Correct Answer - Option 2 : 0.01223
CONCEPT:
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Error: The result of every measurement of experiments by any measuring instrument contains some uncertainty. This uncertainty is called error.
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Absolute error: The magnitude of the difference between the measurement of the experimental readings and the true value of the quantity is called the absolute error.
- This is denoted by |Δa |.
- Absolute error is always positive.
- If there is no true value, we can take the mean of all measured values as a true value.
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Relative error: the ratio of the mean absolute error (or final absolute error) to the mean value of the experimental value measured.
CALCULATION:
- The mean value of gravitational acceleration
\(g= {9.86 \;+ \;9.72\; + \;9.68\; + \;9.98 \over 4}=9.81\)
- Absolute error is the magnitude of the difference between the measured value while doing the experiment measurement and the true value.
- When there is no true value, we take mean value of measurements as a true value.
So true value of g = 9.81
- Now, The errors in the measurements are
Absolute error = |measured value - true value|
Now, The errors in the measurements are
|9.86 - 9.81| = |0.05| = 0.05
|9.72 - 9.81| = |-0.09| = 0.09
|9.64 - 9.81| = |-0.17| = 0.17
|9.98 - 9.81| = |0.17| = 0.17
- The arithmetic mean of all the absolute errors (for the arithmetic mean, we take only the magnitudes i.e. positive value) is
\(\Delta g_{mean} = {0.05+0.09+0.17+0.17 \over 4}\)
\(\Delta g_{mean} = 0.12\)
- So mean absolute error is 0.12 m/s2
- That means the gravitational acceleration at that place is (9.81 ± 0.12) m/s2
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The relative error is the ratio of the mean absolute error (or final absolute error) Δgmean to the mean value gmean of the experimental value measured.
\(Relative~ error = {Δg_{mean} \over g_{mean}}\)
The relative error is = \({0.12 \over 9.81}=0.0122324\)
- The relative error is ≈ 0.01223
- Hence the correct answer is option 2.