# 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?

Details

• 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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