“Add the absolutes, add the relatives”
Which error rule to use
For a sum or difference, add the absolute errors. For a product, quotient or power, add the relative errors. Two sentences cover every error numerical in the paper.
Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Units and Measurements formulas
Units and measurements is the chapter that decides whether the rest of your physics answers score. It is the smallest chapter by formula count and the largest by marks lost, because significant figures and error propagation are applied in every numerical you write for two years.
13 formulas, 3 memory hooks, and the 4 mistakes that cost the most marks.
Errors in a measurement
| What | Formula | Symbols and notes |
|---|---|---|
| Absolute error | Δa = amean − ai | the difference of one reading from the mean; always taken as positive |
| Mean absolute error | Δamean = (|Δa₁| + |Δa₂| + … + |Δan|)/n | average of the absolute errors of n readings |
| Relative error | relative error = Δamean / amean | a pure number, no unit |
| Percentage error | percentage error = (Δamean / amean) × 100% | what the question usually asks for |
How errors combine
| What | Formula | Symbols and notes |
|---|---|---|
| Sum or difference | Z = A + B or A − B, then ΔZ = ΔA + ΔB | absolute errors add, even when the quantities subtract |
| Product or quotient | Z = AB or A/B, then ΔZ/Z = ΔA/A + ΔB/B | relative errors add |
| Power | Z = ApBq/Cr, then ΔZ/Z = p(ΔA/A) + q(ΔB/B) + r(ΔC/C) | a squared term doubles its share of the error |
Dimensions worth knowing
| What | Formula | Symbols and notes |
|---|---|---|
| Force | [F] = M L T−2 | also the dimension of weight and tension |
| Work, energy, heat | [W] = M L2 T−2 | all three share one dimension, so they share one unit |
| Power | [P] = M L2 T−3 | energy per unit time |
| Pressure, stress | [p] = M L−1 T−2 | force per unit area |
| Gravitational constant | [G] = M−1 L3 T−2 | read it off F = Gm₁m₂/r² |
| Planck constant | [h] = M L2 T−1 | same dimension as angular momentum |
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Memory hooks
How to remember this chapter.
“Powers multiply the blame”
Error in a squared or cubed term
A quantity raised to the power p contributes p times its relative error. If radius is measured to 2% and you need volume, the error is 6%, not 2%.
“Last doubtful digit”
Significant figures in an answer
An answer carries as many significant figures as the least precise measurement used. Rounding early is the most common way to lose the mark.
Where marks go
The mistakes that cost the most.
- Subtracting the errors when the quantities subtract. Errors always add, whichever way the quantities go.
- Reporting more significant figures than the data allows, for example writing 2.3456 m when the metre scale reads to 0.1 cm.
- Treating a dimensional check as a proof. A dimensionally correct equation can still be wrong by a numerical factor; dimensions cannot see ½ or 2π.
- Forgetting that angles, relative error and refractive index are dimensionless, so they must never be given a unit.
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