Search any question & find its solution
Question:
Answered & Verified by Expert
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 \( \mathrm{Q} \) ?
Options:
\( Q=\frac{x^{3} y^{2}}{z} \). The percentage error in the measurements of \( x, y \) and \( z \) are \( 1 \%, 2 \% \) and \( 4 \% \)
respectively. What is percentage error in the quantity \( \mathrm{Q} \) ?
Solution:
1676 Upvotes
Verified Answer
The correct answer is:
\( 11 \% \)
$Q=\frac{x^{3} y^{2}}{z}$
Percentage error in measurements of $x=1 \%$
Percentage error in measurements of $y=2 \%$
Percentage error in measurements of $z=4 \%$
Percentage error in $Q=\frac{\Delta Q}{Q}=3 \frac{\Delta x}{x}+2 \frac{\Delta y}{y}+\frac{\Delta z}{z}$
$=3 \times 1+2 \times 2+4=11 \%$
Percentage error in measurements of $x=1 \%$
Percentage error in measurements of $y=2 \%$
Percentage error in measurements of $z=4 \%$
Percentage error in $Q=\frac{\Delta Q}{Q}=3 \frac{\Delta x}{x}+2 \frac{\Delta y}{y}+\frac{\Delta z}{z}$
$=3 \times 1+2 \times 2+4=11 \%$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.