Question:
A physical quantity $P$ is described by the relation $P = a^{1/2} b^2 c^3 d^{-4} $
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\%, 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be :
A physical quantity $P$ is described by the relation $P = a^{1/2} b^2 c^3 d^{-4} $
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\%, 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be :
Updated On: Apr 28, 2025
- 8%
- 12%
- 32%
- 25%
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$\frac{\Delta p}{p}=\frac{1}{2} \frac{\Delta a}{a}+2 \frac{\Delta b}{b}+3 \frac{\Delta c}{c}+4 \frac{\Delta d}{d}$
$\frac{1}{2}\times2+2\times 1+3\times 3+4\times 5$
$=32\%$
$\frac{1}{2}\times2+2\times 1+3\times 3+4\times 5$
$=32\%$
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