What is the percentage error in the physical quantity A If it is related to four other physical quantities a , b , c and d as A=(a2 b3/d √c) ? The percentage error in measurement of a , b , c and d are 1 % , 3 % , 2 % and 1 % respectively.

Question

What is the percentage error in the physical quantity A If it is related to four other physical quantities a , b , c and d as A=(a2 b3/d √c) ? The percentage error in measurement of a , b , c and d are 1 % , 3 % , 2 % and 1 % respectively. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Percentage error in A =2(Δ a/a)+3(Δ b/b)+(1/2)(Δ c/c)+(Δ d/d) =(2 × 1 + 3 × 3 + (1/2) × 2 + 1 × 1) %=13 %

Q. What is the percentage error in the physical quantity $A$ If it is related to four other physical quantities $a$ , $b$ , $c$ and $d$ as $A = \frac{a ^{2} b ^{3}}{d c}$ ? The percentage error in measurement of $a$ , $b$ , $c$ and $d$ are $1%$ , $3%$ , $2%$ and $1%$ respectively.

Percentage error in $A$
$= 2 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + \frac{1}{2} \frac{Δ c}{c} + \frac{Δ d}{d}$
$= (2 \times 1 + 3 \times 3 + \frac{1}{2} \times 2 + 1 \times 1) % = 13%$

Q. What is the percentage error in the physical quantity A If it is related to four other physical quantities a , b , c and d as A=dc​a2b3​ ? The percentage error in measurement of a , b , c and d are 1% , 3% , 2% and 1% respectively.

Percentage error in A =2aΔa​+3bΔb​+21​cΔc​+dΔd​ =(2×1+3×3+21​×2+1×1)%=13%

Q. What is the percentage error in the physical quantity $A$ If it is related to four other physical quantities $a$ , $b$ , $c$ and $d$ as $A = \frac{a ^{2} b ^{3}}{d c}$ ? The percentage error in measurement of $a$ , $b$ , $c$ and $d$ are $1%$ , $3%$ , $2%$ and $1%$ respectively.

Percentage error in $A$
$= 2 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + \frac{1}{2} \frac{Δ c}{c} + \frac{Δ d}{d}$
$= (2 \times 1 + 3 \times 3 + \frac{1}{2} \times 2 + 1 \times 1) % = 13%$