A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The measurement of the diameter is 5.00 mm ± 0.01 mm.
What is the percentage uncertainty in the calculated volume of the sphere, using these values?
A 0.2%
B 0.4%
C 0.6%
D 1.2%
ANSWER: C
The Physics behind the answer:
- By volume, you should know that it considers 3 dimensions. This is implied in the formulas for volume, (4/3)πr3 where r is the radius for the sphere in particular.
- The uncertainty of a result of multiplication/division is the sum of percentage uncertainties of the dimensions [quantities] used in the calculations.
- Since you are given absolute uncertainty, this must be converted to percentage uncertainty first. The diameter 5.00 mm ± 0.01 mm is same as 5.00 mm ± 0.2%.
- Because radius [or half of diameter] is multiplied to itself a couple of times, then the uncertainty as explained above should be 0.2% + 0.2% + 0.2%.
- The answer therefore is C, 0.6%.
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