Question

A physical quantity $A$ is related to four observabels a,b,c and d as follows, $A=\frac{a^2{b}^2}{c\sqrt{d}}$, 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. $14\%$
  
• C. $7\%$
• D. $5\%$

Answer 1

The correct option is B $14\%$


Given,
$A=\frac{a^2{b}^3}{c\sqrt{d}}$
$\frac{\Delta a}{a}\times 100=1\%$
$\frac{\Delta b}{b}\times 100=3\%$
$\frac{\Delta c}{c}\times 100=2\%$
$\frac{\Delta d}{d}\times 100=2\%$
Pecentage error in $A$
$A=\frac{\Delta A}{A}\times 100$
$=2\frac{\Delta a}{a}\times 100+3\frac{\Delta b}{b}\times 100+\frac{\Delta c}{c}\times 100+\frac{1}{2}\times \frac{\Delta a}{d}\times 100$
$=\frac{\Delta A}{A}\times 100=2\times 1+3\times 3+2+\frac{1}{2}\times 2$
$=14\%$