Combination Of Errors
A physical quantity is computed from the relation Z = A^2 B / C, where A, B and C carry percentage errors of 1%, 2% and 3% respectively; what is the maximum percentage error in Z?
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- combination of errors
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
7%
When a derived quantity is formed by products and quotients of measured quantities raised to powers, the maximum fractional error is obtained by adding the fractional errors, each weighted by the magnitude of its exponent. For Z = A^2 B / C, the rule gives (ΔZ/Z) = 2(ΔA/A) + 1(ΔB/B) + 1(ΔC/C), where the power of A is two, B is one, and C carries an exponent of one despite being in the denominator, since errors always add for worst-case estimation. Substituting the percentage errors gives 2(1%) + 2% + 3% = 2% + 2% + 3% = 7%. The choice 4% wrongly omits the contributions of B and C or forgets to double A's error. The choice 6% drops the factor of two on A's term. The choice 9% double-counts by also doubling B or C. This is the standard propagation rule from the NCERT error-analysis section. A plausibility check confirms it: the dominant contribution should come from the squared quantity, and a 7% total sensibly exceeds any single input error.
This medium difficulty physics question is from the chapter physics and measurement, covering the topic of combination of errors. It appeared in the 2025 exam.
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