Time for 20 oscillations of pendulum is measured as t1 = 39.6 s; t2 =

1.	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?
Answer» (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.

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?

Answer»

(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.