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Explain error of a sum or a difference.
Solution
Let two physical quantities $\mathrm{A}$ and $\mathrm{B}$ has measured value $\mathrm{A} \pm \Delta \mathrm{A}$ and $\mathrm{B} \pm \Delta \mathrm{B}$ where, $(i)$ For addition :
Let $Z$ is quantity obtained by addition of $A$ and $B$.
$\therefore \mathrm{Z}=\mathrm{A}+\mathrm{B}$
Let error is $Z$ be $\Delta Z$
$Z \pm \Delta Z=(A \pm \Delta A)+(B \pm \Delta B)$
$A+B=Z$
$\therefore \pm \Delta Z=\pm \Delta A \pm \Delta B$
For maximum absolute error,
$\Delta Z=\Delta A+\Delta B$
$(ii)$ For Subtraction :
Let difference of $A$ and $B$ is $Z$
$\therefore Z=A -B[\text { Let } A>B]$
$Z \pm \Delta Z =(A \pm \Delta A)-(B \pm \Delta B)$
$=(A-B)-(\pm \Delta A \pm \Delta B)$
$A-B =Z$
$\pm \Delta Z =\pm \Delta A \pm \Delta B$
$For maximum error in $Z$,$
$\Delta Z=\Delta A+\Delta B$
