A physical quantity $Q$ is related to four observables $a, b, c, d$ as follows :
$\mathrm{Q}=\frac{\mathrm{ab}{ }^4}{\mathrm{~cd}}$
where, $\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}$ and $\mathrm{d}=(50 \pm 0.1) \mathrm{m}$, then the percentage error in Q is $\frac{x}{1000}$, where $x=$ ________.

Question

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{Q}=\frac{\mathrm{ab}^4}{\mathrm{~cd}} \ & \Rightarrow \frac{\Delta \mathrm{Q}}{\mathrm{Q}} 	imes 100=\left[\frac{\Delta \mathrm{a}}{\mathrm{a}}+4 \frac{\Delta \mathrm{~b}}{\mathrm{~b}}+\frac{\Delta \mathrm{c}}{\mathrm{c}}+\frac{\Delta \mathrm{d}}{\mathrm{d}}ight] 	imes 100 \ & \Rightarrow \frac{\mathrm{x}}{1000}=\left[\frac{3}{60}+4\left(\frac{0.1}{20}ight)+\left(\frac{0.2}{40}ight)+\frac{0.1}{50}ight] 	imes 100 \ & \Rightarrow \mathrm{x}=7700\end{aligned}$

A physical quantity $Q$ is related to four observables $a, b, c, d$ as follows :…

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