From http://www.sgforums.com/forums/2297/topics/392121
To find the density of an aluminium sheet, the mass, length, and breadth were determined within 1%. Its mean thickness was found by folding it twice to give a stack of 4 sheets, the thickness of which was measured to be (11.2 +/- 0.4)mm and the zero reading of the screw gauge was recorded as (1.2+/-0.4)mm. Calculate the percentage uncertainty of its density.
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Answer:
let t = thickness and zero error = z, length = l, breadth = b, mass = m, density = D
D = m / (0.25(t-z) * l * b)
ΔD / D = Δm / m + Δl / l + Δb / b + Δ(t-z) / (t-z)
ΔD / D = Δm / m + Δl / l + Δb / b + [Δt + Δz)]/ (t-z) ===> important part: Δ(t-z) = Δt + Δz
Sub in values
ΔD / D = 0.01 + 0.01 + 0.01 + 0.8/10
ΔD / D = 0.11
Thus, percentage uncertainty = 11%
