What is a physical quantity?

A physical quantity is a property of a system that can be measured and expressed numerically with a unit, such as length, mass, and time.?

A unit is a standard reference chosen to measure a physical quantity, e.g., metre for length, kilogram for mass.?

What are fundamental (base) quantities?

Physical quantities that are independent of other quantities, e.g., length, mass, time, electric current, temperature, amount of substance, luminous intensity.?

How many SI base quantities are there?

There are seven SI base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, luminous intensity.?

What are the SI base units?

Metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).?

What are derived quantities and units?

Quantities defined using base quantities (e.g., velocity, force); their units are combinations of base units (e.g., \(m\ s^{-1},\ kg\ m\ s^{-2}\).?

What are supplementary units in SI?

SI supplementary units are: radian (rad) for plane angle and steradian (sr) for solid angle.?

Why is the SI system preferred?

It is internationally accepted, coherent, and based on seven base units with well-defined standards, simplifying scientific communication.?

What is meant by “coherent system of units”?

A system where derived units are obtained from base units without additional numerical factors, e.g., \(1\ N = 1\ kg\ m\ s^{-2}\).?

What is dimensional formula?

It is the expression of a physical quantity in terms of base dimensions, like \([M^aL^bT^c]\) for mass, length, and time powers.?

What is the dimensional formula of velocity?

Velocity has dimensional formula \([LT^{-1}]\).?

What is the dimensional formula of force?

Force has dimensional formula \([MLT^{-2}]\).?

State the principle of homogeneity of dimensions.

In a physically meaningful equation, the dimensions of all terms on both sides must be the same.?

What are the uses of dimensional analysis?

To check the dimensional consistency of equations, derive relations between quantities, and convert from one system of units to another.?

Give one limitation of dimensional analysis.

It cannot determine dimensionless constants (like 1/2, 2p), and it fails if quantities of different dimensions are added.?

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📏 Master Units & Measurements
NCERT Class 11 · Chapter 1

Real PYQs from top competitive exams — filter by exam, attempt each question, track your progress and submit to see your full score report.

Attempt PYQs Study Strategy

SI UnitsDimensional AnalysisSignificant FiguresErrorsVernier Callipers

Real PYQs

Exam Bodies

15+

Years Covered

~6%

Exam Weightage

PYQs Overview

📐

Dimensional Analysis

Deriving formulae, checking homogeneity, converting units — most-tested numerical.

★★★★★

93% Frequency

⚠️

Error Analysis

Absolute, relative, percentage error; error in sum, product, power.

★★★★★

88% Frequency

🔢

Significant Figures & Rounding

Rules for counting sig figs; arithmetic with sig figs.

★★★★☆

76% Frequency

📏

SI Units & Supplementary Units

7 base quantities, SI units, supplementary (radian, steradian).

★★★★☆

82% Frequency

🔬

Vernier Callipers & Screw Gauge

Least count, zero error, reading measurements — numerical.

★★★★☆

70% Frequency

🌌

Order of Magnitude

Estimations, powers of 10, size comparison of physical quantities.

★★★☆☆

55% Frequency

Topic Frequency

Dimensional Analysis 93%

SI Units 82%

Error Analysis 88%

Significant Figures 76%

Vernier/Screw Gauge 70%

Order of Magnitude 55%

Parallax Method 40%

💡 Did You Know?

Dimensional analysis asked in every JEE paper
Error propagation numerical — 8× in JEE since 2010
SI base units = 7 (kg, m, s, A, K, mol, cd)
Zero error in Vernier — asked every NEET year
Numericals = ~70% of chapter marks

Key Takeaways

🔑

7 base SI units — memorise all

kg, m, s, A, K, mol, cd. Supplementary: rad, sr.

⚡

Dimensional formula of every physical quantity

[M^a L^b T^c] — derive for force, energy, pressure, viscosity etc.

📐

Error in product/quotient: add relative errors

ΔZ/Z = ΔA/A + ΔB/B. For power n: ΔZ/Z = n·ΔA/A.

🌊

Least count = 1 MSD – 1 VSD

For Vernier: LC = 1 MSD/n. For screw gauge: LC = pitch/n.

🧮

Significant figures rules — 3 key cases

Leading zeros: not significant. Trailing zeros after decimal: significant.

🎯

Homogeneity principle: dimensions must match

Use to check formula correctness and derive missing constants.

Study Strategy

SI Units & DimensionsDay 1–2

All 7 base units + dimensional formulae for 30+ quantities.

Dimensional AnalysisDay 3

Checking, deriving, converting — 20 practice problems.

Error AnalysisDay 4

Sum, product, quotient, power rules — 15 numerical problems.

InstrumentsDay 5

Vernier callipers, screw gauge — LC, zero error, readings.

Significant FiguresDay 6

Rules + arithmetic. 15 practice sums.

Attempt All PYQsDay 7

Focus on dimensional analysis and error MCQs.

Mock TestDay 8

Timed 30-Q mock. Dimensional analysis = highest priority.

🗓️ 8-Day Chapter Plan

Day 1–2	SI Units & Dimensions
Day 3	Dimensional Analysis
Day 4	Error Analysis
Day 5	Instruments
Day 6	Significant Figures
Day 7	Attempt All PYQs
Day 8	Mock Test

🧠 Pro Tip: Dimensional analysis alone is worth 3–4 marks in JEE. Master deriving unknowns from given quantities.

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UNITS AND MEASUREMENT – Learning Resources

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Units & Measurements question?