when the result involves the division of two quantity find the maximum possible error. Z=A^nB^m
Answers
Answer:
Thinking............
Explanation:
different mathematical operations such as addition, subtraction, multiplication, division, etc., the errors in the individual measurements of physical quantities combine. The pattern of combination of errors depends upon the nature of the mathematical operation carried out on physical quantities. Thus, the error in the final result depends not only on the nature of the mathematical operation but also on the errors in the individual measurements.
When the result involves the sum of two observed quantities
The maximum possible error is the sum of the maximum absolute errors in the physical quantities. For example, if A + B are two quantities and ‘ Z’ is the absolute error in ‘Z’, then we can write:
Z = A B
Z = ( A + B)
i.e., Z = A + B ( maximum possible error)
When the result involves the difference of two observed quantities
The maximum possible error is again the sum of the maximum absolute errors in the physical quantities.
Z = ( A + B)
When the result involves the product of two observed quantities
The maximum relative error in the result is the sum of the maximum relative errors in the quantities.
i.e.,
In term of percentage,
When the result involves the quotient (division) of two observed quantities
The maximum relative error of the result is the sum of the maximum relative errors of the quantities,
i.e.,
Percentage relative error =
When the result involves the product of some powers of the measured values
A quantity with a power ‘n’ greater than one is an expression, then its error contribution to the final result increases ‘n’ times,
e.g., Z = AnBm
Then
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