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.
(a) When bob is at its extreme position:
The trajectory of the bob if the string is cut at one of it's extreme positions will be in vertically downward direction.
At the extreme position, the velocity of the bob becomes zero. If the string is cut at this moment, then the bob will fall vertically on the ground.
(b) When the bob is at its mean position:
When the string is cut at its mean position, the trajectory of the bob will be a parabolic path.
At the mean position, the velocity of the bob is 1 m/s.
The direction of this velocity is tangential to the arc formed by the oscillating bob. If the bob is cut at the mean position, then it will trace a projectile path having the horizontal component of velocity only.
Hence, the bob will follow a parabolic path.