A physical quantity P is related to four observables a, b, c and d as P = (a³b²) / (√c d). The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2% respectively. What is the percentage error in the quantity P?
Model Answer & Options
Source: Extra Practice13%
7%
10%
14%
Explanation
Using the rule for propagation of errors in products and powers: (ΔP/P) = 3(Δa/a) + 2(Δb/b) + (1/2)(Δc/c) + (Δd/d). Substituting the given percentage errors: % error in P = 3(1%) + 2(3%) + 0.5(4%) + 2% = 3% + 6% + 2% + 2% = 13%. Options 7%, 10%, and 14% are incorrect because they result from miscalculating the power coefficients or incorrectly applying the square root factor.
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