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CBSE Class 11 Physics Chapter 1 Units and Measurements Worksheet with Answers

Units and Measurements is the first chapter in NCERT Class 11 Physics and lays the groundwork for every calculation you will perform in Physics, Chemistry and even Biology practicals. This printable worksheet contains 40+ carefully curated questions covering SI units, dimensional analysis, significant figures, error analysis and measuring instruments. Each section escalates in difficulty, helping you build confidence from basic recall to HOTS problems that appeared in past CBSE board papers.

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Key takeaways

✓SI units form the foundation of all physical measurements; memorising the seven base units and their symbols is essential for Class 11 board exams
✓Dimensional analysis helps verify equations, derive relations between physical quantities, and convert units — a skill tested in 4-5 mark CBSE questions
✓Significant figures reflect measurement precision; rounding rules and arithmetic operations with significant figures appear in both MCQs and numericals
✓The principle of homogeneity states that only quantities with identical dimensions can be added or subtracted — frequently tested in dimensional analysis problems
✓Error analysis distinguishes systematic errors from random errors; understanding absolute, relative and percentage errors is crucial for practical-based questions
✓Vernier callipers and screw gauge questions are standard in CBSE Class 11 practicals; least count calculation and zero error correction are high-weightage topics
✓This worksheet mirrors the CBSE Class 11 Physics paper pattern with 30% weightage to conceptual MCQs and 70% to application-based numerical problems

Quick Chapter Recap — Units and Measurements

Before you attempt the worksheet, revise these core concepts from NCERT Class 11 Physics Chapter 1. The International System of Units (SI) defines seven base units: metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. All other units are derived from these base units. Dimensional analysis uses the dimensions [M], [L], [T], [I], [K], [N] and [J] to express physical quantities and verify the correctness of equations through the principle of homogeneity. Significant figures represent the precision of a measurement; zeros between non-zero digits are always significant, while trailing zeros in a decimal are significant but those in a whole number without a decimal point may or may not be. Errors in measurement can be systematic (instrument zero error, calibration defect) or random (environmental fluctuations, observer limitations). Least count is the smallest measurement a device can reliably make — for a standard metre scale it is 1 mm, for a Vernier calliper it is typically 0.1 mm, and for a screw gauge it is 0.01 mm.

Seven SI base units: m, kg, s, A, K, mol, cd — memorise their symbols and names
Dimensional formula: express every quantity in terms of M, L, T, I, K, N, J
Principle of homogeneity: all terms in an equation must have identical dimensions
Significant figures: 0.00340 has three significant figures; 3400 has two unless written 3.400 × 10³
Least count of Vernier callipers = 1 MSD − 1 VSD; for screw gauge = Pitch / Number of divisions on circular scale
Percentage error = (Absolute error / True value) × 100

Difficulty Level and Time Allocation

This worksheet is pitched at Moderate to Advanced difficulty, suitable for students aiming to score 30+ out of 35 in the Units and Measurements section of their Class 11 Physics term exam. The question mix mirrors the CBSE Class 11 Physics exam pattern: 25% recall-based MCQs, 50% application-level numericals and 25% higher-order thinking problems that test conceptual depth. Allocate 90 minutes to complete the entire worksheet under exam conditions. Section A (MCQs) should take 12–15 minutes, Section B (fill-in-the-blanks) around 8 minutes, Section C (match or true/false) 6 minutes, Section D (short answers) 25 minutes, Section E (long answers and HOTS) 30 minutes, and the case-study question about 9 minutes. Keep a scientific calculator, NCERT Class 11 Physics textbook and a rough notebook handy. After completing the worksheet, spend another 30 minutes cross-checking your answers with the detailed answer key provided at the end. Mark your weak areas — dimensional analysis, significant figures or error propagation — and revisit those NCERT sections before your term exam.

Suggested time: 90 minutes (1.5 hours) under timed conditions
Difficulty: Moderate to Advanced — mirrors CBSE Class 11 term exam standards
Total questions: 40+ across five sections plus one case-study
Materials needed: scientific calculator, NCERT textbook, rough paper
Scoring guideline: 30+ correct answers indicate excellent readiness; 20–29 is good; below 20 requires targeted revision

Section A — Multiple Choice Questions (MCQs)

Attempt all six MCQs. Each question carries 1 mark. Choose the single best answer. These questions test your conceptual clarity on SI units, dimensional analysis and significant figures — topics that frequently appear in the CBSE Class 11 Physics board paper and competitive exams like JEE Main. Read each option carefully; CBSE often includes distractors that are dimensionally correct but conceptually wrong. No negative marking, so attempt every question even if you are unsure. Write your answers in the format Q1: (B), Q2: (C) on a separate answer sheet to simulate real exam conditions.

