C

The period of oscillation of a compound pendulum is given by the formula:
$$T = 2\pi \sqrt{\frac{I}{mgh}}$$
where I is the moment of inertia about the pivot point, m is the mass, g is the acceleration due to gravity, and h is the distance from the pivot to the center of mass.
For minimum period, the mass must be at the end of the pendulum, thus simplifying the situation. The correct formula representing the minimum period involves doubling the length (assuming the pivot is at one end), resulting in the term \(2l\) in the square root.
Therefore, the minimum period is given by the expression:
$$T_{min} = 2\pi \sqrt{\frac{2l}{g}}$$, which matches with Option C.