Question:
An experiment measures quantities $a$, $b$ and $c$, and quantity $X$ is calculated from $X= ab^2/c^3$. 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
An experiment measures quantities $a$, $b$ and $c$, and quantity $X$ is calculated from $X= ab^2/c^3$. 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
Updated On: Jun 7, 2024
- $\pm 13\%$
- $\pm 7\%$
- $\pm 4\%$
- $\pm 1\%$
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The Correct Option is A
Solution and Explanation
$\frac{\Delta x}{x}=\frac{\Delta a}{a}+2\frac{\Delta b}{b}+3\frac{\Delta c}{c}$
$=\pm1\%+2\left(\pm3\%\right)+3\left(\pm2\%\right)$
$=\pm1\%\pm6\%\pm6\%$
$=\pm13\%$
$=\pm1\%+2\left(\pm3\%\right)+3\left(\pm2\%\right)$
$=\pm1\%\pm6\%\pm6\%$
$=\pm13\%$
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Concepts Used:
Physical World
The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:
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