Question

A hollow metal sphere is filled With water and it is hung by a long thread. It is made to oscillate. I f there be a small . hole in the bottom through which water slowly flows out, then its period of oscillation is

• A. goes on increasing until the sphere is empty
• B. goes on decreasing till the sphere is empty
• C. remains unchanged throughout
• D. first increases and later decreases and remains constant when the sphere is empty

Answer 1

Answer: (D)

Initially the center of mass is at the center of the sphere. As the water flows out the center of mass descends down increasing the effective length of pendulum. Thus the time period increases. But as the water has drained out entirely the center of mass again shifts to the center, and the time period decreases.