Question

How do you solve for `g` in `T=2pisqrt(L/g)`?

Answer 1

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

Explanation:

`color(red)("First,")` what you want to do is square both sides of the equation to get rid of the square root, since squaring a number is the inverse of taking the square root of a number:

`T^2 = (2pi)^2sqrt((L/g)^2)`

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

`color(blue)("Second,")` we simplify the `(2pi)^2` part so it's easier to read. Remember, when you square something in parenthesis, you are squaring every single term inside:

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

`color(purple)("third,")` multiply both sides by `g`:
`gxxT^2=4pi^2 (L/cancel"g")xxcancelg`

`gxxT^2=4pi^2L`

`color(maroon)("finally,")` divide both sides by `T^2` to get `g` by itself:

`(gxxcancelT^2)/cancelT^2=(4pi^2L)/T^2`

Thus, `g` is equal to:

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