(c)**along**a tangent
Explanation:
When a particle moves in a circle with a speed v, its instantaneous velocity has a magnitude v and direction along the tangent at that point. The direction of the instantaneous velocity is kept changing by a centripetal force which is tension in the string in this case. As soon as the string breaks, this force disappears and the direction of the instant velocity of the particle can no longer change. So it goes along the tangent to the instantaneous point on the circle.
