In an experiment,four quantities a, b, c and | vedclass

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(B) Given the formula $P = \frac{a^3 b^2}{cd}$.To find the relative error in $P$,we use the formula for propagation of errors:$\frac{\Delta P}{P} = 3

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(B) Given the formula $P = \frac{a^3 b^2}{cd}$.To find the relative error in $P$,we use the formula for propagation of errors:$\frac{\Delta P}{P} = 3 \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{\Delta d}{d}$.Given percentage errors are $\frac{\Delta a}{a} 	imes 100 = 1\%$,$\frac{\Delta b}{b} 	imes 100 = 2\%$,$\frac{\Delta c}{c} 	imes 100 = 3\%$,and $\frac{\Delta d}{d} 	imes 100 = 4\%$.Substituting these values:$\frac{\Delta P}{P} 	imes 100 = 3(1\%) + 2(2\%) + 3\% + 4\%$.$\frac{\Delta P}{P} 	imes 100 = 3\% + 4\% + 3\% + 4\% = 14\%$.Thus,the percentage error in $P$ is $14\%$.

In an experiment,four quantities $a, b, c$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as $P = \frac{a^3 b^2}{cd}$. The percentage error in the measurement of $P$ is .......... $\%$

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