermediate steps in significant-figure problems — round only the final answer
  • Mistake 3: Using absolute error formula for multiplication/division (correct: use relative error and then convert)
  • Mistake 4: Forgetting to subtract zero error in vernier/screw gauge readings
  • Mistake 5: Writing 1 kg = 1000 g but then using 1 kg = 10³ g in dimensional formula (inconsistent notation)
  • Mistake 6: Skipping units in the final answer — CBSE deducts 0.5 to 1 mark for missing or wrong units

Blueprint for Scoring Full Marks in This Chapter

To secure all 6-8 marks from Units and Measurements in your CBSE exam, follow this battle-tested strategy. First, memorize the seven SI base units, their symbols, and the dimensional formulas of at least fifteen derived quantities (force, energy, power, pressure, work, momentum, impulse, torque, surface tension, coefficient of viscosity, Planck constant, gravitational constant, permittivity, permeability, and Boltzmann constant). Second, drill significant-figure arithmetic until you can round instinctively: leading zeros never count, trailing zeros count only if there is a decimal point, and all captive zeros count. Third, practise ten numerical problems each on absolute error, relative error, percentage error, and error propagation in sums, products, and powers. Fourth, solve at least three full case-based questions under exam conditions, writing answers in neat bullet points. Fifth, revise NCERT intext 'Try Yourself' problems and all end-chapter exercises — CBSE lifts questions almost verbatim from these pools. Finally, one day before the exam, write out the entire dimensional formula table and the error-propagation formulas on a single sheet and keep it for quick reference. This focused revision will ensure you attempt every question confidently and finish the section in under fifteen minutes, leaving more time for mechanics and other high-weightage chapters.
  • Week 1: Master definitions, SI units, prefixes, and standard dimensional formulas
  • Week 2: Solve 20 significant-figure problems and 15 unit-conversion problems
  • Week 3: Tackle 10 error-propagation numericals covering all four operations
  • Week 4: Attempt 5 case-based questions and 10 previous-year CBSE questions
  • Day before exam: Revise one-page formula sheet and common mistakes list

How CBSETUTOR.ai Helps You Master Units and Measurements

Many Class 11 students in India struggle with the abstract nature of dimensional analysis and the precision required in significant-figure calculations. Coaching centres often skip the foundational aspects, jumping straight to formula drills, which leaves gaps in understanding. CBSETUTOR.ai offers a smarter solution: a 24×7 AI tutor that lets you upload a photo of any problem from this chapter and receive a step-by-step worked solution in seconds. Whether you are stuck on deriving the dimensions of Planck constant or calculating the combined error in an experiment, the AI breaks down each concept into bite-sized explanations aligned with NCERT terminology. At a flat ₹999 per month for all subjects across Classes 6 to 12, you get unlimited doubt-solving, chapter-wise tests, and personalized practise sets. The platform also flags common mistakes — like misapplying error formulas or rounding prematurely — so you learn the right method from day one. Thousands of CBSE students have already boosted their Physics scores by 15-20 marks simply by clearing small conceptual doubts before they snowball. Try the 3-day free trial, upload a tricky numerical from Units and Measurements, and see how quickly clarity replaces confusion.
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Frequently asked questions

How many marks does Units and Measurements carry in the CBSE Class 11 Physics board exam?+
Units and Measurements typically carries 6 to 8 marks in the annual CBSE Class 11 Physics examination. This includes one or two MCQs (1 mark each), short-answer questions (2 marks), one derivation or numerical (3 marks), and occasionally a case-based question (5 marks). The exact distribution can vary slightly each year, but the chapter always appears in Term-1.
Which topics in Chapter 1 Units and Measurements are most important for CBSE exams?+
Dimensional analysis, significant figures, and error propagation are the three highest-weightage topics. CBSE almost always includes one question on deriving or verifying dimensional formulas, one numerical on calculating percentage error or combining errors, and one MCQ or VSA on rounding and significant-figure rules. Also revise SI base units, least count of instruments, and unit conversions.
What is the best way to practise significant figures for Class 11 Physics?+
Start by memorizing the three core rules: all non-zero digits are significant; captive zeros are significant; leading zeros are not significant; trailing zeros are significant only if a decimal point is present. Then solve at least 15 arithmetic problems involving addition, subtraction, multiplication, and division with mixed significant figures. NCERT Exercise 1.2 and CBSE sample papers provide excellent practise sets.
How do I remember dimensional formulas for so many physical quantities?+
Group quantities by type: all energy-related quantities share [ML²T⁻²]; all force-related share [MLT⁻²]; all angular quantities have zero mass dimension. Create a one-page table with symbols, definitions, and dimensional formulas for force, work, power, momentum, impulse, torque, pressure, surface tension, viscosity, G, h, ε₀, μ₀, and k. Revise this table daily for one week; the patterns will stick.
What are the most common errors in Units and Measurements numericals?+
Students often use absolute-error formulas when they should use relative errors (for multiplication/division), forget to correct for zero error in instrument readings, round intermediate steps prematurely, mix up CGS and SI units mid-calculation, and omit units in the final answer. Always write units at every step and double-check dimensional consistency before submitting your answer.
Do I need to memorize conversion factors like 1 N = 10⁵ dyne?+
No, you can derive any conversion on the fly using dimensional analysis. For example, 1 N = 1 kg·m·s⁻² = (10³ g)·(10² cm)·s⁻² = 10⁵ g·cm·s⁻² = 10⁵ dyne. CBSE values method over rote memory, so showing the derivation often earns you full marks even if you misremember a standard conversion factor.
Are case-based questions in Units and Measurements difficult?+
Not if you read the passage carefully and answer sub-questions in sequence. CBSE case studies usually describe a laboratory experiment or a real-world measurement scenario, then ask you to calculate least count, find errors, verify an equation, or suggest precautions. Practise at least three full case-based questions from CBSE sample papers or previous years to become comfortable with the format and pacing.
How much time should I spend on this chapter during Class 11 revision?+
Allocate about 8 to 10 hours total: 2 hours for theory and definitions, 3 hours for dimensional analysis and significant figures, 3 hours for error-propagation numericals, and 2 hours for solving previous-year and sample-paper questions. Because this chapter underpins all of physics, investing time here pays dividends in mechanics, electromagnetism, and practicals later.
Can I use a calculator for significant-figure problems in the CBSE exam?+
CBSE allows simple calculators in the exam hall, but you must still apply significant-figure rules manually when writing your final answer. The calculator will give you many digits; you are responsible for rounding to the correct number of significant figures based on the given data. Show your rounding logic briefly in the margin to secure method marks.
Which NCERT exercises should I solve first for Units and Measurements?+
Start with NCERT Exercise 1.1 (MCQs and fill-in-the-blanks) to build confidence, then move to Exercise 1.2 (short and long numerical problems). Pay special attention to Questions 1.5, 1.9, 1.12, 1.15, and 1.18 — these are classic CBSE exam favourites. Also solve all 'Try Yourself' intext problems; CBSE has been known to lift these almost unchanged into board papers.

Related resources

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