A hollow metal sphere is filled with water through a small hole in it. It is hanging by a long thread and is made to oscillate. Water slowly flows out of the hole at the bottom. How will the period of oscillation be affected?

Initially the center of mass of sphere is at the center of sphere. As the water slowly flows out of the hole at the bottom, the center of mass of system first goes down and then upward. Hence the time period will first increase then decrease till the sphere is empty.