$A$ bob of mass $m$ suspended by a light string of length $L$ is whirled in a vertical circle as shown in the figure. What will be the trajectory of the particle if the string is cut at $(a)$ point $B$,$(b)$ point $C$,and $(c)$ point $X$?

(N/A) When a bob is whirled in a vertical circle,the required centripetal force is provided by the tension in the string and the component of gravity. When the string is cut,the tension becomes zero,and the bob moves in a straight line path along the direction of its instantaneous velocity,subject only to gravity.
$(a)$ At point $B$,the velocity is vertically downward. Therefore,when the string is cut at $B$,the bob moves vertically downward under the influence of gravity.
$(b)$ At point $C$,the velocity is horizontal (towards the right). When the string is cut at $C$,the bob moves horizontally with an initial velocity $v$ and simultaneously falls under gravity. This results in a parabolic trajectory with its vertex at $C$.
$(c)$ At point $X$,the velocity of the bob is along the tangent drawn at point $X$. When the string is cut at $X$,the bob moves along this tangent direction with an initial velocity $v$ and then follows a parabolic path under the influence of gravity,with the vertex of the parabola higher than point $C$.