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

Percentage Error in a Derived Quantity (P)

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]

4%
14%
10%
7%

Solution:

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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