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In an experiment, the density of a solid sphere is to be found. Its diameter is measured using a screw gauge with pitch 0.5 mm and 50 divisions on the circular scale. The main scale reading is 2.5 mm and the circular scale reading is 20 divisions. If the measured mass of the sphere has a relative error of 2%, what is the relative percentage error in the density?
- 0.9%
- 2.4%
- 3.1%
- 4.2%
Correct answer: 3.1%
Solution
Least count = 0.5/50 = 0.01 mm; diameter = 2.5 + 20*0.01 = 2.7 mm with error 0.01 mm, so dd/d = 0.01/2.7 = 0.37%. Density ~ m/d^3, so error = dm/m + 3*dd/d = 2% + 3*0.37% = 2% + 1.11% = 3.1%.
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