Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum? (a) $g=\frac{2\pi L}{T^2}$
(b) $g=\frac{4{\pi }^{2}L}{T^2}$
(c) $g=\frac{2\pi L}{T}$
(d) $g=\frac{2{\pi }^{2}L}{T}$

Video Transcript

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.