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(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is 9.79 $\mathrm{m} / \mathrm{s}^{2}$ is moved to a location where it the acceleration due to gravity is9.82 $\mathrm{m} / \mathrm{s}^{2} .$ What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.

$T_{2}=2.995 \mathrm{s}$

Physics 101 Mechanics

Physics 103

Chapter 16

Oscillatory Motion and Waves

Periodic Motion

Wave Optics

Cornell University

Rutgers, The State University of New Jersey

Hope College

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So we know that the formula for the period is equaling two pi multiplied by the square root of the length, divided by the acceleration due to gravity. So it's safe to say that the period is inversely proportional to the square root of the acceleration due to gravity. And so we can say T's of one divided by T's. Up to is then gonna be equaling the square root of G's up two, divided by geese of one and solving for t's up to we have that this is gonna be equaling 3.0 000 seconds. So five zeros multiplied by the square root of this would be G sub one. So 9.79 meters per second squared, divided by 9.79 divided by Jesus to so 9.82 meters per second squared. And so the new period is gonna be equaling two point 99541 seconds. We need six significant figures. This would be our answer. Four part, eh, Now, for part B. Ah, we have to We say that the question is rather asking explain why so many digits are needed. Um, and this is Ah, we can say an increased number of significant figures is needed because acceleration due to gravity changes slightly in order to observe the significant, uh noticed observed rather, the slight change in period. So we can say that increased number of significant figures is needed due to the slight change in gravity, causing only a slight change in period. This would be our solution for part B. That is the end of the solution. Thank you for watching.

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