Question

In an experiment four quantities a, b,c, and d are measured with percentage error 0.1%, 0.2%, 0.3% and 0.4% respectively. Quantity P is calculated as follow $P=\frac{a^3\sqrt{b}}{c^{2}d}$ percentage error in P is:

Answer 1

$P=\frac{a^3\sqrt{b}}{c^{2}d}$

$⟹\frac{\Delta P}{P}=3\frac{\Delta a}{a}+\frac{1}{2}\frac{\Delta b}{b}+2\frac{\Delta c}{c}+\frac{\Delta d}{d}$

$=3\times 0.1+\frac{1}{2}\times 0.2+2\times 0.3+0.4$

$⟹\frac{\Delta P}{P}=1.4\%$