Rope in the hole

A rope of uniform mass per unit length \(\lambda\) and length \(L\) lies curled on a table, with a short length \(\delta l\) of it hanging through a hole in the table. At time zero, the rope begins to slide through the hole. At what time \(t_c\) (in seconds) does the end of the rope pass through the hole?


  • The rope is 10 m long.
  • \(\delta l = 0.1\) m
  • \(g=9.81\ \text{m/s}^2\)
  • There is no friction between the rope and itself, or between the rope and the table.

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