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(D) Given the relation: $A = \frac{a^2 b^3}{c \sqrt{d}}$The percentage errors are given as:$\frac{\Delta a}{a} 	imes 100 = 1\%$$\frac{\Delta b}{b}

Vedclass · Accepted Answer

$14$

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(D) Given the relation: $A = \frac{a^2 b^3}{c \sqrt{d}}$The percentage errors are given as:$\frac{\Delta a}{a} 	imes 100 = 1\%$$\frac{\Delta b}{b} 	imes 100 = 3\%$$\frac{\Delta c}{c} 	imes 100 = 2\%$$\frac{\Delta d}{d} 	imes 100 = 2\%$The relative error in $A$ is given by the formula:$\frac{\Delta A}{A} = 2 \frac{\Delta a}{a} + 3 \frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{1}{2} \frac{\Delta d}{d}$Multiplying by $100$ to get the percentage error:$\frac{\Delta A}{A} 	imes 100 = 2 \left( \frac{\Delta a}{a} 	imes 100 ight) + 3 \left( \frac{\Delta b}{b} 	imes 100 ight) + \left( \frac{\Delta c}{c} 	imes 100 ight) + \frac{1}{2} \left( \frac{\Delta d}{d} 	imes 100 ight)$Substituting the given values:$\frac{\Delta A}{A} 	imes 100 = 2(1\%) + 3(3\%) + 2\% + \frac{1}{2}(2\%)$$\frac{\Delta A}{A} 	imes 100 = 2\% + 9\% + 2\% + 1\% = 14\%$Thus,the percentage error in $A$ is $14\%$.

$A$ physical quantity $A$ is related to four observables $a, b, c,$ and $d$ as follows: $A = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors of measurement in $a, b, c,$ and $d$ are $1\%, 3\%, 2\%,$ and $2\%$ respectively. What is the percentage error in the quantity $A$?

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