Answer
$T=\sqrt{\frac{2\pi \lambda}{g}}$
Work Step by Step
We know that
$T=\frac{\lambda}{v}$
As given that $v=\sqrt\frac{{g\lambda}}{{2\pi}}$
$\implies T=\frac{\lambda}{\sqrt\frac{{g\lambda}}{{2\pi}}}$
This simplifies to:
$T=\sqrt{\frac{2\pi \lambda}{g}}$
