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Time for 20 oscillations of a pendulum i...

Time for 20 oscillations of a pendulum is measured as `t_(1)= 39.6 s, t_(2) = 39.9 s and t_(3) = 39.5 s`. What is the precision in the measurements ? What is the accuracy of the measurement ?

Text Solution

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Given `t_(1)=39.6s t_(2)=39.9 s and t_(3)=39.5 s`
Least count of measuring instrument = 0.1 s (As measurements have only one significant figure after decimal point)
Precision in the measurement = Least count of the instrument = 0.1 s

Average time for 20 oscillations is given by
`t=(t_(1)+t_(2)+t_(3))/(3)`
`=(329.6+39.9+39.5)/(3)=39.7 s`
Absolute errors in the measurements
`Deltat_(1)=t-t_(2)=39.7-39.6-39.6=0.1s `
`Deltat_(2)=t-t_(2)=39.7-39.39.5 = 0.2 s`
Average absolute error `=(|Deltat_(1)|+|Deltat_(2)|+|Deltat_(3)|)/(3)`
`=(0.1+0.2+0.2)/(3)`
`=(0.5)/(3)=0.17~~0.2`
(rounding off upto one decimal place)
`:.` Accuracy of measurement `=+-0.2s`
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