Introduction:
In this scenario, a cylinder is completely filled with water. If one-fourth of the volume of water leaks out, we need to determine the effect on the center of mass of the remaining water.

Understanding the Center of Mass:
The center of mass of an object is the point at which its entire mass can be considered to be concentrated. In a uniform density object, the center of mass coincides with the geometric center. However, in non-uniform density objects like water, the center of mass may not necessarily align with the geometric center.

Effects on Center of Mass:
To understand the effect of water leakage on the center of mass, let's analyze the different possibilities:

1. Moves Up:
If the water leakage occurs from the bottom or lower portion of the cylinder, the center of mass would move up. This is because the lower portion of the water mass is being removed, causing the remaining water's center of mass to shift towards the top.

2. Moves Down:
If the water leakage occurs from the top or upper portion of the cylinder, the center of mass would move down. The removal of water from the top reduces the mass concentration in the upper region, causing the center of mass to shift downwards.

3. Does Not Change:
If the water leakage occurs uniformly from all sides of the cylinder, the center of mass would not change. Since the leakage is uniform, the mass distribution remains the same, and the center of mass stays in its original position.

4. Moves Towards Vertical Surface:
The scenario mentioned in the question does not specify any vertical surface or its influence. Therefore, we can eliminate this option as it is not relevant to the given situation.

Conclusion:
In summary, the possible effects on the center of mass of the remaining water depend on the location of the water leakage. If the leakage occurs from the bottom, the center of mass moves up. If the leakage occurs from the top, the center of mass moves down. If the leakage is uniform from all sides, the center of mass does not change.