If you held this string at one end and twirled it in a circle above your head, so that the object moves in a plane parallel to the ground, what is the maximum speed that the object at the end of the string can have without breaking the string

v = √ T L / m  = √ Y L²/ m

Explanation:

The maximum tension in a string is related to Young's modulus, in general the value is Young's modulus by the length of the string, suppose the value is T

                T = Y L

Let's use Newton's second law

              F = m a

The acceleration is centripetal

             a = v² / r

             T = m v² / L

             v = √ T L / m

If we change the tension for

             T = Y L

             v = √ Y L²/ m