Question

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

• A. 12%
• B. 7%
• C. 5%
• D. 14%

Answer 1

Answer: (D)

$\%$ error in
$A=\left(2 \frac{\Delta a}{a}+3 \frac{\Delta b}{b}+\frac{\Delta c}{c}+\frac{1}{2} \frac{\Delta d}{d}\right) \times 100$
$=2 \times 1+3 \times 3+2+\frac{1}{2} \times 2$
$=2+9+2+1$
$=14 \%$