A stone tied to a string is whirled in a circle. As it was revolving, the rope suddenly snaps. Then

In uniform circular motion, the velocity vector of an object is always directed along the tangent to the circular path at any given point. The tension in the string provides the required centripetal force to alter this direction. The moment the rope snaps, this centripetal force drops to zero, and due to inertia of direction, the stone continues to move along its instantaneous linear direction, flying off tangentially.