Q1. The SI unit of luminous intensity is: (A) lumen (B) candela (C) lux (D) watt
Q2. Which of the following pairs has the same dimensions? (A) Work and power (B) Momentum and impulse (C) Torque and energy (D) Stress and strain
Q3. The number of significant figures in 0.00705 is: (A) 2 (B) 3 (C) 4 (D) 5
Q4. A physical quantity X is related to four measurable quantities a, b, c, d as X = a²b³/c√d. The percentage error in X is: (A) Δa/a + Δb/b + Δc/c + Δd/d (B) 2Δa/a + 3Δb/b + Δc/c + ½Δd/d (C) (Δa/a)² + (Δb/b)³ + Δc/c + ½Δd/d (D) 2Δa + 3Δb + Δc + ½Δd
Q5. The least count of a Vernier callipers is 0.1 mm. The zero of the Vernier scale lies to the right of zero of the main scale and the fourth Vernier division coincides with a main scale division. The zero error is: (A) +0.4 mm (B) –0.4 mm (C) +0.04 mm (D) –0.04 mm
Q6. Which of the following is a dimensionless quantity? (A) Gravitational constant (B) Planck constant (C) Strain (D) Angular momentum

Section B — Fill in the Blanks

Complete each sentence with the correct term, unit, formula or numerical value. Each blank carries 1 mark. This section tests precise terminology and factual recall from NCERT Class 11 Physics Chapter 1. Write your answers clearly; spelling mistakes in SI unit names or symbols may cost marks in board exams. If a numerical answer is required, include the unit unless the question specifies otherwise. Attempted all five blanks even if you are uncertain — there is no negative marking. Use standard SI symbols: m for metre, kg for kilogram, s for second, A for ampere, K for kelvin, mol for mole, cd for candela.

Q7. The dimensional formula of pressure is __________.
Q8. 1 parsec equals __________ metres (approximate to two significant figures).
Q9. If the measured value of a quantity is 6.8 cm and the true value is 6.5 cm, the absolute error is __________ cm.
Q10. The SI unit of electric charge is coulomb, which is equivalent to __________ (express in terms of base SI units).
Q11. The principle of __________ states that the dimensions of all terms in a physical equation must be identical.

Section C — Match the Following / True or False

This section contains two parts. Part I: Match each physical quantity in Column A with its correct dimensional formula in Column B. Part II: State whether each statement is True or False. Each correct match or True/False carries 0.5 mark. Write your answers in the format Q12: (i)–(c), (ii)–(a), etc. for matching, and Q17: True, Q18: False for the True/False statements. These questions test your ability to quickly recall dimensional formulas and identify common misconceptions about units and measurements — skills that save time in competitive exams.

Q12. Match the following (4 pairs, 2 marks total):
Column A: (i) Power (ii) Momentum (iii) Surface tension (iv) Frequency
Column B: (a) [T⁻¹] (b) [MLT⁻³] (c) [MT⁻²] (d) [MLT⁻¹] (e) [ML²T⁻³]
Q13–Q16. True or False (0.5 mark each):
Q13. The unit 'light year' measures time. __________
Q14. In the measurement 2.50 × 10³, there are three significant figures. __________
Q15. Dimensional analysis can determine the value of dimensionless constants in a formula. __________
Q16. A screw gauge with 50 divisions on the circular scale and pitch 0.5 mm has a least count of 0.01 mm. __________

Section D — Short Answer Questions (3 marks each)

Answer any five of the following questions in 40–60 words each. Each question carries 3 marks and tests your ability to explain concepts, derive dimensional formulas, perform unit conversions and calculate errors. Show all working; partial credit is awarded for correct methodology even if the final answer is wrong. Use standard SI units unless the question specifies otherwise. These questions are modelled on the 3-mark numericals and theory questions that appear in CBSE Class 11 Physics term exams. Clarity and correct use of terminology from NCERT Class 11 Physics will fetch you full marks. Avoid vague statements like 'it depends on various factors' — be specific and quantitative.

Q17. Define the term 'least count' of a measuring instrument. Calculate the least count of a Vernier callipers in which 1 cm on the main scale is divided into 10 divisions and 10 divisions of the Vernier scale coincide with 9 divisions of the main scale.
Q18. State the principle of homogeneity of dimensions. Use it to check whether the equation v = u + at is dimensionally consistent, where v and u are velocities, a is acceleration and t is time.
Q19. The length of a rod is measured as (25.0 ± 0.1) cm. What is the percentage error in the measurement? If 5 such rods are placed end-to-end, what is the total length and the absolute error in the total length?
Q20. Convert 1 newton into dynes using dimensional analysis. (Given: 1 N = 1 kg·m·s⁻² and 1 dyne = 1 g·cm·s⁻²)
Q21. Distinguish between systematic errors and random errors in measurements. Give one example of each from your Class 11 Physics practicals.
Q22. The period T of a simple pendulum is believed to depend on its length l, mass m and acceleration due to gravity g. Use dimensional analysis to derive an expression for T.

