×

# How do you solve for L in T = 2 π √ L g ?

Mar 8, 2018

$L = \frac{g {T}^{2}}{4 {\pi}^{2}}$

#### Explanation:

As $T = 2 \pi \sqrt{\frac{L}{g}}$

${T}^{2} = 4 {\pi}^{2} \times \frac{L}{g}$

or ${T}^{2} \times \frac{g}{4 {\pi}^{2}} = 4 {\pi}^{2} \times \frac{L}{g} \times \frac{g}{4 {\pi}^{2}}$

or $\frac{g {T}^{2}}{4 {\pi}^{2}} = L$

Hence $L = \frac{g {T}^{2}}{4 {\pi}^{2}}$