An experiment measures quantities x, y and z, and t is calculated as t = xy²/z³. If percentage errors in x, y and z are 1%, 3% and 2%, respectively, find the percentage error in t.
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Question

An experiment measures quantities x, y and z, and t is calculated as t = xy²/z³. If percentage errors in x, y and z are 1%, 3% and 2%, respectively, find the percentage error in t.

G1 Physics · Accepted Answer

For t = xy²/z³, maximum fractional error is Δt/t = Δx/x + 2Δy/y + 3Δz/z. Hence percentage error = 1 + 2×3 + 3×2 = 13%. Correct answer: D.