Problem $3(5$ marks$).$ A thin transparent boiling tube of mass $m$ length $l$ is sealed at both ends. It is suspended from a string so that the bottom of the tube is $l$ above the table. A fly of mass $m$ is sitting at the bottom of the tube. The string is cut, and while the tube is falling, the fly moves from the bottom to the top of the tube. Find the time that elapses between cutting the rope and the bottom of the tube hitting the table.

Hint: recall the above discussion of centres of masses of sizable objects.