A power multiplies the error
"A power multiplies the error" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Uncertainty in calculated results" in Units and Measurements. For Q = aᵖ bᵠ / cʳ (default g = 4π²L/T²), each input's % error is multiplied by its power; stacked bars show which measurement dominates the result's % error. NEET has asked about this idea 3 times in 10 years of papers. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Uncertainty in calculated results in Units and Measurements. Change the values and watch what happens.
What it shows
NCERT §1.3.3
For Q = aᵖ bᵠ / cʳ (default g = 4π²L/T²), each input's % error is multiplied by its power; stacked bars show which measurement dominates the result's % error.
Controls
4 to try
- Slider% error in L 0.1–2 %
- Slider% error in T 0.1–2 %
- Stepperpowers p, q, r 0–3
- Togglepreset formula (g from pendulum, volume of sphere, KE = ½mv²)
Try this
In g = 4π²L/T², bring the total error in g below 1 % by improving only one measurement—pick the one that pays off most (the T² term).
Common mistake
Adding raw % errors without multiplying by the power (forgetting the 2 in T²).
In NEET
10 years of papers
Asked 3 times in 10 years of NEET.
See the past questions: Units and Dimensions, Units and Measurements (chapter)
In JEE Main
42 shifts analysed
61 questions from Units and Measurements across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §1.3.3
- A reading from an instrument carries an uncertainty of about its least count: a length of 16.2 cm read on a metre scale is 16.2 ± 0.1 cm.
- The relative (percentage) error is the uncertainty divided by the value: ±0.1 cm on 16.2 cm is about ±0.6%, and ±0.1 cm on 10.1 cm is about ±1%.
- When measured values are multiplied or divided, their percentage errors add: the area l × b = 163.62 cm² carries ±1.6%, about ±2.6 cm², so it is quoted as 164 ± 3 cm².
- The same absolute uncertainty is a larger relative error on a smaller value: ±0.01 g is ±1% of 1.02 g but only ±0.1% of 9.89 g.
- Uncertainties in a sum or difference follow decimal places, not significant figures, so a difference can lose figures: 12.9 g − 7.06 g is 5.8 g, not 5.84 g.
- If the data are good to n significant figures, a result obtained by combining them is valid to about n significant figures, fewer if data are subtracted.
Questions
5 answers
- What does the "A power multiplies the error" simulation show?
- For Q = aᵖ bᵠ / cʳ (default g = 4π²L/T²), each input's % error is multiplied by its power; stacked bars show which measurement dominates the result's % error.
- What mistake does the "A power multiplies the error" simulation fix?
- A common mistake it clears up: adding raw % errors without multiplying by the power (forgetting the 2 in T²).
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 3 times in 10 years of papers.
- Does JEE Main ask questions from Units and Measurements?
- Yes. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Uncertainty in calculated results" in Units and Measurements (Class 11 Physics).
Embed this simulation
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