Understanding Simple Pendulum Experiment: Water-Filled Sphere Explanation

[bc64846]

This is my first time ever taking a physics class...and needed an explanation. In lab we're doing a simple pendulum experiment. Given the equation T=2pi(sqrt L/g) and noting observations with different pendulum lengths we must then answer this question:

A hollow sphere is filled with water and suspended by a long thread. A small hole is made in the bottom of the sphere and as the water flows out one observes that the period of oscillation of the simple pendulum first increases and then decreases. Explain.

 

[mgb_phys]

The 'L' in the above equation is the length from the fixed end to the centre of gravity of the string+bob (the weight on the end of the string).
Where is the centre of gravity if the bob is much heavier than the string and where if the bob and the string have the same weight?

Slightly nasty question - the simple equation above normally assumes that all the weight is in the bob, there is a more complex equation if you need to take into account different weights.