The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is 

Calculation:
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I₀. The moment of inertia about an axis passing through one of its ends and perpendicular to its length is derived using the parallel axis theorem.

According to the parallel axis theorem, the moment of inertia about an axis through one end of the rod is:

I = I₀ + M × (L/2)²

Substituting the value for I₀ (the moment of inertia through the center), we get:

I = I₀ + M × L²/4

Hence, the correct option is Option 2: I₀ + M × L²/4