An experiment measures quantities a, b, c and X as X=ab2c3 ; if the percentage errors in a, b, c are + 1%; +3%; +2% respectively, the percentage error in X is

ΔXX =Δaa+2(Δbb)+3(Δcc)% ΔXX =1+2(3)+3(2) =±13%

An experiment measures quantities a, b, c and X as X=ab2c3 ; if the percentage errors in a, b, c are + 1%; +3%; +2% respectively, the percentage error in X is

ΔXX =Δaa+2(Δbb)+3(Δcc)% ΔXX =1+2(3)+3(2) =±13%

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An experiment measures quantities a, b, c and $X as X= \frac{{ab}^{2}}{c^{3}};$ if the percentage errors in a, b, c are + 1%; +3%; +2% respectively, the percentage error in $X$ is

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$\pm 1 %$

$\pm 7 %$

$\pm 13 %$

$\pm 4 %$

answer is A.

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Detailed Solution

$\frac{Δ X}{X} = \frac{Δ a}{a} + 2 (\frac{Δ b}{b}) + 3 (\frac{Δ c}{c})$

$% \frac{Δ X}{X} = 1 + 2 (3) + 3 (2) = \pm 13 %$

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An experiment measures quantities a, b, c and X as X=ab2c3 ; if the percentage errors in a, b, c are + 1%; +3%; +2% respectively, the percentage error in X is

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An experiment measures quantities a, b, c and $X as X= \frac{{ab}^{2}}{c^{3}};$ if the percentage errors in a, b, c are + 1%; +3%; +2% respectively, the percentage error in $X$ is