Question

Find the ratio of magnitude of angular momentum of a rolling disc about orgin

Answer 1

your question is incomplete . it seems like you asked " Find the ratio of magnitude of angular momentum of a rolling disc about origin to centre of mass."

disc is assumed to be point mass , as we assume distance from origin to disc is vary large compare to its size.
so, momentum of inertia of disc about origin, I = mr² + M.I about COM
= mr² + mr²/2
= 3mr²/2

if we assume $\omega$ is angular velocity.
so, angular momentum , L= $\frac{3}{2}mr^2\omega$

now, momentum of inertia of disc about an axis passing through centre of mass, I = mr²/2

so, angular momentum, L' = $\frac{1}{2}mr^2\omega$

hence, ratio of L to L' = $\frac{3/2mr^2\omega}{1/2mr^2\omega}=3:1$