Question

A bob of mass 0.1kg hung from the ceiling of a room by a string 2m long is set into oscillation. The speed of the bob at its mean position is 1m/s. 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?

Answer 1

Hint: When a bob is tied to a string and is given a small displacement then it undergoes oscillations and the motion is called Simple harmonic motion. The time period of the pendulum is independent of the mass of the bob and is dependent on the length of the pendulum and the value of acceleration due to gravity

Complete answer:
During the motion of the pendulum, there are two extreme positions and one mean position. At the extreme position the velocity of the bob is zero and at the mean position the velocity of the bob is maximum. Since there is no external force acting on the bob if the string is cut during its motion then under the influence of gravity the bob will continue to trace its path of motion. Now the bob is at one of the extreme positions and when the string is cut, it will fall straight to the ground downwards because at that position it has zero velocity. Now the bob is at the mean position and if the string is cut then the bob has a horizontal velocity. If the string is cut, it will fall along a parabolic path.

Note:
The pendulum executes simple harmonic motion with a natural frequency but if some external force acts on the system then damping takes place. The motion can be summarized as a kind of periodic motion. Here the parameters given such as the mass of the pendulum or the length of the string are of no use.