A student wishes to estimate the value of the acceleration due to gravity in the school laboratory with the help of a simple pendulum.
(i) Describe, step by step, how the apparatus should be arranged and what measurements need to be taken so that an accurate value of the time period can be obtained.
(ii) Starting from the condition for small-angle oscillations of the pendulum, obtain the mathematical relation connecting the length of the pendulum and its time period.
(iii) Explain why it is advisable to measure the time for a large number of oscillations (for example, 20 complete swings) and then divide by that number, rather than timing a single oscillation.
(iv) The length of the pendulum was measured as 80.0cm(±0.1cm). The total time for 20 oscillations was found to be 36.0s(±0.2s). Calculate the value of g obtained by the student and determine the percentage error in this result.