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A quantity $z$, to be estimated has a dependency on the variables $a, b$ and $c$ as $z=a b^2 c^{-2}$. The percentage of error in the measurement of $a, b$ and $c$ are respectively, $2.1 \%, 1.3 \%$ and $2.2 \%$. The percentage of error in the measurement of $z$ would then be
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The correct answer is:
$9.1 \%$
Given, $z=a b^2 c^{-2}$
So, the percentage error in the volume is given by
$\begin{aligned}
& \frac{\Delta z}{z} \times 100=\left[\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}\right] \times 100 \\
& =2.1 \%+2(1.3 \%)+2(2.2 \%)=9.1 \%
\end{aligned}$
So, the correct option is (4).
So, the percentage error in the volume is given by
$\begin{aligned}
& \frac{\Delta z}{z} \times 100=\left[\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}\right] \times 100 \\
& =2.1 \%+2(1.3 \%)+2(2.2 \%)=9.1 \%
\end{aligned}$
So, the correct option is (4).
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