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Question 30157
JEE Physics · Hard

Errors and Measurements: Error Propagation — Subtraction MCQ

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Error Propagation — SubtractionHardQuestion 30157

Question

X = A − B. If A = 50.0 ± 0.1 and B = 49.5 ± 0.1, then X and its relative error are:
  1. A
    0.5 ± 40%
  2. B
    0.5 ± 4%
  3. C
    0.5 ± 0.2 and 40%
    Correct
  4. D
    0.5 ± 0.1 and 20%

Correct answer

0.5 ± 0.2 and 40%

Explanation

X = 0.5, ΔX = 0.1+0.1 = 0.2. Relative error = 0.2/0.5 × 100 = 40%. This shows why subtracting nearly equal quantities amplifies relative error enormously.

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