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In an experiment, four quantities $a, b, c, d$ are measured with percentage errors 2\%, $1 \%, 3 \%$ and 5\%, respectively. Quantity $P$ is measured as $P=\frac{a^2 b^2}{c d}$. Find the percentage error in measuring $P$.
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Verified Answer
The correct answer is:
$14 \%$
Given, $\%$ error in $a, b, c$ and $d$ are $2 \%, 1 \%, 3 \%$ and $5 \%$, respectively, and $P=\frac{a^2 b^2}{c d}$
By using concept of percentage error,
$\begin{aligned}
\frac{\Delta P}{P} \% & =\frac{2 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}+\frac{\Delta d}{d} \\
\therefore \quad \frac{\Delta P}{P} \% & =2 \times 2+2 \times 1+3+5 \\
& =4+2+3+5 \\
& =14 \%
\end{aligned}$
By using concept of percentage error,
$\begin{aligned}
\frac{\Delta P}{P} \% & =\frac{2 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}+\frac{\Delta d}{d} \\
\therefore \quad \frac{\Delta P}{P} \% & =2 \times 2+2 \times 1+3+5 \\
& =4+2+3+5 \\
& =14 \%
\end{aligned}$
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