A physical quantity $z$ depends on four observables $a, b, c$ and $d$, as $z=\frac{a^{2} b^{2 / 3}}{

Question

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

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(d) : Here, $z=\frac{a^2 b^{2 / 3}}{\sqrt{c} d^3}$ $ \  \begin{aligned} & \frac{\Delta z}{z}=\frac{2 \Delta a}{a}+\frac{2}{3} \frac{\Delta b}{b}+\frac{1}{2} \frac{\Delta c}{c}+\frac{3 \Delta d}{d} \ & \left(\frac{\Delta z}{z} 	imes 100ight) \%=\left(\frac{2 \Delta a}{a}+\frac{2}{3} \frac{\Delta b}{b}+\frac{1}{2} \frac{\Delta c}{c}+\frac{3 \Delta d}{d}ight) 	imes 100 \% \end{aligned} $ \  $	herefore \quad$  The percentage error in $z$, \ $ =\left(2 	imes 2+\frac{2}{3} 	imes 1.5+\frac{1}{2} 	imes 4+3 	imes 2.5ight) \%=14.5 \% $