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
$\frac{\Delta A}{A} \times 100 = 3 \frac{\Delta P}{P} \times 100+2 \frac{\Delta Q}{Q} \times 100 \times \frac{1}{2} \times \frac{\Delta R}{R} \times 100+\frac{\Delta S}{S} \times 10$
$=3 \times \frac{0.5}{100} \times 100+2 \times \frac{1}{100} \times 100+\frac{1}{2} \times \frac{3}{100} \times 100+\frac{1.5}{100} \times 100$
$=1.5+2+1.5+1.5$
$\frac{\Delta A}{A} \times 100 =6.5$
$\Rightarrow \frac{\Delta A}{A}=\frac{6.5}{100}=6.5 \%$