A cylindrical wire of mass (0.4 ± 0.01)g has length (8 ± 0.04) cm and radius (6 ± 0.03) mm. The maximum error in its density will be:
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Question

A cylindrical wire of mass (0.4 ± 0.01)g has length (8 ± 0.04) cm and radius (6 ± 0.03) mm. The maximum error in its density will be:

G1 Physics · Accepted Answer

Density of the cylindrical wire is ρ = m/(πr²l) For maximum fractional error: Δρ/ρ = Δm/m + 2Δr/r + Δl/l Substituting: Δm/m = 0.01/0.40 = 0.025 2Δr/r = 2(0.03/6) = 0.010 Δl/l = 0.04/8 = 0.005 Therefore, Δρ/ρ = 0.025 + 0.010 + 0.005 = 0.040 Percentage error = 4%. Hence option A follows.