Q. In an experiment, we measure quantities $a,b$ and $c$. Then $x$ is calculated from the formula $x = \frac{ab^{2}}{c^{3}}.$ The percentage errors in $a,b,c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively. The percentage error in $x$ can be
A) $\pm 1\%$
B) $\pm 4\%$
C) $7\%$
D) $\pm 13\%$
Explanation
Percentage error in $x = 1\% + 2 \times 3\% + 3 \times 2\% = 13\%$. The sign$\ \pm \$ has been used because the words `maximum percentage error’ have not been used. Note percentage error is $\pm$ $\frac{\mathrm{\Delta}A}{A} \times 100$ Maximum percentage error is $\frac{\mathrm{\Delta}A}{A} \times 100$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.