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 follows P = \(\frac{a^3b^2}{cd}\). % error in P is :
Answer & explanation
Correct answer: option 2
\(P = \frac{a^3b^2}{cd} \)
\(\frac{\Delta P}{P} = \pm 3\frac{\Delta a}{a} + 2\frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{\Delta d}{d}\)
\(\frac{\Delta P}{P} = \pm (3(1) + 2(2) + 3 + 4)\)
\(\frac{\Delta P}{P} = \pm 14% \)