Question

A physical quantity A is dependent on other four physical quantities p, q, r and s as given by $A=\frac{\sqrt{pq}}{r^2{s}^3}.$ The percentage error of measurement in p, q, r and s are $1$%, $3$%, $0.5$% and $0.33$% respectively, then the maximum percentage error in A is :

• A. $2$%
• B. $0$%
• C. $4$%
• D. $3$%

Answer 1

The correct option is C $4$%

Using formula for error analysis:
$\frac{\Delta A}{A}=\frac{1}{2}\frac{\Delta p}{p}+\frac{1}{2}\frac{\Delta q}{q}+2\frac{\Delta r}{r}+3\frac{\Delta s}{s}$

$=\frac{1}{2}\times 1+\frac{1}{2}\times 3+2\times 0.5+3\times 0.33=4$
Hence, the percentage of error is $4$%