Question

A physical quantity $Q$ is calculated according to the expression $Q=\frac{A^3{B}^3}{C\sqrt{D}}$. If percentage errors in $A,B,C,D$ are $2\%,1\%,3\%$ and $4\%$ respectively, what is the percentage error in $Q$?

• A. $\pm 8$%
• B. $\pm 10$%
• C. $\pm 14$%
• D. $\pm 12$%

Answer 1

The correct option is C $\pm 14$%

As $Q=\frac{A^3{B}^3}{C\sqrt{D}}$,
% error in Q is given by
$\frac{\Delta Q}{Q}\times 100=\left[3\right(\frac{\Delta A}{A})+3(\frac{\Delta B}{B})+\frac{\Delta C}{C}+\frac{1}{2}(\frac{\Delta D}{D}\left)\right]\times 100$
$=[3\times 2\%+3\times 1\%+3\%+\frac{1}{2}(4\%)$]
$=6\%+3\%+3\%+2\%$
$=\pm 14$%

Why this question? Tip: Remember that fractional errors always get added.