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

Answer 1

Answer: (A)

$100\times \left(\frac{\Delta A}{A}\right)=\left(\frac{3 \Delta P}{P} + \frac{2 \Delta Q}{Q} + \frac{1}{2} \frac{\Delta R}{R} + \frac{\Delta S}{S} \, \right)\times 100$
max percentage error, $A=3 \, \times 0.5+2 \, \times 1+\frac{1}{2} \, \times 3+1.5$
$=1.5+2+1.5+1.5$
$=6.5 \, \%$