Physics Question from JEE Main 2026 · 22 January, Shift 1

A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moments of inertia of both the discs are same and $\frac{R_1}{R_2} = 2, \quad \text{then} \quad \frac{T_1}{T_2} = \frac{1}{\alpha}.$ The value of $\alpha$ is _____.