A laboratory technician uses a single swing of a simple pendulum to estimate the local value of the gravitational field strength g. The technician first measures the distance from the pivot point to the center of mass of the bob and records l=0.992m±0.002m. An electronic photogate then records the time for 20 complete oscillations as T20=40.07s±0.05s. Small-angle conditions are satisfied.
(a) Determine the average period T for one oscillation and its absolute uncertainty.
(b) Using the measured values, calculate the local value of g. Show all algebraic steps in obtaining your result.
(c) Propagate the given uncertainties to obtain the absolute uncertainty in g. State the final result for g with an appropriate number of significant figures and its uncertainty.
(d) Briefly discuss two experimental changes that would reduce the fractional uncertainty in the calculated value of g. Justify your suggestions.