A physical quantity z depends on four observa | vedclass

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(B) The given relation is $z = \frac{a^2 b^{2/3}}{c^{1/2} d^3}$.The relative error in $z$ is given by the formula: $\frac{\Delta z}{z} = 2 \frac{\Delt

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$14$

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(B) The given relation is $z = \frac{a^2 b^{2/3}}{c^{1/2} d^3}$.The relative error in $z$ is given by the formula: $\frac{\Delta z}{z} = 2 \frac{\Delta a}{a} + \frac{2}{3} \frac{\Delta b}{b} + \frac{1}{2} \frac{\Delta c}{c} + 3 \frac{\Delta d}{d}$.Given percentage errors are: $\frac{\Delta a}{a} 	imes 100 = 2\%$,$\frac{\Delta b}{b} 	imes 100 = 1.5\%$,$\frac{\Delta c}{c} 	imes 100 = 4\%$,and $\frac{\Delta d}{d} 	imes 100 = 2.5\%$.Substituting these values into the error formula:$\frac{\Delta z}{z} 	imes 100 = 2(2\%) + \frac{2}{3}(1.5\%) + \frac{1}{2}(4\%) + 3(2.5\%)$.$\frac{\Delta z}{z} 	imes 100 = 4\% + 1\% + 2\% + 7.5\% = 14.5\%$.Thus,the percentage error in $z$ is $14.5\%$.

$A$ 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 percentage errors in the measurement of $a, b, c$ and $d$ are $2\%, 1.5\%, 4\%$ and $2.5\%$ respectively. The percentage error in $z$ is $......\%$. (in $.5$)

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