Numerical answer
In an experiment on a simple pendulum, the string length from the suspension point to the top of the bob is measured as with a metre scale of least count . The bob diameter, measured with a vernier calliper of least count , is . The time for oscillations is with a stopwatch of least count . Taking the maximum possible errors to be the least counts, the percentage error in the value of (with the effective length) is. Give the answer correct to two decimal places.
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Answer: 0.47
The effective length is (radius is half the diameter). Errors add for a sum: the radius error is half the diameter least count, , so and . For the period, so (the number of oscillations is exact). Because , the maximum fractional error is . A mistake is to use only, or to divide the time error by a second time. Percentage errors are simply added because the maximum-error rule is used, not the root-sum-square rule.
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