Question

A physical quantity $P$ is described by the relation $P = a^{1/2} b^2 c^3 d^{-4}$ If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\%, 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be :

• A. 8%
• B. 12%
• C. 32%
• D. 25%

Answer 1

Answer: (C)

32%

Answer 2

$\frac{\Delta p}{p}=\frac{1}{2} \frac{\Delta a}{a}+2 \frac{\Delta b}{b}+3 \frac{\Delta c}{c}+4 \frac{\Delta d}{d}$
$\frac{1}{2}\times2+2\times 1+3\times 3+4\times 5$
$=32\%$