A quantity z,to be estimated,has a dependency | vedclass

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(D) Given the relation: $z = a b^2 c^{-2}$.According to the theory of propagation of errors,the relative error in $z$ is given by:$\frac{\Delta z}{z}

Vedclass · Accepted Answer

$9.1$

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(D) Given the relation: $z = a b^2 c^{-2}$.According to the theory of propagation of errors,the relative error in $z$ is given by:$\frac{\Delta z}{z} = \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + 2 \frac{\Delta c}{c}$.To find the percentage error,multiply the entire equation by $100$:$\frac{\Delta z}{z} 	imes 100 = \left( \frac{\Delta a}{a} 	imes 100 ight) + 2 \left( \frac{\Delta b}{b} 	imes 100 ight) + 2 \left( \frac{\Delta c}{c} 	imes 100 ight)$.Substituting the given percentage errors:$\frac{\Delta z}{z} 	imes 100 = 2.1 \% + 2(1.3 \%) + 2(2.2 \%)$.$\frac{\Delta z}{z} 	imes 100 = 2.1 \% + 2.6 \% + 4.4 \% = 9.1 \%$.Therefore,the percentage error in $z$ is $9.1 \%$.

$A$ quantity $z$,to be estimated,has a dependency on the variables $a, b$ and $c$ as $z = a b^2 c^{-2}$. The percentage errors in the measurement of $a, b$ and $c$ are $2.1 \%$,$1.3 \%$ and $2.2 \%$,respectively. The percentage error in the measurement of $z$ would then be: (in $\%$)

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