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. 6.0%
• B. 7.5%
• C. 8.5%
• D. 6.5%

Answer 1

Answer: (D)

Given physical quantity is $A=\frac{P^3{Q}^2}{\sqrt{R}S}$.
Percentage error is given by
$\frac{\Delta A}{A}\times 100=3\frac{\Delta P}{P}\times 100+2\frac{\Delta Q}{Q}\times 100\times \frac{1}{2}\times \frac{\Delta R}{R}\times 100+\frac{\Delta S}{S}\times 10$
$=3\times \frac{0.5}{100}\times 100+2\times \frac{1}{100}\times 100+\frac{1}{2}\times \frac{3}{100}\times 100+\frac{1.5}{100}\times 100$
$=1.5+2+1.5+1.5$
$\frac{\Delta A}{A}\times 100=6.5$
$\Rightarrow \frac{\Delta A}{A}=\frac{6.5}{100}=6.5\%$