The period of oscillation of a simple pendulum is given by
the measured value of is cm, known to 1 mm accuracy, and the time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch which has s resolution.
What is the maximum difference between the value of determined by this experiment (call it ) and the actual value of (at the point on the Earth where this experiment is performed), as a percentage of
Give your answer to one decimal place.
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Since 0 . 1 9 9 5 < L < 0 . 2 0 0 5 and 0 . 8 9 5 < T < 0 . 9 0 5 , and the formula gives g = T 2 4 π 2 L the experiment tells us that 9 . 6 1 6 2 2 4 4 0 8 5 < g < 9 . 8 8 1 6 1 7 5 9
This experiment uses the values L = 0 . 2 and T = 0 . 9 to calculate g ^ = 9 . 7 4 7 7 7 5 7 4 3 3 Thus the measurement tolerances of the experiment allow that the actual value of g could lie between 9 8 . 7 % and 1 0 1 . 4 % of g ^ . This makes the percentage error of the experiment 1 . 4 %