Question

An experiment measures quantities a, b, c and x is calculated from $x=a{b}^2/c^3$. If the maximum percentage error in a, b and c are 1%, 3% and 2% respectively, the maximum percentage error in x will be

• A. $13$%
• B. $17$%
• C. $14$%
• D. $11$%

Answer 1

The correct option is A $13$%

Error in $a$, $\frac{\Delta a}{a}\times 100=1$%
Error in $b$ $\frac{\Delta b}{b}\times 100=3$%
Error in $c$ $\frac{\Delta c}{c}\times 100=2$%
The quantity is given as $x=\frac{a{b}^2}{c^3}$
Error in measurement of $x$ $\frac{\Delta x}{x}\times 100=\frac{\Delta a}{a}\times 100+$ $2\times \frac{\Delta b}{b}\times 100$ $+3\times \frac{\Delta c}{c}\times 100$
$⟹$ $\frac{\Delta x}{x}\times 100=1+2\times 3+3\times 2=13$%