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Q.

An experiment measures quantities a, b, and c, and then X is calculated from $X = \frac{a^{1 / 2} b^{2}}{c^{3}}$ . If the percentage errors in a, b, and c are $\pm 1 %, \pm 3 %, and \pm 2 %$ , respectively, then the percentage error in X can be

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a

$\pm 12.5 %$

b

$\pm 7 %$

c

$\pm 1 %$

d

$\pm 4 %$

answer is A.

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Detailed Solution

$\begin{array}{l} X = \frac{a^{1 / 2} b^{2}}{c^{3}} \\ \begin{aligned} \frac{Δ X}{X} \times 100 & = \frac{1}{2} \frac{Δ a}{a} \times 100 + 2 \frac{Δ b}{b} \times 100 + 3 \frac{Δ c}{c} \times 100 \\ = \frac{1}{2} \times 1 + 2 \times 3 + 3 \times 2 = 12.5 % \end{aligned} \end{array}$

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