B

In a compound pendulum, the time period depends on the distribution of mass and the pivot point. The time period can be derived from the equations shown in the images.

The maximum time period occurs at the pivot point distance where the effective length of the pendulum is maximized. The general formula for the time period of a compound pendulum is given by
$T = 2\pi \sqrt{\frac{I}{mgh}}$,
where $I$ is the moment of inertia of the pendulum 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.

As observed from the options, the modified formula appears in the reference images. Thus, upon maximizing the associated values, we discover the relation to be similar to the second option, where the effective length and mass distribution yield a precise time period derivation that fits the characteristics expected at the maximum time.
Thus, Option B is correct.