Answer to Question #119941 in Mechanics | Relativity for Umar

Question #119941
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.
Expert's answer

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

  • Therefore, for this question,

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

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

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