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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 measurement X, where X = A² B¹/² C¹/³ D³ will be:

1. (3/13)%
2. 16%
3. −10%
4. 10%

Correct answer: 16%

Solution

The percentage error in a derived quantity is calculated by summing the absolute percentage errors of each term multiplied by their respective powers. For X = A² B¹/² C¹/³ D³, the maximum percentage error is 2(1%) + (1/2)(2%) + (1/3)(3%) + 3(4%) = 2% + 1% + 1% + 12% = 16%.

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