A physical quantity A is related to four observables a, b, c and d as follows A=(a2b3/c√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?

Question

A physical quantity A is related to four observables a, b, c and d as follows A=(a2b3/c√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? (A) 12% (B) 7% (C) 5% (D) 14%

Tardigrade Admin · Accepted Answer

% error in A=(2 (Δ a/a)+3 (Δ b/b)+(Δ c/c)+(1/2) (Δ d/d)) × 100 =2 × 1+3 × 3+2+(1/2) × 2 =2+9+2+1 =14 %

Q. A physical quantity $A$ is related to four observables $a$ , $b$ , $c$ and $d$ as follows $A = \frac{a ^{2} b ^{3}}{c d}$ 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 $A$ ?

12%

7%

5%

14%

$%$ error in
$A = (2 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + \frac{Δ c}{c} + \frac{1}{2} \frac{Δ d}{d}) \times 100$
$= 2 \times 1 + 3 \times 3 + 2 + \frac{1}{2} \times 2$
$= 2 + 9 + 2 + 1$
$= 14%$

Q. A physical quantity A is related to four observables a, b, c and d as follows A=cd​a2b3​ 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?

12%

7%

5%

14%

% error in A=(2aΔa​+3bΔb​+cΔc​+21​dΔd​)×100 =2×1+3×3+2+21​×2 =2+9+2+1 =14%

Q. A physical quantity $A$ is related to four observables $a$ , $b$ , $c$ and $d$ as follows $A = \frac{a ^{2} b ^{3}}{c d}$ 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 $A$ ?

$%$ error in
$A = (2 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + \frac{Δ c}{c} + \frac{1}{2} \frac{Δ d}{d}) \times 100$
$= 2 \times 1 + 3 \times 3 + 2 + \frac{1}{2} \times 2$
$= 2 + 9 + 2 + 1$
$= 14%$