First slide

Accuracy; precision of instruments and errors in measurements

Question

A wire has a mass 0.3 $\pm$ 0.003 g, radius 0.5 $\pm$ 0.005 mm and length 6 $\pm$ 0.06 cm. The maximum percentage error in the measurement of its density is

Easy

A

1
B

2
C

3
D

4

Solution

$∴Density, ρ = \frac{M}{V} = \frac{M}{π r^{2} L}$
$\begin{array}{l} \Rightarrow \frac{Δ ρ}{ρ} = \frac{Δ M}{M} + 2 \frac{Δ r}{r} + \frac{Δ L}{L} \\ = \frac{0.003}{0.3} + 2 \times \frac{0.005}{0.5} + \frac{0.06}{6} \\ = 0.01 + 0.02 + 0.01 = 0.04 \\ ∴ Percentage error = \frac{Δ ρ}{ρ} \times 100 = 0.04 \times 100 = 4 % \end{array}$

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