A physical quantity \(Q\) is given by:\(Q=\frac{a{b}^{4}}{cd}\).If the percentage errors in \(a,b,c\) and \(d\) are 2% …
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A physical quantity \(Q\) is given by:\(Q=\frac{a{b}^{4}}{cd}\).If the percentage errors in \(a,b,c\) and \(d\) are 2%, 1%, 2%, and 1% respectively, determine the percentage error in \(Q\).
(Shift - II Memory Based)
✓ Correct answer: c)
9%
Explanation
We are given the equation:
\(Q=\frac{a{b}^{4}}{cd}\)
To determine the percentage error \(Q\), we use the error propagation rule:
\(\frac{\Delta Q}{Q}=\frac{\Delta a}{a}+4\frac{\Delta b}{b}+\frac{\Delta c}{c}+\frac{\Delta d}{d}\)
Step 1: Substituting Given Errors- Percentage error in a = 2%
- Percentage error in b = 1%
- Percentage error in c = 2%
- Percentage error in d = 1%
Now, substituting these values into the equation:
\(\text{Percentage error in }Q=2+4(1)+2+1\) \(=2+4+2+1=9\mathrm{%}\)
Final Answer:\(C\ 9\mathrm{%}\)C
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