Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio : 

1 : \(\sqrt{2}\)

\(\frac{L_1^2}{2I_1} = \frac{L_2^2}{2I_2}\)

⇒ \(\frac{L_1^2}{2(I)} = \frac{L_2^2}{2(2I)}\)

Ratio : \(\frac{L_1}{L_2} = \frac{1}{\sqrt{2}}\)