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Physics · Class 11

Uncertainty laboratory

Units & Measurements

Separate the best estimate from its uncertainty. For sums and differences, absolute worst-case bounds add. Products, quotients and powers often use first-order relative error rules when errors are small. This lab also calculates exact intervals so the approximation is visible.

Open the interactive experiment →

Carry uncertainty through the calculation.

மதிப்பீட்டையும் அதன் உறுதியின்மையையும் தனித்தனியாகக் குறிப்பிட வேண்டும். கூட்டல் மற்றும் கழித்தலில் முழுமையான பிழை வரம்புகள் சேரும். பெருக்கல், வகுத்தல் மற்றும் அடுக்குகளில் சிறிய சார்புப் பிழைகளுக்கான தோராய விதிகளைப் பயன்படுத்தலாம்.

Key notes, relationships and model limits

Key relationship

Sum/difference: absolute bounds add. For a small-error product xy, Δz ≈ |y|Δx + |x|Δy.

Remember

Compare the first-order bound with the exact endpoint interval when relative errors are appreciable.

Common trap

A mean absolute deviation is not automatically the uncertainty of the mean or a complete accuracy statement.

Model limits

Worst-case bounds are not probabilities. Repeated readings reveal spread but can retain a shared zero or calibration bias.

What you will learn

Compare absolute, relative and percentage bounds; propagate bounds; compare repeated readings; distinguish systematic and random errors.

Try the experiment

Adjust positive values and their bounds. Compare the exact result interval with the first-order approximation; inspect repeatability separately.

Think of it this way

Two uncertain bus journey times create an uncertain total. If both trips take their longest possible time, that gives the longest possible total.

Worked example

For z = xy, the first-order bound is |y|Δx + |x|Δy. At x=2±0.1, y=3±0.2 it is 0.7. The exact product interval is [5.32, 6.72], requiring a symmetric bound of 0.72 about 6.

Why this matters

Repeating a reading can reveal random spread, but a wrong zero or calibration can bias every reading in the same direction. Bounds do not imply a probability distribution.

Before you start

Decimals · fractions · powers of ten

Check your understanding

For A = 2.0 ± 0.1 and B = 3.0 ± 0.2, what is the worst-case bound on A + B?

Read the explanation

Absolute bounds add for a sum: Δ(A+B) = 0.1 + 0.2 = 0.3. The result is 5.0 ± 0.3 in the same unit.

Course connection: CBSE XI Chapter 1; NEET/Main Unit 1; JEE Advanced General. Depth and exam wording differ.