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A physical quantity $z$ depends on four observables $a, b, c$ and $d$ , as $z = \frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}}$ . The percentages of error in the measurement of $a, b, c$ and $d$ are $2 %$ , $1.5 %, 4 % a n d 2.5 %$ respectively. The percentage of error in $z$ is:

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$13.5 %$

$14.5 %$

$16.5 %$

$12.25 %$

answer is A.

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Detailed Solution

$\begin{array}{l} %error in Z =2 (%error in a) + (\frac{2}{3}) (%error in b) + \frac{1}{2} (%error in c) +3 (%error in d) \\ = (2×2) + (\frac{2}{3} (1.5)) + (\frac{1}{2} ×4) + (3 (2.5)) =14.5% \end{array}$

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