Answer to Question #119941 in Mechanics | Relativity for Umar

Question

The dimension of a rectangular shape is 5.9 by 4.1mm s measured with a veneer calliper whose minimum scale is 0.05 mm. The percentage error in its surface area is approximately.

Answer 1

Explanations & Calculations

• Fractional error of a measurement is $\frac{\text{error}}{\text{measurement}}$

• In measuring instruments the least measurement is considered as the maximum error.
• The effect of errors in taking measurements of several quantities, is affected in a way of fractional errors when a product or ratio of those quantities are considered.
• With respect to this situation, l = 5.9 mm, b =4.1 mm & Area = l $\small \times$ b

• If the possible maximum error is noted by $\delta$ ,

$\qquad\qquad \begin{aligned} \small \frac{\delta(Area)}{Area} &= \small \frac{\delta(l)}{l} +\frac{\delta(b)}{b} \end{aligned}$

• Therefore, for this question,

$\qquad\qquad \begin{aligned} \small \frac{\delta(Area)}{Area} &= \small \frac{0.05mm}{5.9mm} +\frac{0.05mm}{4.1mm}\\ &= \small \frac{50}{2419}\\ & =\small 0.020669 \end{aligned}$

• Therefore, percentage error is 0.020669 $\times$ 100% = 2.067%