Hey there,
Many ways to do this. If you have maya 09 or later, ncloth allows you to do this kind of thing. Make a cylindrical n cloth, or model a rope, and make ncloth, then give it a higher shear and stretch resistance. Then transform constrain a few of the top vertices.Then make a polysphere, also ncloth it, make the rigidity super high, and add gravity to it. Select by component the bottom end of your rope and the sphere's components, then component to component constraint. it will fall constrained by the rope elasticity.