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JEE Main 2016 · Errors in Measurement

Errors in Measurement question from JEE Main 2016

Q103JEE Main 2016Medium

Errors in Measurement

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:

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Answer: (c)

  1. Mean =90+91+95+924=3684=92 s= \frac{90 + 91 + 95 + 92}{4} = \frac{368}{4} = 92\text{ s}
  2. Absolute deviations: 2,1,3,02, 1, 3, 0; mean absolute error =64=1.5 s= \frac{6}{4} = 1.5\text{ s}
  3. The clock reads only to 1 s, so the error is rounded to 2 s2\text{ s}: 92±2 s92 \pm 2\text{ s}.
  4. So the answer is (c) 92±292 \pm 2 s.
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