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
AIEEE 2005,AIIMS 2013,KVPY 2010, Medium
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(d) The given system is like a simple pendulum, whose effective length $(l)$ is equal to the distance between point of suspension and $C.G.$ (Centre of Gravity) of the hanging body.
When water slowly flows out the sphere, the $C.G.$ of the system is lowered, and hence $l$ increases, which in turn increases time period (as $T \propto \sqrt l $).
After some time weight of water left in sphere become less than the weight of sphere itself, so the resultant $C.G.$ gets clear the $C.G.$ of sphere itself i.e. $l$ decreases and hence $T$ increases.
Finally when the sphere becomes empty, the resulting $C.G.$ is the $C.G.$ 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. 
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