A physical quantity Q is related to four observables a, b, c, d as follows: , , then the percentage error in Q is , where x = __________. [2025]

Question

A physical quantity Q is related to four observables a, b, c, d as follows:

$Q = \frac{a b^{4}}{c d} where, a = (60 \pm 3) P a; b = (20 \pm 0.1) m$ ,

$c = (40 \pm 0.2) {Nsm}^{- 2} and d = (50 \pm 0.1) m$ ,

then the percentage error in Q is $\frac{x}{1000}$ , where x = __________. [2025]

Smart Achievers · Accepted Answer

(77)

$Q = \frac{a b^{4}}{c d}$

$\Rightarrow \frac{△ Q}{Q} = [\frac{△ a}{a} + 4 \frac{△ b}{b} + \frac{△ c}{c} + \frac{△ d}{d}]$

$\Rightarrow \frac{x}{1000} = [\frac{3}{60} + 4 (\frac{0.1}{20}) + (\frac{0.2}{40}) + \frac{0.1}{50}]$

$\Rightarrow x = 77$

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