First slide

Accuracy; precision of instruments and errors in measurements

Question

The length of a rectangular plate is measured by a meter scale and is found to be $10.0 cm$ . Its width is measured by vernier callipers as $1.00 cm$ . The least count of the meter scale and vernier callipers are $0.1 cm$ and $0.01 cm$ , respectively. Maximum permissible error in area measurement is

Moderate

A

$\pm 0.2 {cm}^{2}$
B

$\pm 0.1 {cm}^{2}$
C

$\pm 0.3 {cm}^{2}$
D

zero

Solution

$A = l \times b = 10 \times 1.0 = 10 {cm}^{2}$
$\frac{Δ A}{A} = \frac{Δ l}{l} + \frac{Δ b}{b}$
$Δ A = \pm (\frac{Δ l}{l} + \frac{Δ b}{b}) \times A$
$= \pm (\frac{0.1}{10.0} + \frac{0.01}{1.00}) \times 10$
$= \pm 0.2 {cm}^{2}$

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