Units and Measurements — Physics STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
Explain errors due to power $($index$)$ of measured quantity.
✓
Answer
Errors due to the power $($index$)$ of measured quantity:
$1.$Suppose
$Z = A^3 = A \times A \times A$
then,
$1.$Hence the relative error in $Z = A^3$ is three times the relative error in $A.$
$2.$This means if $Z = A^n$
$\frac{\Delta Z }{ Z }= n \frac{\Delta A }{ A }$
$3.$ In general, if $Z =\frac{ A ^{ p } B ^q}{ C ^r}$
$\frac{\Delta Z }{ Z }= p \frac{\Delta A }{ A }+ q \frac{\Delta B }{ B }+ r \frac{\Delta C }{ C }$
$4.$This implies, the quantity in the formula which has large power is responsible for maximum error.
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