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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% …

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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)

a

2%

b

5%

c

9%

d

6%

✓ 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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