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Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements2 Marks
Question
The length and breadth of a rectangle are measured as $\text{}(\text{a}\pm\Delta\text{a})$ and $(\text{b}\pm\Delta\text{b})$ respectively. Find:
  1. Relative error.
  2. Absolute error in the measurement of area.
✓

Answer

  1. Relative error in area:
$\frac{\Delta\text{A}}{\text{A}}=\Big[\frac{\Delta\text{a}}{\text{a}}+\frac{\Delta\text{b}}{\text{b}}\Big]$
$\text{as}\text{ A}=\text{ab}$
  1. Absolute error in area
$\Delta\text{A}=\Big(\frac{\Delta\text{a}}{\text{a}}+\frac{\Delta\text{b}}{\text{b}}\Big)\text{A}$
$=\Big(\frac{\Delta\text{a}}{\text{a}}+\frac{\Delta\text{b}}{\text{b}}\Big)\text{ab}$
$\Delta\text{A}=[(\Delta\text{a})\text{b}+(\Delta\text{b})\text{a}]$

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