Work done pulling a string in circular motion equals increase in kinetic energy?

[jgens]

Homework Statement

A mass m whirls on a frictionless table, held to circular motion by a string which passes though a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from l₁ to l₂. Show that the work done in pulling the string equals the increase in kinetic energy of the mass.

Homework Equations

N/A

The Attempt at a Solution

I've already shown that the work done by a central force is path independent. Can I just apply the same manipulations used to get the work energy theorem in cartesian coordinates? I'm really not sure so I could use some guidance here.

 

[tiny-tim]

hi jgens!

i'll guess that they want you to use conservation of angular momentum , the definition of the work done (by the tension in the string), and a bit of integration