Question 211: Units , Dimensions and Error Analysis

Question

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = ${{{P^3}{Q^2}} \over {\sqrt R S}}.$
The maximum percentage error in the value of A will be :

Accepted Answer

Given,
A = ${{{P^3}{Q^2}} \over {\sqrt R S}}$
$	herefore\,\,\,\,$ ${{\Delta A} \over A}$ = 3 ${{\Delta P} \over P}$ + 2 ${{\Delta Q} \over Q}$ + ${1 \over 2}$ ${{\Delta R} \over R}$ + ${{\Delta S} \over S}$
Maximum percentage error in the value of A is
${{\Delta A} \over A}$ $ 	imes $ 100 = 3 $ 	imes $  0.5 + 2 $ 	imes $ 1 + ${1 \over 2}$ $ 	imes $ 3 + 1 $ 	imes $ 1.5
= 6.5 %

Answer

6.0%

Answer

7.5%

Answer

8.5%

Answer

6.5%

Units , Dimensions and Error Analysis

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = {{{P^3}{Q^2}} \over {\sqrt R S}}. The maximum percentage error in the value of A will be :

Choose the correct answer: