A physical quantity P is related to measured quantities a, b, c and d by P = a³b²/(c√d). If the respective percentage measurement errors in a, b, c, d are 1%, 3%, 2%, 4%, find the maximum percentage error in P.
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Question

A physical quantity P is related to measured quantities a, b, c and d by P = a³b²/(c√d). If the respective percentage measurement errors in a, b, c, d are 1%, 3%, 2%, 4%, find the maximum percentage error in P.

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G1 Physics · Accepted Answer

Step 1: Write P = a³ b² c⁻¹ d⁻¹ᐟ². Step 2: In multiplication/division with powers, maximum fractional uncertainty is the sum of the absolute powers times each fractional uncertainty. Step 3: ΔP/P × 100 = 3(Δa/a × 100) + 2(Δb/b × 100) + (Δc/c × 100) + (1/2)(Δd/d × 100). Step 4: Substitute: 3(1%) + 2(3%) + 2% + (1/2)(4%) = 3% + 6% + 2% + 2% = 13%. Final answer: 13%, Option C.