In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C

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NEET is a competitive examination conducted in India. This question is from the 2019 NEET Physics paper.

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Question

In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = (A2B2) / (C1/3D3), will be:

Accepted Answer

Correct Answer: C — 16%Key Concept: For a quantity X = AaBb / (CcDd), the maximum percentage error is:(ΔX/X) × 100 = a(ΔA/A)×100 + b(ΔB/B)×100 + c(ΔC/C)×100 + d(ΔD/D)×100Step-by-step Solution:Given: X = A2B2 / (C1/3D3)Percentage errors: ΔA/A = 1%, ΔB/B = 2%, ΔC/C = 3%, ΔD/D = 4%Maximum percentage error in X:= 2 × 1% + 2 × 2% + (1/3) × 3% + 3 × 4%= 2% + 4% + 1% + 12%= 16%Why other options are wrong:Option A (10%) and Option D (−10%) do not follow from correct application of the error formula. Percentage error is always additive and positive; Option D is physically meaningless. Option B is a fraction far too small.

In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = (A2B2) / (C1/3D3), will be:

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In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = (A2B2) / (C1/3D3), will be:

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