Question

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

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

Answer 1

The correct option is D first increases and later decreases.

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.