Making a spool slide without rolling

[snowflake2357]

1. Homework Statement
As shown in the figure to the right, a spool has outer radius R and axle radius r. A string is wrapped around the axle of the spool and can be pulled in any of the directions labeled by I, II, or III. The spool will slide to the right without rolling on the horizontal surface if it is pulled in which direction(s)?

Homework Equations

τ=Fr
F=ma

The Attempt at a Solution

I thought all the forms of pulling would cause rolling, since each pull will exert a torque on the spool, but that's not right. I'm not sure if it's different because there's an inner and outer spool though, and if so, how to factor that into the problem.

 

[coffeebird]

i think it would be 1, since if you are pulling it from the top, the string won't unravel (normally) and the spool won't have rotation just translation

 

[Doc Al]

Hint: If the spool rolls without slipping, what would be its instantaneous axis of rotation?