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)

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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

*g*by dividing both sides by two Pi giving us square root*L*over*g*is*T*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*g*over*L*on the left and it makes four Pi squared over*T*squared on the right. And then we'll solve for*g*by multiplying both sides by the length. So*g*is four Pi squared*L*over*T*squared. And this is option b.