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If the percentage uncertainties in measuring mass M, length L, and time T are 1%, 1.5%, and 3% respectively, what is the percentage error in a quantity having dimensions M L⁻¹ T⁻¹?
- 1%
- 3.5%
- 3%
- 5.5%
Correct answer: 5.5%
Solution
The percentage error in a derived quantity can be calculated by summing the percentage uncertainties of its constituent measurements, weighted by their respective dimensions. In this case, the quantity M L⁻¹ T⁻¹ has a percentage error of 1% from mass, 1.5% from length (which is inverted, thus it contributes negatively), and 3% from time, resulting in a total of 5.5%.
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