Question

In the given formula $A=\frac{xy}{\sqrt{z}}$. The percentage errors of measurements in $x,y$ and $z$ are $2\%,3\%$ and $1\%$ respectively. What is the percentage error in quantity $A$ ?

• A. $5\%$
• B. $5.5\%$
• C. $6\%$
• D. $6.5\%$

Answer 1

The correct option is B $5.5\%$

$A=\frac{xy}{\sqrt{z}}$
$\frac{\Delta A}{A}\times 100=(\frac{\Delta x}{x}\times 100)+(\frac{\Delta y}{y}\times 100)+\frac{1}{2}(\frac{\Delta z}{z}\times 100)$

$=2+3+\frac{1}{2}\left(1\right)$

$(\frac{\Delta A}{A}\times 100)=5.5\%$

$\%$ Error in $A$ is $5.5\%$