(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.