A uniform inextensible rope length of 30 cm is lying on a table in such a manner that a part of it is hanging down from an edge of the table. It is known that the rope is in equilibrium, if the maximum length of the rope that can hang without sliding is 10 cm. A girl is attaching another same rope length of 6 cm to the end of the first rope and then putting the rope on the table. So that it is again in equilibrium. What is the length of the part of the rope that is on the table?

Solution. Posted on Saturday, November 8, 2014.

If the rope is in equilibrium when the maximum length of the rope that can hang without sliding is 10 cm, then it is meant that 2/3 of the rope must be on the table. The length of the extended rope is 36 cm. So, the length of the part of the rope that is on the table is 24 cm.