Question

How would you rearrange this equation to find g instead?

Answer 1

Given:

The period of a pendulum,

`T=2\pi\sqrt{(L)/(g)}`

To find:

The equation to find the acceleration due to gravity.

Step-by-step explanation:

On taking the square of the equation,

`T^2=4\pi^2((L)/(g))`

On multiplying g on both sides of the equation,

`\begin{gathered} T^2g=(4\pi^2L)/(g)* g \\ \implies T^2g=4\pi^2L \end{gathered}`

On dividing both sides of the equation by T²,

`\begin{gathered} (T^2)/(T^2)g=4\pi^2(L)/(T^2) \\ \implies g=(4\pi^2L)/(T^2) \end{gathered}`

Final answer:

The equation to calculate the acceleration due to gravity is

`\begin{equation*} g=(4\pi^2L)/(T^2) \end{equation*}`