Section E — Long Answer and HOTS Questions (5 marks each)

Answer all three questions in 80–120 words each. Each question carries 5 marks and demands in-depth conceptual understanding, multi-step problem-solving or critical analysis. These HOTS (Higher Order Thinking Skills) questions mirror the 5-mark questions in the CBSE Class 11 Physics board exam and are designed to differentiate top scorers from average performers. Show detailed working, state assumptions clearly and write final answers with correct units and significant figures. Partial credit is generous if your approach is sound. Drawing neat diagrams or tables where appropriate (e.g. for screw gauge readings) will earn you extra clarity marks. Spend at least 8–10 minutes per question; do not rush.

Q23. (a) What are significant figures? State the rules for determining the number of significant figures in a given measurement. (b) Perform the following calculations and express the result with the correct number of significant figures: (i) 6.2 × 10³ + 4.3 × 10² (ii) (2.50 × 10⁻³) × (3.2 × 10⁴) / (8.0 × 10²)
Q24. (a) Derive the dimensional formula for the universal gravitational constant G from Newton's law of gravitation. (b) If the percentage errors in measuring mass and distance are 2% and 3% respectively, find the maximum percentage error in calculating the gravitational force between two masses.
Q25. In a screw gauge, the zero of the circular scale lies 6 divisions below the reference line when the faces are in contact (negative zero error). The pitch of the screw is 1.0 mm and there are 100 divisions on the circular scale. When a wire is placed between the jaws, the main scale reads 3 mm and the 47th division on the circular scale coincides with the reference line. Calculate: (a) the least count, (b) the zero correction, (c) the corrected diameter of the wire.

Section F — Case Study Question (4 marks)

Read the passage below and answer the questions that follow. Case-study questions appeared for the first time in CBSE Class 11 Physics term exams from 2021–22 and are now a regular feature. They test your ability to apply chapter concepts to real-world scenarios, interpret data and solve multi-part problems. Each sub-question carries 1 mark. Answer all four parts; no negative marking. Write concise answers — one or two sentences are sufficient for 1-mark questions. Use data from the passage; do not rely solely on external knowledge. This case study is based on a laboratory experiment measuring the diameter of a wire using a screw gauge, a common CBSE Class 11 Physics practical.

Passage: A student is assigned to measure the diameter of a thin copper wire using a screw gauge. The screw gauge has a pitch of 0.5 mm and 50 divisions on the circular scale. Before starting, she checks for zero error by bringing the faces of the screw gauge into contact. She observes that the zero of the circular scale lies 3 divisions above the reference line. She then places the wire between the jaws; the main scale reading is 2.5 mm and the 28th division on the circular scale coincides with the reference line. She repeats the measurement at five different points along the wire and records the circular scale readings as 28, 29, 27, 28 and 30 divisions (main scale reading remains 2.5 mm in all trials).
Q26. What is the least count of the screw gauge used?
Q27. What is the zero error and zero correction for this screw gauge?
Q28. Calculate the observed diameter of the wire (without zero correction) for the first trial.
Q29. What is the mean corrected diameter of the wire? Express your answer with appropriate significant figures.

Full Answer Key with Explanations

Below is the complete answer key for all sections of the worksheet. Each answer includes a brief explanation or working to help you understand the reasoning. Cross-check your answers carefully. For numerical problems, ensure your final answer matches both the value and the number of significant figures given here. If you scored below 70%, revisit the relevant NCERT Class 11 Physics sections and attempt the worksheet again after a week. Consistent practice with worksheets like this one is the surest way to master Units and Measurements and score full marks in your term exam. Students can also upload their doubts or incorrect answers to CBSETUTOR.ai, where an AI tutor will provide step-by-step photo solutions and personalised explanations 24×7 at just ₹999/month — one flat price for all subjects and classes 6–12, with a 3-day free trial to get started.

