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 $A=\frac{P^3{Q}^2}{\sqrt{R}S}$.
The maximum percentage error in the value of $A$ will be

• A. $8.5\%$
• B. $6.0\%$
• C. $7.5\%$
• D. $6.5\%$

Answer 1

The correct option is D $6.5\%$

Percentage error $\frac{\Delta A}{A}\times 100=3\frac{\Delta P}{P}\times 100+2\frac{\Delta Q}{Q}+\frac{1}{2}\frac{\Delta R}{R}\times 100+\frac{\Delta S}{S}\times 100$

$=3\times 0.5+2\times 1+0.5\times 3+1.5=6.5$