First slide

Accuracy; precision of instruments and errors in measurements

Question

The radius of a cylindrical wire is measured by screw gauge is $1.25 mm$ . The length of wire is $25.0 cm$ and the mass of wire is $12 g$ . The density of wire is

Moderate

A

$(9.8 \pm 1.0) {gcm}^{- 3}$
B

$(9.8 \pm 1.01267) {gcm}^{- 3}$
C

$(9.8 \pm 0.1) {gcm}^{- 3}$
D

$(9.80 \pm 0.01) {gcm}^{- 3}$

Solution

Density, $ρ = \frac{Mass}{Volume} = \frac{m}{π r^{2} l}$
$= \frac{12}{3.14 \times {(1.25 \times 10^{- 1})}^{2} \times 25.0}$
$= 9.8 {gcm}^{- 3}$
$ρ = \frac{m}{π r^{2} l}$
$\frac{Δ ρ}{ρ} = \frac{Δ m}{m} + \frac{2 Δ r}{r} + \frac{Δ l}{l}$
$Δ ρ = (\frac{1}{12} + \frac{2 \times 0.01}{125} + \frac{01}{25.0}) \times 9.8 = 1.0$
$ρ = (9.8 \pm 1.0) {gcm}^{- 1}$

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