A swinging rod is not a point bob

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Problem: A swinging rod is not a point bob
A uniform thin rod of length 0.60 m swings through small angles about a horizontal axis through one end. Its moment of inertia about this pivot is ML²/3. Take g = 10 m/s².
Question: Find the period.
Givens:
- L = 0.60 m
- I = ML²/3
- Center of mass is L/2 from pivot
- g = 10 m/s²
Assumptions: Small angles in radians, fixed frictionless pivot, no damping and uniform gravity.
Choices (LaTeX):
A. 0.20\pi\ \mathrm s
B. 0.40\pi\ \mathrm s
C. 2\pi\sqrt{0.06}\ \mathrm s
D. 2\pi\sqrt{0.03}\ \mathrm s

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.