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 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.?

Class XI Physics · Chapter 1

Units & Measurement

Q: What are the SI base units?

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

NCERT | Class 11 | Physics

Before you can describe the universe, you must agree on how to measure it. The language of physics is precision.

\(\text{[M}^a\text{L}^b\text{T}^c\text{]}\)

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SI Base Units

Supplementary Units

NCERT Exercises

Significant Figures Rules

JEE/NEET

High-Yield Chapter

Conceptual Framework

Core Topics at a Glance

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Physical Quantities & Units

Physical quantities are classified as fundamental (7 SI base units) and derived. The SI system ensures global consistency in measurement.

\(SI: kg, m, s, A, K, mol, cd\)

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Dimensional Analysis

Every physical quantity has dimensions in terms of M, L, T, I, θ, N, J. Used to verify formulae, convert units, and derive relations.

\([Force] = MLT^{-2}\)

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Significant Figures

Rules for counting sig figs determine the precision of a result. Operations follow strict rounding rules to avoid false precision.

\(3.14 × 2.5 = 7.9 (2 s.f.)\)

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Errors in Measurement

Absolute, relative, and percentage errors quantify uncertainty. Random errors can be reduced by repeated measurement; systematic errors require correction.

\(\Delta a / a = \text{relative error}\)

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Measurement of Large & Small Distances

Parallax method (large distances), echo method, laser, SONAR, Rutherford scattering (nuclear radius) are key techniques.

\(D = b/\theta\)

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Units of Length, Mass & Time

From femtometre (nuclear scale) to light-year (cosmic scale); from electron mass to solar mass — physics spans 85 orders of magnitude in mass.

\(1\text{ ly} = 9.46\times10^{15}\text{ m}\)

Quick Reference

Key Formulae

Quantity	Formula	Remarks
Parallax	\(D = b/\theta\)	b = baseline; θ in radians
Absolute Error	\(\Delta a_i = \|\bar{a} - a_i\|\)	Mean absolute error = (Σ\|Δaᵢ\|)/n
Relative Error	\(\delta a = \Delta a_{\text{mean}}/\bar{a}\)	Dimensionless
% Error	\(\delta a\% = (\Delta a_{\text{mean}}/\bar{a})\times100\)
Error in Product	\(\frac{\Delta Z}{Z} = \frac{\Delta A}{A}+\frac{\Delta B}{B}\)	Z = AB
Error in Power	\(\frac{\Delta Z}{Z} = n\frac{\Delta A}{A}\)	Z = Aⁿ
Dimensional Formula	\([A^a B^b] = M^xL^yT^z\)	Balancing exponents
1 Parsec	\(1\text{ pc} = 3.08\times10^{16}\text{ m}\)	Parallax second

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Exam-Ready Insights

Important Points to Remember

There are 7 SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).

Dimensional analysis can verify equations and derive unknown relations but cannot determine pure numerical constants.

Significant figures in a result of multiplication/division = minimum sig figs among the operands.

Random errors are reduced by averaging; systematic errors require calibration or method correction.

Least count of a vernier calliper = 1 MSD − 1 VSD. For a screw gauge = Pitch/no. of divisions.

1 light-year = 9.46×10¹⁵ m; 1 parsec = 3.08×10¹⁶ m; 1 AU = 1.496×10¹¹ m.

Principle of homogeneity: only quantities of the same dimensions can be added or equated.

Competitive Exams

Exam Corner

Units & Measurement is tested across all major competitive examinations. Here are the most frequently tested topics:

⚡ JEE Main🔷 JEE Advanced🟢 NEET🟡 CBSE Board

AllDimensional analysis — verify & derive

AllError propagation — formulae & numericals

JEELeast count of vernier & screw gauge

NEETSI units and their symbols

BoardSignificant figures — rules & operations

JEEUnit conversion using dimensional method

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NCERT Class 11 Physics Chapter 1: Units & Measurement | Notes, MCQs, PYQs for JEE & NEET

NCERT Class 11 Physics Chapter 1: Units & Measurement | Notes, MCQs, PYQs for JEE & NEET — Complete Notes & Solutions · academia-aeternum.com

Physical quantities divide into fundamental (length, mass, time, etc.) and derived types, with SI providing seven base units (metre, kilogram, second, ampere, kelvin, mole, candela) plus supplementary units (radian, steradian). Dimensions in [M][L][T] enable analysis for equation verification, relation derivation, and unit conversions across CGS, FPS, MKS systems, though limited by dimensionless constants. Accuracy measures true value closeness, precision indicates reproducibility; significant…

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