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Time for 20 oscillations of 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?

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(a) Precision is given by the least count of the instrument.

For 20 oscillations, precision = 0.1 s

For 1 oscillation, precision = 0.005 s.

Average time for 20 oscillations

\(t=\frac{39.6+39.9+39.5}{3}s=39.7sec\)

Absolute errors, 

∆t1 = t − t1

= 39.7 – 39.6

= 0.1 s.

∆t2 = t − t2

= 39.7 – 39.9 = −0.2s

∆t3 = t − t3

= 39.7 – 39.5 

= 0.2s

Mean absolute error,

\(=\frac{|Δt_1|+|Δt_2|+|Δt_3|}{3}\)

\(=\frac{0.1+0.2+0.3}{3}\)=\(\frac{0.5}{3}\)

= 0.17

≈ ±0.2s.

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