Percentage of g ^ \hat{g}

The period of oscillation of a simple pendulum is given by

T = 2 π L g , T =2\pi\sqrt {\dfrac {L}{g}},

the measured value of L L is 20.0 20.0 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 1 1 s resolution.

What is the maximum difference between the value g g of determined by this experiment (call it g ^ \ \hat{g} ) and the actual value of g g (at the point on the Earth where this experiment is performed), as a percentage of g ^ ? \hat{g}?

Give your answer to one decimal place.


The answer is 1.4.

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1 solution

Mark Hennings
Aug 11, 2017

Since 0.1995 < L < 0.2005 0.1995 < L < 0.2005 and 0.895 < T < 0.905 0.895 < T < 0.905 , and the formula gives g = 4 π 2 L T 2 g \; = \; \frac{4\pi^2 L}{T^2} the experiment tells us that 9.6162244085 < g < 9.88161759 9.6162244085 < g < 9.88161759

This experiment uses the values L = 0.2 L = 0.2 and T = 0.9 T = 0.9 to calculate g ^ = 9.7477757433 \hat{g} = 9.7477757433 Thus the measurement tolerances of the experiment allow that the actual value of g g could lie between 98.7 98.7 % and 101.4 101.4 % of g ^ \hat{g} . This makes the percentage error of the experiment 1.4 \boxed{1.4} %

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