A quantity z, to be estimated has a dependency on the variables a, b and c as z=a b2 c-2. The percentage of error in the measurement of a, b and c are respectively, 2.1 %, 1.3 % and 2.2 %. The percentage of error in the measurement of z would then be

Question

A quantity z, to be estimated has a dependency on the variables a, b and c as z=a b2 c-2. The percentage of error in the measurement of a, b and c are respectively, 2.1 %, 1.3 % and 2.2 %. The percentage of error in the measurement of z would then be (A) 5.6 % (B) 1.6 % (C) 1.0 % (D) 9.1 %

Tardigrade Admin · Accepted Answer

Given , z =a b2 c-2 So, the percentage error in the volume is given by (Δ z/z) × 100=[(Δ a/a)+2 (Δ b/b)+2 (Δ c/c)] × 100 =2.1 %+2(1.3 %)+2(2.2 %)=9.1 %

Q. A quantity $z$ , to be estimated has a dependency on the variables $a, b$ and $c$ as $z = a b^{2} c^{- 2}$ . The percentage of error in the measurement of $a, b$ and $c$ are respectively, $2.1%, 1.3%$ and $2.2%$ . The percentage of error in the measurement of $z$ would then be

$5.6%$

$1.6%$

$1.0%$

$9.1%$

Given , $z = a b^{2} c^{- 2}$
So, the percentage error in the volume is given by
$\frac{Δ z}{z} \times 100 = [\frac{Δ a}{a} + 2 \frac{Δ b}{b} + 2 \frac{Δ c}{c}] \times 100$
$= 2.1% + 2 (1.3%) + 2 (2.2%) = 9.1%$

Q. A quantity z, to be estimated has a dependency on the variables a,b and c as z=ab2c−2. The percentage of error in the measurement of a,b and c are respectively, 2.1%,1.3% and 2.2%. The percentage of error in the measurement of z would then be

5.6%

1.6%

1.0%

9.1%