Question:
In an experiment four quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are measured with percentage \(3 \%, 2 \%, 3 \%\) and \(1 \%\) respectively. Quantity ' \(A\) ' is calculated as follows
\(\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}\), the percentage error in ' A ' is
In an experiment four quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are measured with percentage \(3 \%, 2 \%, 3 \%\) and \(1 \%\) respectively. Quantity ' \(A\) ' is calculated as follows
\(\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}\), the percentage error in ' A ' is
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Powers multiply the percentage errors of each quantity, and all contributions are added.
Updated On: Nov 13, 2026
\(17\%\)
\(12\%\)
\(18\%\)
\(19\%\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
For a product or quotient, the maximum percentage error is the sum of each quantity's percentage error multiplied by its power.
Step 2: Apply to A
\(\dfrac{\Delta A}{A}\times100=\dfrac{\Delta p}{p}\times100+2\dfrac{\Delta q}{q}\times100+2\dfrac{\Delta r}{r}\times100+4\dfrac{\Delta s}{s}\times100\).
Step 3: Calculation
\(=3+2(2)+2(3)+4(1)=3+4+6+4=17\%\).
Final Answer:
The percentage error in A is 17 percent. \[ \boxed{\text{(A) }17\%} \]
For a product or quotient, the maximum percentage error is the sum of each quantity's percentage error multiplied by its power.
Step 2: Apply to A
\(\dfrac{\Delta A}{A}\times100=\dfrac{\Delta p}{p}\times100+2\dfrac{\Delta q}{q}\times100+2\dfrac{\Delta r}{r}\times100+4\dfrac{\Delta s}{s}\times100\).
Step 3: Calculation
\(=3+2(2)+2(3)+4(1)=3+4+6+4=17\%\).
Final Answer:
The percentage error in A is 17 percent. \[ \boxed{\text{(A) }17\%} \]
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