A silver wire has a mass 0 . 6 ± 0 . 006 g , radius 0 . 5 ± 0 . 005 mm and length 4 ± 0 . 04 cm . The maximum percentage error in the measurement of its density will be

Step-by-step solution

Volume of the wire is V = π r 2 l . Density of the wire is ρ = m π r 2 l Relative error in measurement of density ⇒ Δ ρ ρ = Δ m m + 2 × Δ r r + Δ l l = 0 . 006 0 . 6 + 2 × 0 . 005 0 . 5 + 0 . 04 4 = 0 . 01 + 0 . 02 + 0 . 01 = 0 . 04 ∴ Percentage error in ρ = 0 . 04 × 100 = 4 %