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1. units,dimensions and measurement — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
An experiment measures quantities $a, b$ and $c$, and quantity $X$ is calculated from $X=a b^{2} / c^{3}$. If the percentage error in $a$, $b$ and $c$ are $\pm 1 \%, \pm 3 \%$ and $\pm 2 \%$, respectively, then the percentage error in $X$ will be
  • ✓
    $\pm 13\%$
  • B
    $\pm 7\%$
  • C
    $\pm 4\%$
  • D
    $\pm 1\%$
✓

Answer

Correct option: A.
$\pm 13\%$
a
$\frac{{\Delta x}}{x} = \frac{{\Delta a}}{a} + 2\frac{{\Delta b}}{b} + 3\frac{{\Delta c}}{c}$

$ =  \pm 1 + 2\left( { \pm 3} \right) + 3\left( { \pm 2} \right) =  \pm 1 \pm 6 \pm 6 =  \pm 13\% $

 

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