Physics - Errors and Uncertainties

Audi SG

Ok 3 questions which I'm unsure of.

1. 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. Answer is 11%.

2(a) 2 measurements are made with the same half-meter rule. One is stated as 3.0cm, the other as 2.0cm.

What is the likely absolute error in each value?

What is the fractional error in each?

The answers given are 0.33 and 0.05 respectively... which I find quite weird. Can someone explain?

Thanks

eagle SG

I do question 1 first, then u attempt Q2 with my explanations ok?

Q1) 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%