What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Name the seven SI base quantities and their units.

Length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole) and luminous intensity (candela).

How is the SI metre defined in the 2018 revision?

By fixing the speed of light in vacuum \(c\) at exactly 299792458 m s\(^{-1}\), with the second defined through the caesium frequency.

State the rule for significant figures in multiplication or division.

The result retains as many significant figures as the input number with the fewest significant figures.

State the rule for addition or subtraction.

The result retains as many decimal places as the input number with the fewest decimal places.

Why is scientific notation used to report measurements?

It removes ambiguity about trailing zeros and clearly shows the number of significant figures and the order of magnitude.

What are the dimensions of force?

\([M\,L\,T^{-2}]\) — one power of mass, one of length and minus two of time.

State the principle of homogeneity of dimensions.

All terms that are added or equated in a physical equation must have the same dimensions; otherwise the equation is wrong.

Does a dimensionally correct equation have to be physically correct?

No — dimensional consistency is necessary but not sufficient; the equation may still have a wrong numerical constant or missing dimensionless factor.

What are the limitations of dimensional analysis?

It cannot determine dimensionless constants, cannot handle equations with sums of terms easily, and cannot distinguish quantities having the same dimensions.

Why are radian and steradian dimensionless?

They are defined as ratios — arc to radius (plane angle) and area to radius squared (solid angle) — so the dimensions cancel.

Units and Measurement

Class 11 Physics · Physics Part I · Chapter 1

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Summary

Physics is a quantitative science in which every physical quantity is expressed as a number accompanied by a unit, a number obtained by comparing the quantity with an internationally accepted reference standard. Units of the chosen base quantities are called base units, and units of all other (derived) quantities are combinations of these. The Systeme International (SI), revised in 2018, uses seven base units — metre, kilogram, second, ampere, kelvin, mole and candela — now defined through fixed numerical values of fundamental constants such as the speed of light \(c\), the Planck constant \(h\) and the caesium frequency. Because every measurement carries error, results are reported using significant figures, with rules for non-zero digits, embedded zeros and trailing zeros, and arithmetic operations preserve the precision of the least precise input. Scientific notation \(a\times10^{b}\) avoids ambiguity and gives the order of magnitude. The dimensions of a quantity are the powers to which the base quantities \([M],[L],[T]\) etc. are raised; force, for example, has dimensions \([M\,L\,T^{-2}]\). Dimensional analysis, based on the principle of homogeneity, is used to check the consistency of equations, convert units and deduce relations among quantities, though it cannot find dimensionless constants and a dimensionally correct equation need not be physically correct.

The international system of unitsSignificant figuresDimensions of physical quantitiesDimensional formulae and equationsDimensional analysis and its applicationsOrder of magnitude and scientific notation

Key terms

Unit

An internationally accepted reference standard used to measure a physical quantity, against which the quantity is compared.

Base unit

The unit of a fundamental quantity; SI has seven — metre, kilogram, second, ampere, kelvin, mole and candela.

Significant figures

The reliably known digits of a measurement plus the first uncertain digit, indicating the precision of the result.

Order of magnitude

The power of ten nearest to a quantity, found by writing it as \(a\times10^{b}\) and rounding \(a\).

Dimensions

The powers to which the base quantities are raised to represent a physical quantity, written in square brackets.

Principle of homogeneity

The rule that every term in a physically meaningful equation must have the same dimensions.

Extra questions & answers

Try one from this chapter

How many base units does the SI system have?

Flashcards & interactive practice