Question 197: 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: