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1.Units, Dimensions and Measurement
normal
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 is $a, b\,\,$ 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\,\% \,$
Solution
$x=a^{1/2} b^{2} / c^{3}$
Thus, $\frac{\Delta x}{x}={1/2}\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+3 \frac{\Delta c}{c}$
$=0.5(\pm1)+2(\pm 3)+3(\pm 2)$
$=\pm 0.5 \pm 6 \pm 6$
$=\pm 12.5 \%$
Standard 11
Physics