Section A Answers: Q1.(B) candela, Q2.(C) torque and energy both [ML²T⁻²], Q3.(B) three (7,0,5 are significant), Q4.(B) percentage error formula with exponents as coefficients, Q5.(B) –0.4 mm (zero to the right means negative zero error = –4×0.1), Q6.(C) strain is change in dimension / original dimension, dimensionless
Section B Answers: Q7.[ML⁻¹T⁻²], Q8. 3.1×10¹⁶ m (1 parsec ≈ 3.09×10¹⁶ m), Q9. 0.3 cm (6.8–6.5), Q10. A·s (coulomb = ampere second), Q11. homogeneity
Section C Answers: Q12. (i)–(b), (ii)–(d), (iii)–(c), (iv)–(a); Q13. False (light year measures distance), Q14. True, Q15. False (dimensional analysis cannot find dimensionless constants), Q16. True (LC = 0.5/50 = 0.01 mm)
Section D sample answers provided in detailed explanations for Q17–Q22 in next subsection
Section E sample answers provided in detailed explanations for Q23–Q25 in next subsection
Section F Answers: Q26. 0.01 mm, Q27. Zero error +0.03 mm, zero correction –0.03 mm, Q28. 2.5 + 28×0.01 = 2.78 mm, Q29. Mean observed diameter = 2.5 + (28+29+27+28+30)/5 × 0.01 = 2.5 + 0.284 = 2.784 mm; corrected = 2.784 – 0.03 = 2.754 mm ≈ 2.75 mm (3 significant figures)

Detailed Solutions for Short and Long Answer Questions

Q17 Answer: Least count is the smallest measurement a device can reliably detect. For the given Vernier callipers, 1 MSD = 1 cm/10 = 1 mm. 10 VSD = 9 MSD, so 1 VSD = 0.9 mm. Least count = 1 MSD – 1 VSD = 1.0 – 0.9 = 0.1 mm. (3 marks). Q19 Answer: Percentage error = (0.1/25.0)×100 = 0.4%. Total length = 5×25.0 = 125.0 cm. Absolute error in total = 5×0.1 = 0.5 cm. Final result (125.0 ± 0.5) cm. (3 marks). Q20 Answer: 1 N = 1 kg·m·s⁻². In CGS, 1 kg = 10³ g, 1 m = 10² cm. Hence 1 N = 10³ g × 10² cm × s⁻² = 10⁵ g·cm·s⁻² = 10⁵ dyne. (3 marks). Q21 Answer: Systematic errors are reproducible inaccuracies with a known cause, e.g. zero error in a Vernier callipers. Random errors fluctuate unpredictably, e.g. parallax error when reading a scale from different angles. (3 marks). Q22 Answer: Let T ∝ lᵃ mᵇ gᶜ. [T] = [L]ᵃ [M]ᵇ [LT⁻²]ᶜ = [Mᵇ Lᵃ⁺ᶜ T⁻²ᶜ]. Equating powers: M: b=0, T: –2c=1 ⇒ c=–1/2, L: a+c=0 ⇒ a=1/2. Hence T ∝ √(l/g) or T = k√(l/g), where k is dimensionless. (3 marks). Q23 Answer: (a) Significant figures are digits in a measurement that carry meaningful information. Rules: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not significant; trailing zeros in a decimal number are significant. (b)(i) 6.2×10³ + 0.43×10³ = 6.63×10³. Least decimal place in 6.2×10³ is hundreds, so answer is 6.6×10³. (ii) (2.50×3.2×10¹)/(8.0) = 10.0. Each factor has 2 or 3 sig figs; result should have 2 sig figs: 10. or 1.0×10¹. (5 marks). Q25 Answer: (a) LC = 1.0 mm / 100 = 0.01 mm. (b) Zero error = –6×0.01 = –0.06 mm (below reference line is negative). Zero correction = +0.06 mm. (c) Observed diameter = 3.0 + 47×0.01 = 3.47 mm. Corrected diameter = 3.47 + 0.06 = 3.53 mm. (5 marks)

How CBSETUTOR.ai Helps You Master Units and Measurements

After solving this worksheet, many students still have lingering doubts about dimensional analysis tricks, error propagation formulas or interpreting Vernier scale diagrams. CBSETUOR.ai is an AI-powered tutor available 24×7 to answer exactly those questions. Simply upload a photo of any problem from this worksheet — or from your NCERT Class 11 Physics textbook, coaching material or previous year papers — and get an instant step-by-step solution in clear Indian English. The AI tutor explains not just what the answer is, but why each step follows logically, helping you build genuine conceptual understanding rather than rote formulas. Whether you are stuck at 11 PM the night before your exam or want to explore a HOTS problem in depth on a Sunday morning, CBSETUTOR.ai is there. The subscription is a flat ₹999 per month for every class from 6 to 12, covering Physics, Chemistry, Maths, Biology and more — no hidden charges, no per-question fees. Start with a 3-day free trial and see how personalised AI tutoring transforms your confidence in Units and Measurements and every other chapter. Thousands of CBSE students across India are already using CBSETUTOR.ai to clarify doubts instantly and score higher in term exams.

