Question
Make $L$ the subject of formula $T=2 \pi \sqrt{\frac{L}{G}}$
✓
Answer
$T =2 \pi \sqrt{\frac{ L }{ G }} $
$\Rightarrow \frac{ T }{2 \pi}=\sqrt{\frac{ L }{ G }}$
squaring both sides
$\Rightarrow\left(\frac{ T }{2 \pi}\right)^2=\frac{ L }{ G } $
$\Rightarrow G \left(\frac{ T }{2 \pi}\right)^2= L $
$\Rightarrow L =\frac{ GT ^2}{4 \pi^2} .$
$\Rightarrow \frac{ T }{2 \pi}=\sqrt{\frac{ L }{ G }}$
squaring both sides
$\Rightarrow\left(\frac{ T }{2 \pi}\right)^2=\frac{ L }{ G } $
$\Rightarrow G \left(\frac{ T }{2 \pi}\right)^2= L $
$\Rightarrow L =\frac{ GT ^2}{4 \pi^2} .$
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