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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:
A
4%
B
14%
C
10%
D
7%
Detailed Solution
$\frac{\Delta P}{P} = \pm\left(3\frac{\Delta a}{a} + 2\frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{\Delta d}{d}\right)$
$= \pm(3\times1 + 2\times2 + 3 + 4) = \pm14\%$
$= \pm(3\times1 + 2\times2 + 3 + 4) = \pm14\%$