First slide

Accuracy; precision of instruments and errors in measurements

Question

A wire has a mass $0.4 \pm 0.004 g$ and length $8 \pm 0.08 (cm)$ The maximum percentage error in the measurement of its density is 4%. The radius of the wire is $r \pm Δ r$ , find $Δ r$ .

Moderate

A

0.02r
B

0.01r
C

0.03r
D

0.1r

Solution

$\begin{array}{l} ρ = \frac{m}{π r^{2} L} \\ \begin{aligned} \frac{Δ ρ}{ρ} \times 100 & = [\frac{Δ m}{m} + 2 \frac{Δ r}{r} + \frac{Δ L}{L}] \times 100 \\ = (0.01 + 2 \frac{Δ r}{r} + 0.01) \times 100 = 4 (given) \end{aligned} \\ or 100 \frac{Δ r}{r} = 1 \Rightarrow Δ r = 0.01 r \end{array}$

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