$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.

(N/A) At the extreme position,the velocity of the bob is zero. If the string is cut at this moment,the bob will fall vertically downward under the influence of gravity. The trajectory is a straight line.
$(b)$ At the mean position,the velocity of the bob is $1\; m s^{-1}$ in the horizontal direction. If the string is cut at this moment,the bob will have an initial horizontal velocity and will be subject to gravity. Therefore,it will follow a parabolic trajectory.