A physical quantity Q is found to depend on o | vedclass

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Question

(C) Given the relation: $Q = \frac{x^3 y^2}{z}$.Using the formula for propagation of errors,the relative error in $Q$ is given by: $\frac{\Delta Q}{Q}

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) Given the relation: $Q = \frac{x^3 y^2}{z}$.Using the formula for propagation of errors,the relative error in $Q$ is given by: $\frac{\Delta Q}{Q} = 3 \frac{\Delta x}{x} + 2 \frac{\Delta y}{y} + \frac{\Delta z}{z}$.Given percentage errors:$\frac{\Delta x}{x} 	imes 100 = 1\%$$\frac{\Delta y}{y} 	imes 100 = 2\%$$\frac{\Delta z}{z} 	imes 100 = 4\%$Substituting these values into the error equation:$\frac{\Delta Q}{Q} 	imes 100 = 3(1\%) + 2(2\%) + 1(4\%)$$= 3\% + 4\% + 4\% = 11\%$.Therefore,the percentage error in $Q$ is $11\%$.

$A$ physical quantity $Q$ is found to depend on observables $x, y$ and $z$,obeying the relation $Q = \frac{x^3 y^2}{z}$. The percentage errors in the measurements of $x, y$ and $z$ are $1\%, 2\%$ and $4\%$ respectively. What is the percentage error in the quantity $Q$ (in $\%$)?

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