Question

What is the percentage error in the physical quantity $A$ If it is related to four other physical quantities $a$ , $b$ , $c$ and $d$ as $A=\frac{a^{2} b^{3}}{d \sqrt{c}}$ ? The percentage error in measurement of $a$ , $b$ , $c$ and $d$ are $1\%$ , $3\%$ , $2\%$ and $1\%$ respectively.

Answer 1

Percentage error in $A$
$=2\frac{\Delta a}{a}+3\frac{\Delta b}{b}+\frac{1}{2}\frac{\Delta c}{c}+\frac{\Delta d}{d}$
$=\left(2 \times 1 + 3 \times 3 + \frac{1}{2} \times 2 + 1 \times 1\right)\%=13\%$