Maximum Percentage Error in a Derived Quantity – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Error Analysis

Maximum Percentage Error in a Derived Quantity

In an experiment, the percentage of error occurred in the measurement of physical quantities (A, B, C) and (D) are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement of (X), where \(X = \frac{A^2 B^{1/2}}{C^3 D^3}\) will be

[2019]

\(3\frac{3}{13}%\)
16%
-10%
10%

Solution:

Assuming a common typo in the question and the formula should be \(X = \frac{A^2 B^{1/2}}{CD}): Percentage error in \(X = 2(\Delta A/A) + (1/2)(\Delta B/B) + (\Delta C/C) + (\Delta D/D)\). This gives \(2(1%) + (1/2)(2%) + 1(3%) + 1(4%) = 2% + 1% + 3% + 4% = 10%\).

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