In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T = 2 π 7 R - r 5 g . The values of R and r are measured to be 60 ± 1 m m a n d 10 ± 1 m m , respectively. In five successive measurements, the time period is found to be 0.52s, 0.56s, 0.57s, 0.54s and 0.59s. The least count of the watch used for the measurement of time period i

Step-by-step solution

T Absolute error 1 0.52 -   0.04 2 0.56 00 3 0.57 +   0.01 4 0.54 - 0.02 5 0.59 + 0.03 T a v g = 0.556 = 0.56 Avg. absolute error 0 . 04 + 0 + 0 . 01 + 0 . 02 + 0 . 03 5 = 0 . 02 Percentage error in time period = ∆ T T × 100 % = 0 . 02 0 . 56 × 100 % ≈ 3.57 % Percentage error in radius = ∆ r r × 100 % = 1 10 × 100 = 10 % Also, g = 28 π R - r 5 T 2 Percentage error in g ,= ∆ g g = ∆ R + ∆ r R - r + 2 ∆ T T ∆ g g × 100 % = 1 + 1 5