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Physics · UNITS AND MEASUREMENT

हिन्दी

The mean length of a rod measured by Vernier callipers is to be reported. Why is a set of 100 measurements expected to yield a more reliable estimate than a set of 5 measurements?

  1. A
    Random error decreases by a factor of 20
  2. B
    Random error decreases by a factor of \( \sqrt{20} \)
  3. C
    Systematic error is reduced to zero
  4. D
    Least count of Vernier callipers improves by 20 times
View Answer & Solution

Correct answer · Option B

Random error decreases by a factor of \( \sqrt{20} \)

Explanation

Random errors are reduced by a factor of \( \sqrt{N} \) when the number of observations increases by \( N \) times. Increasing measurements from 5 to 100 (\( 20 \) times) reduces random error by \( \sqrt{20} \).

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