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

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(C) Given,percentage errors in $a, b, c$ and $d$ are $\frac{\Delta a}{a} 	imes 100 = 2\%$,$\frac{\Delta b}{b} 	imes 100 = 1\%$,$\frac{\Delta c}{c} \

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(C) Given,percentage errors in $a, b, c$ and $d$ are $\frac{\Delta a}{a} 	imes 100 = 2\%$,$\frac{\Delta b}{b} 	imes 100 = 1\%$,$\frac{\Delta c}{c} 	imes 100 = 3\%$ and $\frac{\Delta d}{d} 	imes 100 = 5\%$.The quantity $P$ is given by $P = \frac{a^2 b^2}{c d}$.The relative error in $P$ is given by the formula:$\frac{\Delta P}{P} = 2 \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{\Delta d}{d}$To find the percentage error,multiply by $100$:$\frac{\Delta P}{P} 	imes 100 = 2 \left( \frac{\Delta a}{a} 	imes 100 ight) + 2 \left( \frac{\Delta b}{b} 	imes 100 ight) + \left( \frac{\Delta c}{c} 	imes 100 ight) + \left( \frac{\Delta d}{d} 	imes 100 ight)$Substituting the given values:$\frac{\Delta P}{P} \% = 2(2\%) + 2(1\%) + 3\% + 5\%$$\frac{\Delta P}{P} \% = 4\% + 2\% + 3\% + 5\% = 14\%$Thus,the percentage error in $P$ is $14\%$.

In an experiment,four quantities $a, b, c, d$ are measured with percentage errors $2\%$,$1\%$,$3\%$ and $5\%$,respectively. Quantity $P$ is calculated as $P = \frac{a^2 b^2}{c d}$. Find the percentage error in measuring $P$. (in $\%$)

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