Let x = frac{a^2 b^2}{c} be a physical quanti | vedclass

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(B) The given physical quantity is $x = \frac{a^2 b^2}{c}$.Using the formula for propagation of errors,the relative error in $x$ is given by:$\frac{\D

Vedclass · Accepted Answer

$14$

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(B) The given physical quantity is $x = \frac{a^2 b^2}{c}$.Using the formula for propagation of errors,the relative error in $x$ is given by:$\frac{\Delta x}{x} = 2 \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + \frac{\Delta c}{c}$.Given percentage errors are $\frac{\Delta a}{a} 	imes 100 = 2\%$,$\frac{\Delta b}{b} 	imes 100 = 3\%$,and $\frac{\Delta c}{c} 	imes 100 = 4\%$.Substituting these values into the error equation:$\frac{\Delta x}{x} 	imes 100 = 2(2\%) + 2(3\%) + 4\%$.$\frac{\Delta x}{x} 	imes 100 = 4\% + 6\% + 4\% = 14\%$.Therefore,the percentage error in $x$ is $14\%$.

Let $x = \frac{a^2 b^2}{c}$ be a physical quantity. If the percentage errors in the measurement of physical quantities $a, b,$ and $c$ are $2\%, 3\%,$ and $4\%$ respectively,then the percentage error in the measurement of $x$ is: (in $\%$)

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