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Frequently asked questions

What is the weightage of Units and Measurements in the CBSE Class 11 Physics board exam?+

Units and Measurements typically carries 5–7 marks in the CBSE Class 11 Physics term exam, distributed across 2–3 MCQs (1 mark each), one short-answer question (3 marks) and sometimes part of a 5-mark numerical or case-study question. Mastering this chapter also builds foundational skills for every subsequent numerical problem in Mechanics, Thermodynamics and Electromagnetism, so its indirect weightage is much higher.

How do I remember the seven SI base units and their symbols quickly?+

Use the mnemonic 'My Kilo Second Amazes Kelvin's Mole Candy': Metre (m), Kilogram (kg), Second (s), Ampere (A), Kelvin (K), Mole (mol), Candela (cd). Write them out ten times before your exam and associate each with a physical object — a metre scale, a 1 kg weight, a stopwatch, a battery, a thermometer, a chemistry mole concept and a candle.

What are the most common mistakes students make in dimensional analysis questions?+

Students often forget that angles, strain and all trigonometric ratios are dimensionless, leading to incorrect dimensional formulas. Another frequent error is treating [M], [L] and [T] as algebraic variables without respecting their physical meaning — for example, writing [M] + [L] as if it were valid. Also, many students confuse the principle of homogeneity with dimensional correctness; an equation can be dimensionally correct yet physically wrong if dimensionless constants differ.

How many significant figures should I use in my final answer for CBSE board exam numericals?+

Follow the rule: your answer should have the same number of significant figures as the measurement with the fewest significant figures in the problem. For example, if the question gives 9.8 m/s² (2 sig figs) and 5.234 s (4 sig figs), report your answer to 2 significant figures. In CBSE marking schemes, ±1 significant figure tolerance is usually allowed, but always show at least two to avoid mark deduction.

What is the difference between zero error and zero correction in a screw gauge?+

Zero error is the faulty reading displayed when the screw gauge faces are in perfect contact; it is positive if the zero of the circular scale lies above the reference line and negative if below. Zero correction is the value you add algebraically to the observed reading to get the true measurement: zero correction = –(zero error). For instance, a zero error of +0.03 mm means you subtract 0.03 mm from every observed reading.

Can dimensional analysis determine the value of dimensionless constants like π or ½ in a formula?+

No. Dimensional analysis can only tell you the form of the relationship between physical quantities — the exponents of each dimension — but cannot determine pure numbers. For example, dimensional analysis of a simple pendulum gives T ∝ √(l/g), but it cannot tell you that the full formula is T = 2π√(l/g). You need experimental data or theoretical derivation to find such constants.

Why do we need to learn about errors and least count? Do they come in board exams?+

Yes, error analysis and least count are part of both theory and practical exams. CBSE often includes a 3-mark question on calculating absolute error, percentage error or combining errors in derived quantities. In practicals, you must report least count and zero error for Vernier callipers and screw gauge in your observation table. Understanding these concepts also helps you interpret experimental data scientifically, a skill tested in case-study questions.

How should I prepare for the case-study question on Units and Measurements?+

Read the passage carefully and underline key data: numerical values, instrument specifications, what is being measured. Answer each sub-question using only the data provided in the passage; do not overcomplicate. Practice at least five case studies from CBSE sample papers and previous year questions. Case studies usually test least count calculation, error correction and data interpretation — all skills you practice in your Class 11 Physics lab. Time management is crucial; spend no more than 8–9 minutes on a 4-mark case study.

Is solving one worksheet enough to score full marks in Units and Measurements?+

One worksheet builds foundational confidence, but top scorers solve 3–4 worksheets plus all NCERT Class 11 Physics back exercises and at least two previous year CBSE board questions on this chapter. After each worksheet, identify weak areas — dimensional analysis, significant figures or error propagation — and do focused practice. Also, rework every problem you got wrong until you can solve it independently. Consistent, spaced practice over two weeks yields much better retention than last-minute cramming.

Where can I get instant help if I am stuck on a dimensional analysis or error calculation problem?+

You can upload a photo of your problem to CBSETUTOR.ai and receive a step-by-step solution within seconds, available 24×7. The AI tutor explains each step in simple Indian English, perfect for clearing doubts at any hour. The subscription is ₹999/month for all subjects and classes 6–12, with a 3-day free trial so you can try it risk-free before your exams. Thousands of CBSE students rely on CBSETUTOR.ai for instant doubt resolution and concept clarity, especially in Physics numericals and derivations.

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