A physical quantity is given by P = a²b³/(c√d). The percentage errors in a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in P is:
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Question

A physical quantity is given by P = a²b³/(c√d). The percentage errors in a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in P is:

G1 Physics · Accepted Answer

For P = a²b³ c⁻¹ d⁻¹ᐟ², the maximum fractional error is ΔP/P = 2(Δa/a) + 3(Δb/b) + (Δc/c) + (1/2)(Δd/d) In percentage form: % error = 2(1) + 3(2) + 3 + (1/2)(4) = 2 + 6 + 3 + 2 = 13% Hence option B follows.