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 ?

Time for 20 oscillations of a pendulum is measured as t_(1)= 39.6 s, t

1.	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 ?
Answer» Solution :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`