Error Analysis: Practice Problem & Solution
In an experiment four quantities (a, b, c) and (d) are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity (P) is calculated as follows \(P = \frac{a^3 b^2}{cd}\). \(\text{%}\) error in (P) is: [2013]
Solution Explained:
To solve this problem, we apply the core principles of Error Analysis. Understanding the underlying formula is key to arriving at the correct answer below:
Percentage error in \(P = 3(\Delta a/a) + 2(\Delta b/b) + (\Delta c/c) + (\Delta d/d)\). Given errors: 3×1% + 2×2% + 1×3% + 1×4% = 3% + 4% + 3% + 4% = 14%.
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