The ball with a mass of 100 g is tied to a string that is 1 m long and moves in a circular path at 120 rpm. If the string were to snap the magnitude of the velocity at which the ball moves is the magnitude of the instantaneous linear velocity of the ball as it moves in the circular path.
The instantaneous linear velocity is given by V = w*R where w is the angular velocity and R is the radius.
The angular velocity is 2*pi*(120/60) = 4*pi
This gives the magnitude of the linear velocity of the ball at which it moves as 4*pi*1 m/s which is approximately 12.56 m/s. The direction in which the ball moves is in a direction along the tangent to the circle at the point at which the string snaps.