Question

Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?

- $g=\dfrac{2\pi L}{T^2}$
- $g=\dfrac{4\pi^2 L}{T^2}$
- $g=\dfrac{2\pi L}{T}$
- $g=\dfrac{2\pi^2 L}{T}$

Final Answer

(b)

Solution Video

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This is College Physics Answers with Shaun Dychko. The period of a pendulum is two Pi times square root of its length divided by the acceleration to the gravity. We're going to solve for <i>g</i> by dividing both sides by two Pi giving us square root <i>L</i> over <i>g</i> is <i>T</i> two Pi. And then we'll raise both sides to the exponent negative two. The negative sign serves to flip both fractions and then afterwards we square them. So this makes <i>g</i> over <i>L</i> on the left and it makes four Pi squared over <i>T</i> squared on the right. And then we'll solve for <i>g</i> by multiplying both sides by the length. So <i>g</i> is four Pi squared <i>L</i> over <i>T</i> squared. And this is option b.