An experiment measures quantities a, b and c, and quantity X is calculated from X= ab2/c3. If the percentage error in a, b and c are ± 1 %, ± 3 % and ± 2 %, respectively, then the percentage error in X will be

Question

An experiment measures quantities a, b and c, and quantity X is calculated from X= ab2/c3. If the percentage error in a, b and c are ± 1 %, ± 3 % and ± 2 %, respectively, then the percentage error in X will be (A) ± 13 % (B) ± 7 % (C) ± 4 % (D) ± 1 %

Tardigrade Admin · Accepted Answer

(Δ x/x)=(Δ a/a)+2(Δ b/b)+3(Δ c/c) =±1 %+2(±3 %)+3(±2 %) =±1 %±6 %±6 % =±13 %

Q. An experiment measures quantities $a$ , $b$ and $c$ , and quantity $X$ is calculated from $X = a b^{2} / c^{3}$ . If the percentage error in $a$ , $b$ and $c$ are $\pm 1%$ , $\pm 3%$ and $\pm 2%$ , respectively, then the percentage error in $X$ will be

$\pm 13%$

$\pm 7%$

$\pm 4%$

$\pm 1%$

$\pm$ 3%

$\frac{Δ x}{x} = \frac{Δ a}{a} + 2 \frac{Δ b}{b} + 3 \frac{Δ c}{c}$
$= \pm 1% + 2 (\pm 3%) + 3 (\pm 2%)$
$= \pm 1% \pm 6% \pm 6%$
$= \pm 13%$

Q. An experiment measures quantities a, b and c, and quantity X is calculated from X=ab2/c3. If the percentage error in a, b and c are ±1%, ±3% and ±2%, respectively, then the percentage error in X will be

±13%

±7%

±4%

±1%

± 3%

xΔx​=aΔa​+2bΔb​+3cΔc​ =±1%+2(±3%)+3(±2%) =±1%±6%±6% =±13%