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Question
Time for 20 oscillations of a pendulum is measured as t1 = 39.6 s; t2 = 39.9 s; t3 = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?
Solution
Given, t1 = 39.6 s, t2 = 39.9 s and t3 = 39.5 s
The least count of measuring instruments = 0.1 s ......(As measurements have only one decimal place)
Precision in the measurement = Least count of the measuring instrument = 0.1 s
The mean value of time for 20 oscillations is given by
t = `(t_1 + t_2 + t_3)/3`
= `(39.6 + 39.9 + 39.5)/5`
= 39.7 s
Absolute errors in the measurements
Δt1 = t – t1 = 39.7 – 39.6 = 0.1 s
Δt2 = t – t2 = 39.7 – 39.9 = – 0.2 s
Δt3 = t – t3 = 39.7 – 39.5 = 0.2 s
Mean absolute error = `(|Δt_1| + |Δt_2| + |Δt_3|)/3`
= `(0.1 + 0.2 + 0.2)/3`
= `0.5/3` = 0.17 ≈ 0.2 .....(Rounding off up to one decimal place)
∴ Accuracy of measurement = ± 0.2 s
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