A hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will 

 

The given system is like a simple pendulum, whose effective length (I) is equal to the distance between point of suspension and CG (centre of gravity) of the hanging body.

When water slowly flows out the sphere, the CG of the system is lowered, and hence l increases, which in turn increases time period (as $(\mathrm{T} \propto \sqrt{\mathrm{l}} )$.

After some time weight of water left in sphere become less than the weight of sphere itself, so the resultant CG gets clear the CG of sphere itself i.e. / decreases and hence T increases.

Finally when the sphere becomes empty, the resulting CG is the CG of sphere i.e. length becomes equal to the original length and hence the time period becomes equal to the same value as when it was full of water.