Bucked is going circular Motion Therefore the bucked will be under cenyripcent force.

At the highest point for minimum speed the tension in the string will be equal to zero

Therefore 

mv2/r=mg

We have r=1

Therefore

v= square root of g

Hence the minimum velocity possible.

Hello,

This questions can be termed both in physics and quantative tools.

These type of questions can come in aptitude test.

Thank you!

Gokd luck!