A physical quantity $X$ is related to four measurable quantities $a, b, c$ and $d$ as given, $X=a^{2

Question

A physical quantity $X$ is related to four measurable quantities $a, b, c$ and $d$ as given, $X=a^{2} b^{3} c^{5 / 2} d^{-2}$. The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 2 \%$ and $4 \%$ respectively. What is the percentage error in quantity $X$ ?\

Professor PC Thomas Classes · Answer

(c) : As $X=a^2 b^3 c^{5 / 2} d^{-2}$ The percentage error in $X$ is $ \ \begin{aligned} \frac{\Delta X}{X} 	imes 100 & =\left[2\left(\frac{\Delta a}{a}ight)+3\left(\frac{\Delta b}{b}ight)+\frac{5}{2}\left(\frac{\Delta c}{c}ight)+2\left(\frac{\Delta d}{d}ight)ight] 	imes 100 \ & =2 	imes 1 \%+3 	imes 2 \%+\frac{5}{2} 	imes 2 \%+2 	imes 4 \%=21 \% \end{aligned} $