Answer
Axis locates L/6 distance away from the center of the rod.
Work Step by Step
Here we use the parallel - axis theorem,
$I= I_{cm}+Md^{2}$
Where, $I$ - the new rotational inertia, d - Distance from the axis through the center of mass to parallel axis & M is the total mass of the object.
Let's plug known values into this equation.
$\frac{ML^{2}}{9}=\frac{ML^{2}}{12}+Md^{2}$
$L^{2}\frac{(4-3)}{36}=d^{2}$
$\frac{L^{2}}{36}=d^{2}=\gt d=\frac{L}{6}$
Axis locates L/6 distance away from the center of the rod.
