Question
Explain errors in sum and in difference of measured quantity.
✓
Answer
Errors in sum and in difference:
$i)$ Suppose two physical quantities $A$ and $B$ have measured values $A ± \triangle A$ and $B ± \triangle B.$
respectively, where $\triangle A$ and $\triangle B$ are their mean absolute errors.
$ii)$ Then, the absolute error $\triangle Z$ in their sum.
$Z=A+B$
$Z \pm \Delta Z=(A \pm \Delta A)+(B \pm \Delta B)$
$=(A+B) \pm \Delta A \pm \Delta B$
$\therefore \pm \Delta Z= \pm \Delta A \pm \Delta B$
$iii)$ For difference. i.e.. if $Z = A – B.$
$Z \pm \Delta Z=A \pm \Delta A)-(B \pm \Delta B)$
$=(A-B) \pm \Delta A \mp \Delta B$
$\therefore \pm \Delta Z= \pm \Delta A \mp \Delta B$
$i)$ Suppose two physical quantities $A$ and $B$ have measured values $A ± \triangle A$ and $B ± \triangle B.$
respectively, where $\triangle A$ and $\triangle B$ are their mean absolute errors.
$ii)$ Then, the absolute error $\triangle Z$ in their sum.
$Z=A+B$
$Z \pm \Delta Z=(A \pm \Delta A)+(B \pm \Delta B)$
$=(A+B) \pm \Delta A \pm \Delta B$
$\therefore \pm \Delta Z= \pm \Delta A \pm \Delta B$
$iii)$ For difference. i.e.. if $Z = A – B.$
$Z \pm \Delta Z=A \pm \Delta A)-(B \pm \Delta B)$
$=(A-B) \pm \Delta A \mp \Delta B$
$\therefore \pm \Delta Z= \pm \Delta A \mp \Delta B$
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