In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as, $\displaystyle P=\frac{a^3b^2}{cd}$ . Error in P is

Answer (1)

Given,

$\displaystyle \frac{\Delta a}{a}\times 100=1\% ,\ \frac{\Delta b}{b}\times 100=2\%$

$\displaystyle \frac{\Delta c}{c}\times 100=3\%,\ \frac{\Delta d}{d} \times 100=4\%$

Also, $\displaystyle P=\frac{a^3b^2}{cd}$

$\displaystyle \begin{aligned}\therefore \frac{\Delta P}{P}\times 100 &=\Bigg( \frac{3\Delta a}{a} +\frac{2\Delta b}{b}+\frac{\Delta c}{c}+\frac{\Delta d}{d}\Bigg)\times 100\\&=(3\times 1+2\times 2+3+4)\% =14\% \end{aligned}$