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You use a meter ruler to measure the length of a metal rod. Select the most suitable category for the uncertainty in this measurement.

Question

BlackTom AI · Accepted Answer

The resolution of the metre ruler (its smallest division) sets the typical random uncertainty in a single length reading: you cannot read between the smallest marks precisely, so the measured value has a scatter of about ±half a division.

1) Relevant knowledge points and concepts
- Random uncertainty (also called statistical) arises from unpredictable variations between repeated measurements (e.g., slightly different eye position, small shifts of the rod, reading fluctuations).
- Systematic uncertainty is a reproducible bias that shifts all readings in the same direction (e.g., a zero-offset on the ruler, a calibration error, thermal expansion of the ruler).
- For a scale with smallest division d (1 mm here), a common estimate of absolute reading uncertainty is ±d/2. If the distribution of possible true values within that half-division is assumed uniform, the standard uncertainty is (d/2)/√3.

2) Step-by-step reasoning
- You use a metre ruler with divisions of 1 mm to read the rod length.
- Different readings taken (or different observers) will scatter by about ±0.5 mm because you cannot resolve smaller increments reliably — this is random variation in readings.
- Systematic effects (zero error, a bent ruler, or wrong calibration) could exist but are separate and must be identified explicitly; they are not the default dominant uncertainty for a normal ruler reading.

3) Calculations / intermediate steps
- Smallest division d = 1 mm → half-division a = d/2 = 0.5 mm.
- If uniform distribution within ±0.5 mm, standard uncertainty u = a/√3 = 0.5/√3 ≈ 0.29 mm. This quantifies the random uncertainty from resolution.

4) Why the correct answer is correct
- The main uncertainty when simply reading a length from a metre ruler is the unpredictable, irreproducible reading variation (resolution and human reading) — i.e., random uncertainty.

5) Why the other option is incorrect
- Systematic uncertainty would imply a consistent bias (e.g., ruler has wrong zero or is permanently stretched). Those are specific issues; they are not the typical uncertainty category for an ordinary single reading without evidence of bias.

6) Conclusion
- Therefore the most suitable category is Random uncertainty, which matches the provided answer.

You may find it useful to watch the video below before attempting this question or viewing it on theBox here: . You use a meter ruler to measure the length of a metal rod. Select the most suitable category for the uncertainty in this measurement.单项选择题

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