A hollow metal sphere is filled with water and hung by a long thread to form a pendulum. A small hol

Question

A hollow metal sphere is filled with water and hung by a long thread to form a pendulum. A small hole is made at the bottom allowing water to drain slowly. How does the time period change as the water empties?

Professor PC Thomas Classes · Answer

As water drains, the center of mass (COM) initially shifts downward, increasing the effective length $L$, so $T$ increases. When completely empty, the COM returns to the sphere's geometric center, decreasing $L$ back to original, so $T$ decreases.