How do you solve for $g$ $g$ in $T = 2 π \sqrt{\frac{L}{g}}$ $T=2pisqrt(L/g)$ ?

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How do you solve for $g$ $g$ in $T = 2 π \sqrt{\frac{L}{g}}$ $T=2pisqrt(L/g)$ ?

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Answer 1 · 2016-08-10T00:20:43

$g = \frac{4 π^{2} L}{T^{2}}$ $g=(4pi^2L)/T^2$

Explanation:

$First,$ $color(red)("First,")$ 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:

$T^{2} = {(2 π)}^{2} \sqrt{{(\frac{L}{g})}^{2}}$ $T^2 = (2pi)^2sqrt((L/g)^2)$

$T^{2} = {(2 π)}^{2} (\frac{L}{g})$ $T^2=(2pi)^2 (L/g)$

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

$T^{2} = 4 π^{2} (\frac{L}{g})$ $T^2=4pi^2 (L/g)$

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

$gxxT^2=4pi^2L$

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

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

Thus, $g$ is equal to:

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

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How do you solve for $g$ $g$ in $T = 2 π \sqrt{\frac{L}{g}}$ $T=2pisqrt(L/g)$ ?

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How do you solve for ggg in T=2pisqrt(L/g)T=2π√LgT=2pisqrt(L/g)?

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How do you solve for $g$ $g$ in $T = 2 π \sqrt{\frac{L}{g}}$ $T=2pisqrt(L/g)$ ?