Q121 / 180 · KCET 2014 · Physics
A physical quantity \( \mathrm{Q} \) is found to depend on observable \( \mathrm{x}, \mathrm{y} \) and \( \mathrm{z} \), obeying relation
\( Q=\frac{x^{3} y^{2}}{z} \). The percentage error in the measurements of \( x, y \) and \( z \) are \( 1 \%, 2 \% \) and \( 4 \% \)
respectively. What is percentage error in the quantity \( \mathrm{Q} \) ?
\( Q=\frac{x^{3} y^{2}}{z} \). The percentage error in the measurements of \( x, y \) and \( z \) are \( 1 \%, 2 \% \) and \( 4 \% \)
respectively. What is percentage error in the quantity \( \mathrm{Q} \) ?
- A(1\%
- B\( 3 \% \)
- Correct answerC\( 11 \% \)
- D\( 1 \% \)
Solution
$Q=\frac{x^{3} y^{2}}{z}$
Percentage error in measurements of $x=1 \%$
Percentage error in measurements of $y=2 \%$
Percentage error in measurements of $z=4 \%$
Percentage error in $Q=\frac{\Delta Q}{Q}=3 \frac{\Delta x}{x}+2 \frac{\Delta y}{y}+\frac{\Delta z}{z}$
$=3 \times 1+2 \times 2+4=11 \%$
Hence, the correct answer is option: 'C'.