When Does a Bob Attached to a String Become Slack?

[atavistic]

When does a bob attached to a string become slack?When mgcos@ = mv^2/r?

 

[Kurdt]

When doing what? You're going to have to provide a bit more information about what the bob on the string is doing?

 

[nrqed]

When does a bob attached to a string become slack?When mgcos@ = mv^2/r?

It depends if you are restricting the angle to be below 90 degrees or if you may go above.
The equation (for theta smaller or equal to 90 degrees) is

T - mg cos theta = m v^2/R

The rope becomes slack if T=0.

what can you say about theta and v in that case?