Question:
A physical quantity A can be determined by measuring parameters \(\mathrm{B}, \mathrm{C}, \mathrm{D}\) and E using the relation \(A=\frac{B^a C^\beta}{D^\gamma E^\delta}\). If the maximum errors in the measurement are \(\mathrm{b} \%, \mathrm{c} \%, \mathrm{~d} \%\) and \(\mathrm{e} \%\) then maximum error in the value of A is
A physical quantity A can be determined by measuring parameters \(\mathrm{B}, \mathrm{C}, \mathrm{D}\) and E using the relation \(A=\frac{B^a C^\beta}{D^\gamma E^\delta}\). If the maximum errors in the measurement are \(\mathrm{b} \%, \mathrm{c} \%, \mathrm{~d} \%\) and \(\mathrm{e} \%\) then maximum error in the value of A is
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For a product of powers, maximum percentage errors add up, each multiplied by its power.
Updated On: Nov 13, 2026
- \((\alpha b+\beta c-\gamma d-\delta e)\%\)
- \((b+c-d-e)\%\)
- \((\alpha b+\beta c+\gamma d+\delta e)\%\)
- \((b+c+d+e)\%\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
For \(A=\dfrac{B^{\alpha}C^{\beta}}{D^{\gamma}E^{\delta}}\), the maximum fractional error is the sum of each power times the fractional error of that quantity.
Step 2: Applying the rule
Division does not subtract errors; every term is added in the worst case.
Step 3: Result
\(\dfrac{\Delta A}{A}\times100=(\alpha b+\beta c+\gamma d+\delta e)\%\), which is option (C).
Final Answer:
The maximum percentage error in A is alpha b plus beta c plus gamma d plus delta e. \[ \boxed{\text{(C) }(\alpha b+\beta c+\gamma d+\delta e)\%} \]
For \(A=\dfrac{B^{\alpha}C^{\beta}}{D^{\gamma}E^{\delta}}\), the maximum fractional error is the sum of each power times the fractional error of that quantity.
Step 2: Applying the rule
Division does not subtract errors; every term is added in the worst case.
Step 3: Result
\(\dfrac{\Delta A}{A}\times100=(\alpha b+\beta c+\gamma d+\delta e)\%\), which is option (C).
Final Answer:
The maximum percentage error in A is alpha b plus beta c plus gamma d plus delta e. \[ \boxed{\text{(C) }(\alpha b+\beta c+\gamma d+\delta e)\%} \]
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