Question

When two quantities are added or subtracted then the absolute error will be equal to the-
1. product of the absolute error of the individual quantities
2. mean of the sum of the absolute error of the individual quantities
3. sum of the absolute error of the individual quantities 
4. difference in the absolute error of the individual quantities

Answer 1

Correct Answer - Option 3 : sum of the absolute error of the individual quantities 

CONCEPT:

• Error: It is the uncertainty in measurement by any measuring instrument.

Error in measurement can be broadly classified

1. Systematic errors 
2. Random errors.

• The relative error is the ratio of mean absolute error to the mean value of the quantity measured.

EXPLANATION:

• When two quantities are added or subtracted absolute error in the final result is sum of the absolute error of the individual quantities.

Let the two physical quantities A and B have measured value A ± Δ A and B ± Δ B, where Δ A and Δ B are the absolute errors of A and B respectively

sum Z is given by

⇒  Z = A + B          (i)

So by addition

 ⇒ Z ± Δ Z = ( A ± Δ A )+ (B ± Δ B), where  Δ Z is the maximum error in the sum                     (ii)

So from (i) and (ii), we obtain

 ⇒ ± Δ Z = ± Δ A ± Δ B

Hence option 3) is correct.