Correct Answer - Option 1 : the sum of the relative errors in the two quantities
The correct answer is option 1) i.e. the sum of the relative errors in the two quantities
CONCEPT:
-
Combination of errors: When physical quantities involving a mathematical operation have errors associated with them, there will be an error in the result arising from its combination.
- This is identified based on the following rules:
- The error of a sum or a difference: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = A ± B is given by:
± ΔZ = ± ΔA ± ΔB
- The error of a product or a quotient: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = AB or Z = A ÷ B is given by:
\( \frac{\Delta Z}{ Z} = \frac{∆A}{A} + \frac{∆B}{B}\)
- The error in case of a measured quantity raised to a power:
If Z = Ax then
\(\frac{\Delta Z}{Z} = x\frac{\Delta A}{A}\)
EXPLANATION:
- When two quantities A and B are multiplied or divided, the error in their result Z is given by:
\( \frac{\Delta Z}{ Z} = \frac{∆A}{A} + \frac{∆B}{B}\).
- So, the relative error in their result is the sum of the relative errors in the two quantities.
