The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values are m = 97.42 ± 0.02 g, l = 8.35 ± 0.05 mm and d = 20.20 ± 0.02 mm. What is the calculated percentage fractional error in ρ?
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Question

The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values are m = 97.42 ± 0.02 g, l = 8.35 ± 0.05 mm and d = 20.20 ± 0.02 mm. What is the calculated percentage fractional error in ρ?

Options

G1 Physics · Accepted Answer

For a uniform cylinder, ρ = 4m ÷ (πd²l). For maximum fractional error in a product or quotient, Δρ ÷ ρ = Δm ÷ m + 2(Δd ÷ d) + Δl ÷ l. Substitute the measured uncertainties: Δρ ÷ ρ = 0.02 ÷ 97.42 + 2(0.02 ÷ 20.20) + 0.05 ÷ 8.35 ≈ 0.00817. Therefore, percentage error ≈ 0.817% ≈ 0.82%. Correct option: B.