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A physical quantity x is related to four measurable quantities a, b, c and d as : $x = a^{2} b^{3} c^{5 / 2} d^{- 2}$ . The percentage error in the measurement of a, b, c and d are 1%,2%,3% and 4% respectively. What is the percentage error in x.

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35.6%

32.4%

33.4%

23.5%

answer is A.

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Detailed Solution

$\frac{Δ x}{x} = 2 [\frac{Δ a}{a}] + 3 (\frac{Δ b}{b}) + \frac{5}{2} (\frac{Δ c}{c}] + 2 [\frac{Δ d}{d}]$ $= 2 (1) + 3 (2) + \frac{5}{2} (3) + 2 (4)$ $= 2 + 6 + 7.5 + 8 = 23.5 %$

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