Question

A physical quantity X is related to four measurable quantities a, b, c and d as given, 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%, 2% and 4% respectively. What is the percentage error in quantity X?

• A. 15%
• B. 17%
• C. 21%
• D. 23%

Answer 1

The correct option is C 21%

$X=a^2{b}^3{c}^{5/2}{d}^{-2}$

Percentage error in X is

$\frac{\Delta X}{x}\times 100=\left[2\right(\frac{\Delta a}{a})+3(\frac{\Delta b}{b})+\frac{5}{2}(\frac{\Delta c}{c})+2(\frac{\Delta d}{d}\left)\right]\times 100$

$=2\times 1+3\times 2+\frac{5}{2}\times 2+2\times 4$

$=21$%

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