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1.Units, Dimensions and Measurement
easy
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
A
$\pm 13\%$
B
$\pm 7\%$
C
$\pm 4\%$
D
$\pm 1\%$
Solution
$\frac{{\Delta x}}{x} = \frac{{\Delta a}}{a} + 2\frac{{\Delta b}}{b} + 3\frac{{\Delta c}}{c}$
$ = \pm 1 + 2\left( { \pm 3} \right) + 3\left( { \pm 2} \right) = \pm 1 \pm 6 \pm 6 = \pm 13\% $
Standard 11
Physics
