A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows: $ P=a^3 b^2 /

Question

A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows: $ P=a^3 b^2 / c \sqrt{d} $ The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 2 \%$ and $4 \%$ respectively. The percentage error in the quantity $P$ is

Professor PC Thomas Classes · Answer

(a) : Given, $P=\frac{a^3 b^2}{c \sqrt{d}}$ Percentage error in quantity $P$, $ \begin{aligned} \frac{\Delta P}{P} 	imes 100 & =\left(\frac{3 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}+\frac{1}{2} \frac{\Delta d}{d}ight) 	imes 100 \ & =3(1)+2(3)+2+\frac{1}{2} 	imes 4=3+6+2+2=13 \% \end{aligned} $