Question

An experiment measures quantities $a, b$, and $c$, and then $X$ is calculated from $X=\frac{a^{1 / 2} b^{2}}{c^{3}}$. If the percentage errors in $a, b$, and $c$ are $\pm 1 \%, \pm 3 \%$, and $\pm 2 \%$, respectively, then the percentage error in $X$ can be

• A. $\pm 12.5 \%$
• B. $\pm 7 \%$
• C. $\pm 1 \%$
• D. $\pm 4 \%$

Answer 1

Answer: (A)

$X=\frac{a^{1 / 2} b^{2}}{c^{3}}$
$ \frac{\Delta X}{X} \times 100 =\frac{1}{2} \frac{\Delta a}{a} \times 100+2 \frac{\Delta b}{b} \times 100+3 \frac{\Delta c}{c} \times 100 $
$=\frac{1}{2} \times 1+2 \times 3+3 \times 2=12.5 \% $