The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is $I_1$. The same rod is bent into a ring and its moment of inertia about a diameter is $I_2$. If $\frac{I_1}{I_2}$ is $\frac{x\pi^2}{3}$, then the value of $x$ will be $\_\_\_\_$.